Table
  
  
    
  
  
  of
  
  
    
  
  
  contents





  
    general
  
  
  
    &IndentingNewLine;
  


geometry
structural
Chemistry
Pressure
Thermal



  
    
  
  
  
    
      Cold
      
      
        
      
      
      Cooling
      
      
        
      
      
      side
    
  





  
    
  
  
  
    
      Cooling
      
      
        
      
      
      Hot
      
      
        
      
      
      side
    
  


propulsion
startup
legend



  
    results
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  see
  
  
    
  
  
  
    also
    :
    
      
    
    
    
      
        rocket
        
        
          
        
        
        testbook
        
        
          
        
        
        left
        
        
          
        
        
        as
        
        
          
        
        
        an
        
        
          
        
        
        exercise
        
        
          
        
        
        for
        
        
          
        
        
        the
        
        
          
        
        
        reader
      
    
  


rocket engine calculations

General

A rotary rocket pumps its fuel by rotating, and the centrifugal effects pump the fuel.  The design I'll describe here is ultra simple.  Its design optimizes for simplicity and manufacuurability, and incidentally has very high Thrust/Weight as a result of that simplicity.  Some of the design choices drive the design, in particular the choice of fuels, LOX and liquid propane.  Since both are liquid at 90K the require no insulation in the engine or tankage  We start with the assumption of  600m/s rotational velocity and a combustion chamber pressure of 10,000 psi, we may adjust those upwards later.

The engine is made out of aluminum or some superalloy.  Aluminum is preferable because of its high strength/.weight combined with its superb thermal conductivity.  A high temperature superalloy is second choice, though a lower strength/weight hurts doubly,  in the conventional way, it weighs more thus reducing thrust/weight, but much more importantly, it can't be spun as fast, thus reducing the chamber pressure possible.  Note however that as thrust/weight exceeds 200:1 further improvement starts to get lost in the noise, at least for my system design, as confirmed by my simulator.  This and the desire for fast  prototype turn around precludes using any hitech ceramic or other exotic materials. However, there are other options for the center piece, the "spindle", if the thermal requirements on cooling the nozzles are too much it could be made of a machenable ceramic or tungsten, or elconite, or graphite or something.  Thermal coefficients of expansion, thermal conductivity and such may override strength and strength/weight factors for the spindle, it doesn't have nearly the same forces on it as the rotor does.

NOTE: about this set of calculations:
    this stuff is meant to be a formalization of my calculations for several purposes.  There are several semiemperical equations here from Sutton and other sources if there are any better formulas or methods, I want to know about them, so this is for review.  Also I expect to run this on a lot of configurations, both manually to develop an intuition, and as part of my rocket system simulator, to explore optima and trade-offs.  In particular, there may be temperature:ISP trade-offs, the simulator can integrate those into an entire system.  As real engines burn, both success and failure will give values and directions to the simulator(s).  The current simulator flies a rocket second by second a 100,000 times under an adaptive simulated annealer, a variety of numerical hill climbing algorithm.  The addition of this engine calculation along with an interface to chemical calculations will give a more complete model, and the addition of manufacturing cost rules of thumb can lead to trade-offs between manufacturing costs, of the engine for instance, and the fuel mix, for temperature and ISP, which will define tankage ratios & etc.  If this design in;t in a n unexplored realm of design space, it isn't worth investigating, and if it is unexplored as I expect, normal intuitions will be misleading!
    
    measurements in meters& SI unless otherwise noted




  
    &IndentingNewLine;
  
  
  
    (*
    
    6894.8
    
    *)
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  
  
  
    
      cf
      
      
        
      
      =
      
        
      
      
      2.0
    
    ;
  
  
  
    

  
  
  
    &IndentingNewLine;
  





  
    metalname
    =.
  
  ;





  
    
  
  
  
    
      
        nominalISP
        
        
          
        
        =
        
          
        
        
        350
      
      ;
    
    
    
      
    
    
    
      (*
      
      
        
      
      
      
        a
        
        
          
        
        
        guess
        
        
          
        
        
        so
        
        
          
        
        
        that
        
        
          
        
        
        we
        
        
          
        
        
        can
        
        
          
        
        
        guess
        
        
          
        
        
        at
        
        
          
        
        
        fuel
        
        
          
        
        
        flow
      
      
      
        
      
      
      *)
    
  





  
    
      lStar
      
      
        
      
      =
      
        
      
      
      
        .
        275
      
    
    ;
  
  
  
    
  
  
  
    (*
    
    
      
    
    
    
      11
      
      
        
      
      
      inches
      
      
        
      
      
      agressive
      
      
        
      
      
      but
      
      
        
      
      
      defensible
    
    
    
      
    
    
    *)
  





  
    alname
    
    
      
    
    =
    
      
    
    
    aluminum
  
  ;





  
    
      
        aluminum
        =
        
          {
          
            
              metalname
              
              
                
              
              ->
              
                
              
              
              aluminum
            
            ,
            
              thermalcoeff
              
              
                
              
              ->
              
                
              
              
              .000023
            
            ,
            
              degreesinterference
              
              
                
              
              ->
              
                
              
              
              374
            
            ,
            
              density
              ->
              
                
              
              
              2800
            
            ,
            
              modulusElasticity
              
              
                
              
              
              
                
              
              
              
                6.6
                *
                
                  10
                  10
                
              
            
            ,
            
              thermalconducttivity
              
              
                .29
                *
                4.1840
                ×
                
                  10
                  2
                
              
            
          
          }
        
      
      ;
    
    
    
      
    
    
    
      (*
      
      
        
      
      
      
        aluminum
        
        
          
        
        =
        
          
        
        
        7075
      
      
      
        
      
      
      *)
    
  
  
  
    &IndentingNewLine;
  





  
    
      superalloy
      
      
        
      
      =
      
        
      
      
      
        {
        
          
            metalname
            
            
              
            
            ->
            
              
            
            
            superalloy
          
          ,
          
            thermalcoeff
            
            
              
            
            ->
            
              
            
            
            
              .
              000012
            
          
          ,
          
            degreesinterference
            
            
              
            
            ->
            
              
            
            
            600
          
          
          
            
          
          ,
          
            density
            ->
            
              
            
            
            8250
          
          ,
          
            modulusElasticity
            
            
              
            
            
            
              
            
            
            
              2
              ×
              
                10
                11
              
            
          
          ,
          
            thermalconducttivity
            
            
              .0001
              *
              4.1840
              ×
              
                10
                2
              
            
          
        
        }
      
    
    ;
  
  
  
    
  
  
  
    (*
    
    
      
    
    
    
      *
      4.1840
      ×
      
        10
        2
      
      
      
        
      
      
      converts
      
      
        
      
      
      from
      
      
        
      
      
      
        cal
        /
        cm
      
      
      
        
      
      
      s
      
      
        
      
      
      degC
      
      
        
      
      
      to
      
      
        
      
      
      
        W
        /
        m
      
      
      
        
      
      
      K
    
    
    
      
    
    
    *)
  





  
    copper
    =
    
      
    
    
    
      {
      
        
          metalname
          
          
            
          
          ->
          
            
          
          
          copper
        
        ,
        
          thermalcoeff
          
          
            
          
          ->
          
            
          
          
          
            .
            000017
          
        
        ,
        
          degreesinterference
          
          
            
          
          ->
          
            
          
          
          
            5
            
            50
          
        
        
        
          
        
        ,
        
          density
          ->
          
            
          
          
          
            896
            
            0
          
        
        ,
        
          modulusElasticity
          
          
            
          
          
          
            
          
          
          
            18.1
            ×
            
              10
              6
            
            ×
            6894.8
          
        
        ,
        
          thermalconducttivity
          
          
            .81
            *
            4.1840
            ×
            
              10
              2
            
          
        
      
      }
    
  
  ;





  
    titanium
    =
    
      
    
    
    
      {
      
        
          metalname
          
          
            
          
          ->
          
            
          
          
          titanium
        
        ,
        
          thermalcoeff
          
          
            
          
          ->
          
            
          
          
          
            .
            000005
          
        
        ,
        
          degreesinterference
          
          
            
          
          ->
          
            
          
          
          650
        
        
        
          
        
        ,
        
          density
          ->
          
            
          
          
          4507
        
        ,
        
          modulusElasticity
          
          
            
          
          
          
            
          
          
          
            17.4
            ×
            
              10
              6
            
            ×
            6894.8
          
        
        
        
          
        
        ,
        
          thermalconducttivity
          
          
            .20
            *
            4.1840
            ×
            
              10
              2
            
          
        
      
      }
    
  
  ;





  
    tungsten
    =
    
      
    
    
    
      {
      
        
          metalname
          
          
            
          
          ->
          
            
          
          
          tungsten
        
        ,
        
          thermalcoeff
          
          
            
          
          ->
          
            
          
          
          
            .
            0000046
          
        
        ,
        
          degreesinterference
          
          
            
          
          ->
          
            
          
          
          
            30
            
            00
          
        
        
        
          
        
        ,
        
          density
          ->
          
            
          
          
          
            1930
            
            0
          
        
        ,
        
          modulusElasticity
          
          
            
          
          
          
            
          
          
          
            59.6
            ×
            
              10
              6
            
            ×
            6894.8
          
        
        ,
        
          thermalconducttivity
          
          
            .397
            *
            4.1840
            ×
            
              10
              2
            
          
        
      
      }
    
  
  ;





  
    
      graphite
      =
      
        
      
      
      
        {
        
          
            metalname
            
            
              
            
            ->
            
              
            
            
            graphite
          
          ,
          
            thermalcoeff
            
            
              
            
            ->
            
              
            
            
            
              .
              000001
            
          
          ,
          
            degreesinterference
            
            
              
            
            ->
            
              
            
            
            
              15
              
              00
            
          
          
          
            
          
          ,
          
            density
            ->
            
              
            
            
            2.25
          
          ,
          
            modulusElasticity
            
            
              
            
            
            
              
            
            
            
              .7
              ×
              
                10
                6
              
              ×
              6894.8
            
          
          ,
          
            thermalconducttivity
            
            
              .057
              *
              4.1840
              ×
              
                10
                2
              
            
          
        
        }
      
    
    ;
  
  
  
    (*
    
    
      
    
    
    
      very
      
      
        
      
      
      approximate
    
    
    
      
    
    
    *)
  





  
    
      brass
      
      
        
      
      =
      
        
      
      
      
        {
        
          
            metalname
            
            
              
            
            ->
            
              
            
            
            brass
          
          ,
          
            thermalcoeff
            
            
              
            
            ->
            
              
            
            
            
              .
              000020
            
          
          ,
          
            degreesinterference
            
            
              
            
            ->
            
              
            
            
            400
          
          
          
            
          
          ,
          
            density
            ->
            
              
            
            
            
              847
              
              0
            
          
          ,
          
            modulusElasticity
            
            
              
            
            
            
              
            
            
            
              14.6
              ×
              
                10
                6
              
              ×
              6894.8
            
          
          ,
          
            thermalconducttivity
            
            
              .28
              *
              4.1840
              ×
              
                10
                2
              
            
          
        
        }
      
    
    ;
    
      silver
      =
      
        
      
      
      
        {
        
          
            metalname
            
            
              
            
            ->
            
              
            
            
            silver
          
          ,
          
            thermalcoeff
            
            
              
            
            ->
            
              
            
            
            
              .
              00001968
            
          
          ,
          
            degreesinterference
            
            
              
            
            ->
            
              4
              
              00
            
          
          
          
            
          
          ,
          
            density
            ->
            
              
            
            
            10490
          
          ,
          
            modulusElasticity
            
            
              
            
            
            
              
            
            
            
              12.0
              ×
              
                10
                6
              
              ×
              6894.8
            
          
          ,
          
            thermalconducttivity
            
            
              1.0
              *
              4.1840
              ×
              
                10
                2
              
            
          
        
        }
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  
    
      fuel
      
      
        
      
      =
      
        
      
      
      
        {
        
          densityFuel
          
          
            
          
          ->
          
            
          
          
          700.
        
        }
      
    
    ;
  
  
  
    
  
  
  
    (*
    
    
      
    
    
    
      C3H8
      
      
        
      
      
      Propane
      
      
        
      
      
      in
      
      
        
      
      
      
        kg
        /
        
          m
          ^
          3
        
      
      
      
        
      
      
      at
      
      
        
      
      
      90
      
      K
    
    
    *)
  





  
    
      
        oxidizer
        
        
          
        
        =
        
          
        
        
        
          {
          
            densityOxidizer
            
            
              
            
            ->
            
              
            
            
            1140
          
          }
        
      
      ;
    
    
    
      
    
    
    
      (*
      
      
        
      
      
      LOX
      
      
        
      
      
      *)
    
  
  
  
    

  
  
  
    

  
  
  
    

  
  
  
    

  
  
  
    
  





  
    chamberPressure
    
    
      
    
    =
    
      .8
      *
      
        
      
      
      
        
          (
          
            densityFuel
            
            
              
            
            *
            
              
            
            
            
              rotationalVelocityNominal
              ^
              2
            
          
          )
        
        /
        2
      
    
  
  ;





  
    
      velocity
      
      
        
      
      =
      
        
      
      
      
        {
        
          rotationalVelocityNominal
          
          
            
          
          ->
          
            
          
          
          500
        
        }
      
    
    ;
  
  
  
    

  




Null

Geometry




  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  
  
  
    
      geometry
      
      
        
      
      =
      
        
      
      
      
        {
        
          
            thicknessOfChamberWall
            
            
              
            
            ->
            
              
            
            
            
              .
              01
            
          
          ,
          
            combustionChamberHeight
            
            
              
            
            ->
            
              
            
            
            .03
          
          
          
            
          
          ,
          
            rBot
            
            
              
            
            ->
            
              
            
            
            .005
          
          ,
          
            rTubesInner
            
            
              
            
            ->
            
              
            
            
            .003
          
          ,
          
            rTubesOuter
            
            
              
            
            ->
            
              
            
            
            .003
          
          ,
          
            
          
          
          
            lStar
            
            
              
            
            ->
            
              
            
            
            .275
          
        
        }
      
    
    ;
  





  
    densityOfSpindle
    
    
      
    
    =
    
      
    
    
    density
  
  ;





  
    densityOfRotor
    
    
      
    
    =
    
      
    
    
    density
  
  ;





  
    thicknessOfChamberWall
    
    
      
    
    =.
  
  ;





  
    combustionChamberHeight
    
    
      
    
    
    
      =
      .
    
  
  ;





  
    rBot
    
    
      
    
    =.
  
  ;





  
    rTubesInner
    
    
      
    
    
    
      =
      .
    
  
  ;





  
    
      rTubesOuter
      
      
        
      
      
      
        =
        .
      
    
    ;
  
  
  
    

  





  
    
  
  
  
    
      combustionChamberLength
      
      
        
      
      =
      combustionChamberHeight
    
    ;
  





  
    
      wallchamberratio
      
      
        
      
      =
      
        
      
      
      
        combustionChamberHeight
        /
        
          (
          
            2
            *
            thicknessOfChamberWall
          
          )
        
      
    
    
    
      
    
    ;
  
  
  
    

  





  
    rInner
    
    
      
    
    =
    
      
    
    
    
      rBot
      
      
        
      
      +
      
        combustionChamberHeight
        /
        2
      
    
  
  ;





  
    rOuter
    
    
      
    
    =
    
      
    
    
    
      rBot
      
      
        
      
      +
      combustionChamberHeight
      +
      
        
      
      
      thicknessOfChamberWall
    
  
  ;





  
    rInjector
    
    
      
    
    =
    
      
    
    
    
      rBot
      
      
        
      
      +
      combustionChamberHeight
    
  
  ;





  
    
      linterference
      
      
        
      
      =
      
        
      
      
      
        rInner
        
        
          
        
        *
        
          
        
        
        degreesinterference
        
        
          
        
        *
        
          
        
        
        thermalcoeff
      
    
    
    
      
    
    ;
  
  
  
    

  





  
    lEngine
    
    
      
    
    =
    
      combustionChamberLength
      
      
        
      
      +
      
        
      
      
      
        2
        *
        
          
        
        
        thicknessOfChamberWall
      
    
  
  ;





  
    hEngine
    
    
      
    
    =
    
      
    
    
    
      2
      
      
        (
        
          
        
        
        
          thicknessOfChamberWall
          
          
            
          
          +
          
            
          
          
          combustionChamberHeight
          
          
            
          
          +
          rBot
        
        )
      
    
  
  ;





  
    thicknessCutoff
    
    
      
    
    =
    
      
    
    
    
      thicknessOfChamberWall
      *
      
        Sin
        
        
          [
          
            π
            /
            8
          
          ]
        
      
    
  
  ;





  
    
      lOverlap
      
      
        
      
      =
      
        
      
      
      thicknessOfChamberWall
    
    ;
  
  
  
    

  
  
  
    

  





  
    rTop
    
    
      
    
    =
    
      
    
    
    
      rBot
      
      
        
      
      +
      
        com
        
        bustionChamberHeight
      
    
  
  ;





  
    rCenter
    
    
      
    
    =
    
      
    
    
    
      rBot
      
      
        
      
      +
      
        
          com
          
          bustionChamberHeight
        
        /
        2
      
    
  
  ;





  
    thicknesTop
    
    
      
    
    =
    
      com
      
      bustionChamberHeight
    
  
  ;





  
    lTop
    
    
      
    
    =
    
      
    
    
    
      
        
          2
        
        /
        2
      
      
      
        (
        
          rOuter
          
          
            
          
          -
          rTop
        
        )
      
    
  
  ;
  
    
  
  
  
    (*
    
    
      
    
    
    
      this
      
      
        
      
      
      makes
      
      
        
      
      
      the
      
      
        
      
      
      chamber
      
      
        
      
      
      walls
      
      
        
      
      
      the
      
      
        
      
      
      same
      
      
        
      
      
      thickness
      
      
        
      
      
      as
      
      
        
      
      
      the
      
      
        
      
      
      top
    
    
    
      
    
    
    *)
  
  
  l





  
    
      lTube
      
      
        
      
      =
      
        
      
      
      
        
          com
          
          bustionChamberHeight
        
        /
        
          2
        
      
    
    ;
  
  
  
    

  





  
    
      nTubesInner
      
      
        
      
      =
      
        
      
      
      
        Floor
        
        
          [
          
            2
            
            Pi
            
            
              
            
            
            
              
                (
                
                  rBot
                  -
                  rTubesInner
                
                )
              
              /
              
                (
                
                  1.1
                  
                  
                    
                  
                  *
                  2
                  
                  
                    
                  
                  *
                  rTubesInner
                
                
                
                  
                
                )
              
            
          
          ]
        
      
    
    ;
  
  
  
    
  
  
  
    

  
  
  
    

  
  
  
    

  





  
    
  
  
  
    
      nTubesOuter
      
      
        
      
      =
      
        
      
      
      
        Floor
        
        
          [
          
            2
            
            Pi
            
            
              
            
            
            
              
                (
                
                  rInner
                  -
                  rTubesOuter
                
                )
              
              /
              
                (
                
                  1.1
                  
                  
                    
                  
                  *
                  2
                  
                  
                    
                  
                  *
                  rTubesOuter
                
                
                
                  
                
                )
              
            
          
          ]
        
      
    
    ;
  
  
  
    
  





  
    areaTubesInner
    
    
      
    
    =
    
      
    
    
    
      2
      
      
        
      
      
      nTubesInner
      
      
        
      
      
      Pi
      
      
        
      
      
      
        (
        
          rTubesInner
          ^
          2
        
        )
      
    
  
  ;





  
    areaTubesOuter
    
    
      
    
    =
    
      
    
    
    
      2
      
      
        
      
      
      nTubesOuter
      
      
        
      
      
      Pi
      
      
        
      
      
      
        (
        
          rTubesOuter
          ^
          2
        
        )
      
    
  
  ;





  
    areaTubesInnerPropane
    
    
      
    
    =
    
      
    
    
    
      nTubesInner
      
      
        
      
      
      Pi
      
      
        
      
      
      
        (
        
          rTubesInner
          ^
          2
        
        )
      
    
  
  ;





  
    areaTubesOuterPropane
    
    
      
    
    =
    
      
    
    
    
      nTubesOuter
      
      
        
      
      
      Pi
      
      
        
      
      
      
        (
        
          rTubesOuter
          ^
          2
        
        )
      
    
  
  ;





  
    areaTubesInnerLOX
    
    
      
    
    =
    
      
    
    
    
      nTubesInner
      
      
        
      
      
      Pi
      
      
        
      
      
      
        (
        
          rTubesInner
          ^
          2
        
        )
      
    
  
  ;





  
    areaTubesOuterLOX
    
    
      
    
    =
    
      
    
    
    
      nTubesOuter
      
      
        
      
      
      Pi
      
      
        
      
      
      
        (
        
          rTubesOuter
          ^
          2
        
        )
      
    
  
  ;





  
    volumeOfCombustionChamberRotor
    
    
      
    
    =
    
      
    
    
    
      2
      
      Pi
      
      
        
          
          rInner
          rTop
        
        
        
          
        
        
        
          x
          
          
            (
            
              combustionChamberHeight
              -
              
                
              
              
              
                2
                
                
                  (
                  
                    x
                    -
                    rInner
                  
                  )
                
              
            
            )
          
          
          
            
            x
          
        
      
    
  
  ;





  
    volumeOfCombustionChamberSpindle
    
    
      
    
    =
    
      
    
    
    
      2
      
      Pi
      
      
        
          
          rBot
          rInner
        
        
        
          2
          
          x
          
          
            (
            
              x
              -
              rBot
            
            )
          
          
          
            
            x
          
        
      
    
  
  ;





  
    
  
  
  
    
      volumeOfCombustionChamber
      
      
        
      
      =
      
        
      
      
      
        volumeOfCombustionChamberRotor
        
        
          
        
        +
        volumeOfCombustionChamberSpindle
      
    
    ;
  





  
    
  
  
  
    
      volumeOfCombustionChamberIn3
      
      
        
      
      =
      
        
      
      
      
        61023.774
        
        
          
        
        
        volumeOfCombustionChamber
      
    
    
    
      
    
    ;
  
  
  
    

  
  
  
    
  
  
  
    

  
  
  
    

  





  
    rCutoff
    
    
      
    
    =
    
      
    
    
    
      rInner
      +
      thicknessCutoff
    
  
  ;





  
    
      volumeOfRotorTubes
      
      
        
      
      =
      
        
      
      
      
        2
        
        
          
        
        
        Pi
        
        
          
        
        
        nTubesOuter
        
        
          
        
        
        
          rTubesOuter
          ^
          2
        
        
        
          
        
        
        
          combustionChamberHeight
          /
          2
        
      
    
    ;
  
  
  
    (*
    
    
      
        
          times
          
          
            
          
          
          2
          
          
            
          
          
          for
          
          
            
          
          
          LOX
        
        
        
          
        
        &
      
      
      
        
      
      
      probane
      
      
        
      
      
      sets
      
      
        
      
      
      of
      
      
        
      
      
      tubes
    
    
    
      
    
    
    *)
  





  
    volumeOfInjectors
    =
    
      
    
    
    0
  
  ;





  
    volumeOfCorners
    
    
      
    
    =
    
      2
      
      Pi
      
      
        
          
          rCutoff
          rOuter
        
        
        
          2
          
          x
          
          
            (
            
              x
              -
              rCutoff
            
            )
          
          
          
            
            x
          
        
      
    
  
  ;





  
    volumeOfRotor
    =
    
      
    
    
    
      Re
      
      
        [
        
          
            Pi
            
            
              (
              
                
                  rOuter
                  ^
                  2
                
                
                
                  
                
                -
                
                  rInner
                  ^
                  2
                
              
              )
            
            
            
              (
              lEngine
              )
            
          
          -
          volumeOfCorners
          
          
            
          
          -
          volumeOfCombustionChamberRotor
          
          
            
          
          -
          
            
          
          
          volumeOfRotorTubes
          
          
            
          
          -
          
            
          
          
          volumeOfInjectors
        
        ]
      
    
  
  ;





  
    localvolumeOfRotor
    =
    
      volumeOfRotor
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
        
        ]
      
    
  
  ;





  
    otherSpindleVolume
    
    
      
    
    =
    
      
        
      
      
      
        
      
    
    
    
      
        Pi
        
        
          
        
        
        
          rInner
          ^
          2
        
        
        
          
        
        
        lEngine
      
      
      
        
      
      -
      volumeOfCombustionChamberSpindle
    
  
  ;





  
    
      volumeOfSpindleTubes
      
      
        
      
      =
      
        2
        
        
          
        
        
        Pi
        
        
          
        
        
        nTubesInner
        
        
          
        
        
        
          rTubesInner
          ^
          2
        
        
        
          
        
        
        
          combustionChamberHeight
          /
          2
        
      
    
    ;
  
  
  
    (*
    
    
      
        
          times
          
          
            
          
          
          2
          
          
            
          
          
          for
          
          
            
          
          
          LOX
        
        
        
          
        
        &
      
      
      
        
      
      
      probane
      
      
        
      
      
      sets
      
      
        
      
      
      of
      
      
        
      
      
      tubes
    
    
    
      
    
    
    *)
  





  
    volumeOfSpindleFeeds
    
    
      
    
    =
    
      
    
    
    0
  
  ;





  
    volumeOfNozzles
    
    
      
    
    =
    
      
    
    
    0
  
  ;





  
    volumeOfSpindle
    =
    
      
    
    
    
      Re
      
      
        [
        
          
            -
            
              
            
            
            volumeOfSpindleTubes
          
          
          
            
          
          +
          
            
          
          
          otherSpindleVolume
          
          
            
          
          -
          
            
          
          
          volumeOfSpindleTubes
          
          
            
          
          -
          
            
          
          
          volumeOfSpindleFeeds
          
          
            
          
          -
          volumeOfNozzles
        
        ]
      
    
  
  ;





  
    localvolumeOfSpindle
    
    
      
    
    =
    
      
    
    
    
      volumeOfSpindle
      
      
        
      
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
        
        ]
      
    
  
  ;





  
    volumeOfEngine
    
    
      
    
    =
    
      
    
    
    
      volumeOfSpindle
      
      
        
      
      +
      
        
      
      
      volumeOfRotor
    
  
  ;





  
    
  
  
  
    
      localvolumeOfEngine
      
      
        
      
      =
      
        
      
      
      
        volumeOfEngine
        /.
        
          Join
          [
          
            
          
          
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
    ;
  





  
    weightOfSpindle
    
    
      
    
    =
    
      
    
    
    
      densityOfSpindle
      
      
        
      
      *
      
        
      
      
      volumeOfSpindle
    
  
  ;





  
    weightOfRotor
    
    
      
    
    =
    
      
    
    
    
      densityOfRotor
      
      
        
      
      *
      
        
      
      
      volumeOfRotor
    
  
  ;





  
    weightOfEngine
    
    
      
    
    =
    
      
    
    
    
      weightOfSpindle
      
      
        
      
      +
      
        
      
      
      weightOfRotor
    
  
  ;





  
    localweightOfEngine
    
    
      
    
    =
    
      
    
    
    
      weightOfEngine
      
      
        
      
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
          ,
          superalloy
        
        ]
      
    
  
  ;





  
    weightOfEnginelb
    
    
      
    
    =
    
      
    
    
    
      2.2
      
      
        
      
      
      weightOfEngine
    
  
  
  
    
  
  ;





  
    localweightOfEnginelb
    
    
      
    
    =
    
      
    
    
    
      weightOfEnginelb
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
          ,
          superalloy
        
        ]
      
    
  
  ;





  
    calculatedArea
    
    
      
    
    =
    
      
    
    
    
      (
      
        volumeOfCombustionChamber
        /
        lStar
      
      
      
        
      
      )
    
  
  ;





  
    
      calculatedAreaSqIn
      
      
        
      
      =
      
        
      
      
      
        1550.0031
        
        
          
        
        
        calculatedArea
      
    
    ;
  
  
  
    

  
  
  
    
  





  
    
  
  
  
    
      aNozzles
      
      
        
      
      =
      
        
      
      
      calculatedArea
    
    ;
  





  
    
      nNozzles
      
      
        
      
      =
      3
    
    ;
  
  
  
    

  
  
  
    
  





  
    
      rNozzles
      
      
        
      
      =
      
        
      
      
      
        
          aNozzles
          /
          
            (
            
              nNozzles
              *
              Pi
            
            )
          
        
      
    
    
    
      
        
      
      
      
        
      
    
    ;
  
  
  
    
  
  
  
    

  
  
  
    
  
  
  
    

  
  
  
    
  
  
  
    

  





  
    nominalThrust
    
    
      
    
    =
    
      
    
    
    
      
        (
        
          volumeOfCombustionChamber
          /
          lStar
        
        
        
          
        
        )
      
      *
      
        
      
      
      chamberPressure
      
      
        
      
      *
      cf
    
  
  ;





  
    localnominalThrust
    
    
      
    
    =
    
      
    
    
    
      nominalThrust
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
        
        ]
      
    
  
  ;





  
    nominalThrustlbf
    
    
      
    
    =
    
      
    
    
    
      2.2
      
      
        
      
      
      
        nominalThrust
        /
        32
      
    
  
  ;





  
    localnominalThrustlbf
    
    
      
    
    =
    
      
    
    
    
      nominalThrustlbf
      
      
        
      
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
        
        ]
      
    
  
  ;





  
    
      nominalFuelFlowMass
      
      
        
      
      =
      
        
      
      
      
        
          (
          
            nominalThrustlbf
            /
            nominalISP
          
          )
        
        /
        2.2
      
    
    ;
  
  
  
    
  





  
    nominalFuelFlowVol
    
    
      
    
    =
    
      nominalFuelFlowMass
      
      
        
      
      /
      1000
    
  
  ;





  
    specificThrust
    
    
      
    
    =
    
      
    
    
    
      nominalThrustlbf
      /
      weightOfEnginelb
    
  
  ;





  
    localspecificThrust
    
    
      
    
    =
    
      
    
    
    
      specificThrust
      
      
        
      
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
          ,
          superalloy
        
        ]
      
    
  
  ;





  
    volapprroxcone
    
    
      
    
    =
    
      
    
    
    
      
        
          1
          /
          3
        
        
        
          
        
        *
        
          (
          
            π
            
            
              
            
            
            
              
                (
                
                  rBot
                  +
                  combustionChamberHeight
                  +
                  thicknessOfChamberWall
                  +
                  
                    lTop
                    /
                    2
                  
                
                )
              
              ^
              2
            
            
            
              
            
            *
            
              
            
            
            
              (
              
                
                  lEngine
                  *
                  2
                
                +
                thicknessCutoff
              
              )
            
          
          )
        
      
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
        
        ]
      
    
  
  ;





  volapprroxcone
  
  
    
  
  *
  
    
  
  
  
    3
    /
    4
  





  
    volapprroxcone2
    
    
      
    
    =
    
      
    
    
    
      
        
          1
          /
          3
        
        
        
          
        
        *
        
          (
          
            π
            
            
              
            
            
            
              
                (
                
                  rBot
                  +
                  combustionChamberHeight
                  +
                  thicknessOfChamberWall
                  +
                  thicknessCutoff
                
                )
              
              ^
              2
            
            
            
              
            
            *
            
              
            
            
            
              (
              
                
                  (
                  
                    rBot
                    +
                    combustionChamberHeight
                    +
                    thicknessOfChamberWall
                    +
                    thicknessCutoff
                  
                  )
                
                *
                2
              
              )
            
          
          )
        
      
      /.
      
        Join
        [
        
          
        
        
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
        
        ]
      
    
  
  ;





  volapprroxcone2
  
  
    
  
  *
  
    
  
  
  
    3
    /
    4
  





  totalvol
  
  
    
  
  =
  
    
  
  
  
    
      volumeOfCombustionChamber
      
      
        
      
      +
      
        
      
      
      volumeOfEngine
    
    
    
      
    
    /.
    
      Join
      [
      
        
      
      
      
        geometry
        ,
        fuel
        ,
        oxidizer
        ,
        velocity
      
      ]
    
  




l



0.0001920963516445262`



0.0001828502592707781`



0.00022427414952976558`




  Print
  
  
    [
    
      nTubesInner 
      ,
      
        nTubesInner
        /.
        geometry
      
    
    ]
  





  
    
  
  
  
    Print
    
    
      [
      
        nTubesOuter 
        ,
        
          nTubesOuter
          /.
          geometry
        
      
      ]
    
  
  
  
    
  
  
  
    

  
  
  
    (*
    
    
      
        Print
        
        
          [
          
            nTubesInner 
            
            
              
            
            ,
            
              
            
            
            nTubesInner
            ,
             nTubesOuter 
            ,
            
              
            
            
            nTubesOuter
          
          ]
        
      
      ;
    
    
    *)
  





  
    Print
    
    
      
    
    [
    
      
    
    
    
      rTop 
      ,
      
        
      
      
      
        rTop
        /.
        geometry
      
      ,
       rBot 
      ,
      
        
      
      
      
        rBot
        /.
        geometry
      
      ,
      
        
      
      
       combustionChamberHeight 
      
      
        
      
      ,
      
        combustionChamberHeight
        /.
        geometry
      
      ,
       lTop 
      ,
      
        
      
      
      
        lTop
        /.
        geometry
      
    
    ]
  
  
  
    &IndentingNewLine;
  





  Print
  
  
    [
    
      lEngine 
      ,
      
        
      
      
      
        lEngine
        /.
        geometry
      
      ,
       lOverlap 
      ,
      
        lOverlap
        /.
        geometry
      
    
    ]
  





  
    localvolumeOfCombustionChamber
    
    
      
    
    =
    
      volumeOfCombustionChamber
      /.
      
        
      
      
      geometry
    
  
  ;





  
    
  
  
  
    
      Print
      
      
        
      
      [
      
        
      
      
      
        volumes: engine_combustionchamber 
        ,
        
          
        
        
        localvolumeOfCombustionChamber
      
      ]
    
    ;
  





  
    
      local
      
      volumeOfCombustionChamberIn3
    
    
    
      
    
    =
    
      
    
    
    
      
        61023.774
        
        
          
        
        
        volumeOfCombustionChamber
      
      
      
        
      
      /.
      
        
      
      
      geometry
    
  
  ;





  Print
  
  
    [
    
       
      ,
      localvolumeOfCombustionChamberIn3
    
    ]
  





  Print
  
  
    [
    
      
         m^3 
        
        
          
        
        
         volumes: spindle 
      
      ,
      
        volumeOfCombustionChamberSpindle
        /.
        geometry
      
      ,
      
        
      
      
       volumes: rotor 
      ,
      
        volumeOfCombustionChamberRotor
        /.
        geometry
      
    
    ]
  





  Print
  
  
    
  
  [
  
    
  
  
  
    volumes: engine  
    ,
    localvolumeOfEngine
    ,
     
    ,
    
      61023.774
      
      
        
      
      
      localvolumeOfEngine
    
    ,
    
      

    
    
    
      
    
    
     volumes: spindle 
    ,
    localvolumeOfSpindle
    ,
     
    ,
    
      61023.774
      
      
        
      
      
      localvolumeOfSpindle
    
    ,
    
      
    
    
     volumes: rotor 
    ,
    localvolumeOfRotor
    ,
     
    ,
    
      61023.774
      
      
        
      
      
      localvolumeOfRotor
    
  
  ]





  Print
  
  
    [
    
      weightOfEngine = 
      ,
      
        
      
      
      localweightOfEngine
    
    ]
  





  Print
  
  
    [
    
      weightOfEngine lb = 
      ,
      
        
      
      
      localweightOfEnginelb
    
    ]
  





  Print
  
  
    
  
  [
  
    length of engine m = 
    
    
      
    
    ,
    
      lEngine
      /.
      geometry
    
    ,
    
      
    
    
     in = 
    ,
    
      
    
    
    
      
        lEngine
        /
        .0254
      
      /.
      geometry
    
  
  
  
    
  
  ]





  
    
      Print
      
      
        
      
      [
      
        height  of engine m = 
        
        
          
        
        ,
        
          hEngine
          /.
          geometry
        
        ,
        
          
        
        
         in = 
        ,
        
          
        
        
        
          
            hEngine
            /
            .0254
          
          /.
          geometry
        
      
      
      
        
      
      ]
    
    
    
      Print
      
      
        [
        
          CalculatedNozzle Area = 
          ,
          
            calculatedArea
            /.
            geometry
          
          ,
           
          ,
          
            
              1550.0031
              
              
                
              
              
              calculatedArea
            
            
            
              
            
            /.
            geometry
          
          ,
          
            
          
          
           in^2
        
        ]
      
    
  
  
  
    
  





  
    Print
    
    
      [
      
        nominalThrust = 
        ,
        
          
        
        
        localnominalThrust
        
        
          
        
        ,
         newtons = 
        ,
        localnominalThrustlbf
        ,
         lbf 
      
      ]
    
  
  
  
    

  





  
    Print
    
    
      [
      
        specific thrust = 
        ,
        localspecificThrust
        ,
         lbf/lb !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
      
      ]
    
  
  
  
    
  





  Print
  
  
    [
    
      nominalfuelflowmass 
      ,
      
        
          
            
              nominalFuelFlowMass
              
              
                
              
              /.
              
                
              
              
              geometry
            
            /.
            fuel
          
          /.
          oxidizer
        
        /.
        velocity
      
      
      
        
      
      ,
      nominalfuelflowvol 
      ,
      
        
          
            
              nominalFuelFlowVol
              
              
                
              
              /.
              
                
              
              
              geometry
            
            /.
            fuel
          
          /.
          oxidizer
        
        /.
        velocity
      
    
    ]
  




Null




  nTubesInner 
  
  
  
  1





  nTubesOuter 
  
  
  
  16





  rTop 
  
  
  
  0.034999999999999996`
  
  
  
   rBot 
  
  
  
  0.005`
  
  
  
   combustionChamberHeight 
  
  
  
  0.03`
  
  
  
   lTop 
  
  
  
  0.007071067811865476`





  lEngine 
  
  
  
  0.05`
  
  
  
   lOverlap 
  
  
  
  0.01`





  volumes: engine_combustionchamber 
  
  
  
  0.000056548667764616275`





   
  
  
  
  3.4508131216690288`





  
     m^3 
    
    
      
    
    
     volumes: spindle 
  
  
  
  
  0.000021205750411731104`
  
  
  
   volumes: rotor 
  
  
  
  0.00003534291735288517`





  volumes: engine  
  
  
  
  0.0001677254817651493`
  
  
  
   
  
  
  
  10.235241893277593`
  
  
  
   volumes: spindle 
  
  
  
  0.00003992964262712628`
  
  
  
   
  
  
  
  2.43665748757852`
  
  
  
   volumes: rotor 
  
  
  
  0.00012779583913802303`
  
  
  
   
  
  
  
  7.798584405699072`





  weightOfEngine = 
  
  
  
  1.3837352245624819`





  weightOfEngine lb = 
  
  
  
  3.0442174940374604`





  length of engine m = 
  
  
  
  0.05`
  
  
  
   in = 
  
  
  
  1.968503937007874`





  height  of engine m = 
  
  
  
  0.09`
  
  
  
   in = 
  
  
  
  3.543307086614173`





  CalculatedNozzle Area = 
  
  
  
  0.00020563151914405919`
  
  
  
   
  
  
  
  0.31872949213100105`
  
  
  
   in^2





  Null
  2





  nominalThrust = 
  
  
  
  28788.412680168287`
  
  
  
   newtons = 
  
  
  
  1979.2033717615698`
  
  
  
   lbf 





  specific thrust = 
  
  
  
  650.1517633474367`
  
  
  
   lbf/lb !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!





  nominalfuelflowmass 
  
  
  
  2.57039398930074`
  
  
  
  nominalfuelflowvol 
  
  
  
  0.0025703939893007397`





  





  
    

  
  
  
    

  
  
  
    
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      =
      
        
      
      
      
        
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            [
            
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                  [
                  
                    {
                    
                      
                        {
                        
                          0
                          ,
                          rInner
                        
                        }
                      
                      ,
                      
                        {
                        
                          0
                          ,
                          
                            rInner
                            
                            
                              
                            
                            +
                            
                              
                            
                            
                            thicknessCutoff
                          
                        
                        }
                      
                      ,
                      
                        {
                        
                          
                            
                              (
                              
                                lEngine
                                -
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                              )
                            
                            /
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                          ,
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                      ,
                      
                        {
                        
                          
                            
                              (
                              
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                              )
                            
                            /
                            2
                          
                          ,
                          rOuter
                        
                        }
                      
                      ,
                      
                        {
                        
                          lEngine
                          ,
                          
                            rInner
                            
                            
                              
                            
                            +
                            
                              
                            
                            
                            thicknessCutoff
                          
                        
                        }
                      
                      ,
                      
                        

                      
                      
                      
                        
                      
                      
                      
                        {
                        
                          lEngine
                          ,
                          rInner
                        
                        }
                      
                      
                      
                        
                      
                      ,
                      
                        {
                        
                          
                            lEngine
                            
                            
                              
                            
                            -
                            
                              
                            
                            
                            lOverlap
                          
                          ,
                          rInner
                        
                        }
                      
                      ,
                      
                        {
                        
                          
                        
                        
                        
                          
                            lEngine
                            /
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                          ,
                          
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                              combustionChamberHeight
                              /
                              2
                            
                          
                        
                        }
                      
                      ,
                      
                        {
                        
                          lOverlap
                          ,
                          rInner
                        
                        }
                      
                    
                    }
                  
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              }
            
            ]
          
        
        /.
        
          
        
        
        geometry
      
    
    ;
  





  
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        [
        
          {
          
            
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                [
                
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                {
                
                  
                    {
                    
                      0
                      ,
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                    }
                  
                  ,
                  
                    {
                    
                      0
                      ,
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                    }
                  
                  ,
                  
                    {
                    
                      lOverlap
                      ,
                      rInner
                    
                    }
                  
                  ,
                  
                    {
                    
                      
                        lEngine
                        
                        
                          
                        
                        /
                        2
                      
                      ,
                      
                        rInner
                        -
                        
                          combustionChamberHeight
                          /
                          2
                        
                      
                    
                    
                    
                      
                    
                    }
                  
                  ,
                  
                    {
                    
                      
                        lEngine
                        -
                        lOverlap
                      
                      ,
                      rInner
                    
                    
                    
                      
                    
                    }
                  
                  ,
                  
                    
                  
                  
                  
                    {
                    
                      lEngine
                      ,
                      rInner
                    
                    }
                  
                  ,
                  
                    

                  
                  
                  
                    
                  
                  
                  
                    {
                    
                      lEngine
                      ,
                      0
                    
                    }
                  
                
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        ]
      
      /.
      geometry
    
  
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    Show
    
    
      [
      
        g1
        ,
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        ,
        
          AspectRatio
          ->
          
            
          
          
          Automatic
        
      
      ]
    
  
  ;




Null

[Graphics:Images/index_gr_1.gif]




  


structural

I don't have all the answers here.  I need closed form solution here, as this is meant to be part of a adaptive annealing simulator, and will be evaluated for different values of all the structural parameters, and different fuel mixes.So I need a closed form solution, as it will be evaluated 100,000 times a run for hundreds or thousands of runs. Due to the simplicity of this design, there should be a closed form solution, but till I learn how to do that, I'll look for upper and lower bounds.  

The expected failure modes are strains sufficient to separate the rotor from the spindle, and stresses sufficient to cause rotor failure. The intent is to use a thermal shrink interference fit to join the two.

The first approximation is to look at various stresses on radial disks, ignoring the torsional component that would tie things together.  
    Stresses for the pressure component are given by the Lamé equations
    S r = r 1 2 p 1 r 2 2 - r 1 2 (1+ r 2 2 r 2 )
     S t = r 1 2 p 1 r 2 2 - r 1 2 (1- r 2 2 r 2 )
    Stresses for the rotational component are
    σ r = 3 + μ 8 ρ ω 2 ( r 2 2 + r 1 2 - r 2 2 r 1 2 r 2 - r 2 )
    σ t = 3 + μ 8 ρ ω 2 ( r 2 2 + r 1 2 - r 2 2 r 1 2 r 2 - ( 1 + 3` μ ) 3 + μ r 2 )
    
    We will look at the stresses on the interior edge of a disk at the edge of the rotor looking for the strain that
    will cause the two pieces to seperate. (Note that I'm cheating here, there isn't pressure there, but this is a good start, upper bound to speed.)




  Sr
  
  
    
  
  =
  
    
      
        
          r1
          2
        
        
        
          p
          
          
            
          
        
      
      
        
          r2
          
          
            
              
            
            
              2
              
              
                
              
            
          
          
          
            
          
        
        -
        
          r1
          2
        
      
    
    
    
      (
      
        1
        -
        
          
            r2
            
            
              
                
              
              
                2
                
                
                  
                
              
            
          
          
            r
            
            
              
                
              
              
                2
                
                
                  
                
              
            
          
        
      
      )
    
  





  
    St
    =
    
      
        
          
            r
            1
          
          
          
            
              
            
            
              2
              
              
                
              
            
          
          
          
            p
            
            
              
            
          
        
        
          
            r2
            
            
              
                
              
              
                2
                
                
                  
                
              
            
            
            
              
            
          
          -
          
            r1
            
            
              
                
              
              
                2
                
                
                  
                
              
            
          
        
      
      
      
        (
        
          1
          +
          
            
              r2
              
              
                
                  
                
                
                  2
                  
                  
                    
                  
                
              
            
            
              r
              
              
                
                  
                
                
                  2
                  
                  
                    
                  
                
              
            
          
        
        )
      
    
  
  ;





  
    σr
    =
    
      
        
          3
          +
          μ
        
        8
      
      
      ρ
      
      
        ω
        2
      
      
      
        (
        
          
            
              r2
              2
            
            
            
              
            
            +
            
              
            
            
            
              r1
              2
            
          
          -
          
            
              
                r2
                2
              
              
              
                
              
              
              
                r1
                2
              
            
            
              r
              2
            
          
          -
          
            r
            2
          
        
        )
      
    
  
  ;





  
    σt
    =
    
      
        
          3
          +
          μ
        
        8
      
      
      ρ
      
      
        ω
        2
      
      
      
        (
        
          
            r2
            2
          
          
          
            
          
          +
          
            
          
          
          
            r1
            2
          
          +
          
            
              
                r2
                2
              
              
              
                
              
              
              
                r1
                2
              
            
            r2
          
          -
          
            
              
                (
                
                  1
                  +
                  
                    3`
                    
                    μ
                  
                
                )
              
              
                3
                +
                μ
              
            
            
            
              r
              2
            
          
        
        )
      
    
  
  ;





  


So using these at the interior edge where r = rInner, first we set the stresses to the interference pressure:

But we may have better use for the radial elongation form of this stuff , as that is likely the

design factor we have direct control of

radialelongation = ( r1 2 p r2 2 - r1 2 ( 1 + r2 2 r 2 ) + 3 + μ 8 ρ ω 2 ( r2 2 + r1 2 - r2 2 r1 2 r 2 - r 2 ) ) ( 1 - μ ) / E ;




  
    ω
    
    
      
    
    =.
  
  ;





  
    radialelongation
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    modulusElasticity
    
    
      
    
    =.
  
  ;





  
    μ
    
    
      
    
    =.
  
  ;





  
    ρ
    
    
      
    
    =.
  
  ;





  
    r
    
    
      
    
    =.
  
  ;





  
    p
    =.
  
  ;





  
    ω
    
    
      
    
    =.
  
  ;





  
    r1
    
    
      
    
    =.
  
  ;





  
    r2
    
    
      
    
    =.
  
  ;





  
    linterference
    
    
      
    
    =.
  
  ;





  
    
      rotationsolution
      
      
        
      
      =
      
        Simplify
        
        
          [
          
            Solve
            
            
              [
              
                
                  radialelongation
                  
                  
                    
                  
                  
                  
                    
                      
                        
                          r1
                          
                          
                            
                          
                          
                          p
                          
                          
                            
                          
                          
                          wallchamberratio
                        
                        modulusElasticity
                      
                      
                      
                        (
                        
                          
                            
                              (
                              
                                1
                                +
                                
                                  
                                    r1
                                    2
                                  
                                  
                                    r2
                                    2
                                  
                                
                              
                              )
                            
                            
                              (
                              
                                1
                                -
                                
                                  
                                    r1
                                    2
                                  
                                  
                                    r2
                                    2
                                  
                                
                              
                              )
                            
                          
                          +
                          μ
                        
                        )
                      
                    
                    +
                    
                      
                        (
                        
                          
                            
                              3
                              +
                              μ
                            
                            8
                          
                          
                          ρ
                          
                          
                            ω
                            2
                          
                          
                          
                            (
                            
                              
                                
                                  r2
                                  2
                                
                                
                                
                                  
                                
                                +
                                
                                  
                                
                                
                                
                                  r1
                                  2
                                
                              
                              -
                              
                                
                                  
                                    r2
                                    2
                                  
                                  
                                  
                                    
                                  
                                  
                                  
                                    r1
                                    2
                                  
                                
                                
                                  r
                                  2
                                
                              
                              -
                              
                                r
                                2
                              
                            
                            )
                          
                        
                        )
                      
                      
                      
                        
                          (
                          
                            1
                            -
                            μ
                          
                          )
                        
                        /
                        modulusElasticity
                      
                    
                  
                
                ,
                ω
              
              ]
            
          
          ]
        
      
    
    ;
  
  
  
    
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  




Null




  
    ros
    
    
      
    
    =
    
      
        
          
            
              
                
                  rotationsolution
                  
                  
                    
                  
                  [
                  
                    [
                    1
                    ]
                  
                  ]
                
                /.
                
                  {
                  
                    
                      r1
                      
                      
                        
                      
                      
                      rInner
                    
                    ,
                    
                      ρ
                      
                      density
                    
                    ,
                    
                      radialelongation
                      
                      
                        
                      
                      
                      
                        
                      
                      
                      linterference
                    
                    ,
                    
                      p
                      
                      chamberPressure
                    
                    ,
                    
                      μ
                      
                      .3
                    
                    ,
                    
                      r
                      
                      
                        rInner
                        
                        
                          
                        
                        +
                        
                          
                        
                        
                        linterference
                      
                    
                    ,
                    
                      r2
                      
                      
                        
                      
                      
                      
                        
                      
                      
                      rOuter
                    
                  
                  }
                
              
              /.
              geometry
            
            /.
            fuel
          
          /.
          oxidizer
        
        /.
        superalloy
      
      /.
      velocity
    
  
  ;





  
    ros
    
    
      
    
    =
    
      
        
          rotationsolution
          
          
            
          
          [
          
            [
            1
            ]
          
          ]
        
        /.
        
          {
          
            
              r1
              
              
                
              
              
              rInner
            
            ,
            
              ρ
              
              density
            
            ,
            
              radialelongation
              
              
                
              
              
              
                
              
              
              linterference
            
            ,
            
              p
              
              chamberPressure
            
            ,
            
              μ
              
              .3
            
            ,
            
              r
              
              
                rInner
                
                
                  
                
                +
                
                  
                
                
                linterference
              
            
            ,
            
              r2
              
              
                
              
              
              
                
              
              
              rOuter
            
          
          }
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            superalloy
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    wextreme
    
    
      
    
    =
    
      
    
    
    
      
        
          ω
          
          
            
          
          *
          r2
        
        
        
          
        
        /.
        
          
        
        
        
          {
          
            
              r2
              
              
                
              
              
              
                
              
              
              rInjector
            
            ,
            
              ros
              
              
                [
                
                  [
                  1
                  ]
                
                ]
              
            
          
          }
        
      
      /.
      geometry
    
  
  ;





  (*
  
  
    
      `maxtstressformula
      
      
        
      
      =
      
        (
        
          
            (
            
              
            
            
            
              
                
                  
                    r1
                    
                    
                      
                    
                    
                    p
                    
                    
                      
                    
                    
                    wallchamberratio
                  
                  modulusElasticity
                
                
                
                  (
                  
                    
                      
                        (
                        
                          1
                          +
                          
                            
                              r1
                              2
                            
                            
                              r2
                              2
                            
                          
                        
                        )
                      
                      
                        (
                        
                          1
                          -
                          
                            
                              r1
                              2
                            
                            
                              r2
                              2
                            
                          
                        
                        )
                      
                    
                    +
                    μ
                  
                  )
                
              
              +
              
                (
                
                  
                    
                      3
                      +
                      μ
                    
                    8
                  
                  
                  ρ
                  
                  
                    ω
                    2
                  
                  
                  
                    (
                    
                      
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        +
                        
                          
                        
                        
                        
                          r1
                          2
                        
                      
                      -
                      
                        
                          
                            r2
                            2
                          
                          
                          
                            
                          
                          
                          
                            r1
                            2
                          
                        
                        
                          r
                          2
                        
                      
                      -
                      
                        r
                        2
                      
                    
                    )
                  
                
                )
              
            
            )
          
          
          
            
          
          *
          modulusElasticity
          *
          
            
              (
              
                
                  r1
                  2
                
                +
                
                  r2
                  2
                
              
              )
            
            /
            
              (
              
                4
                
                r1
                *
                
                  
                
                
                
                  r2
                  2
                
              
              )
            
          
        
        )
      
    
    ;
  
  
  *)





  
    &IndentingNewLine;
  
  
  
    
      maxtstressformula
      
      
        
      
      =
      
        (
        
          
            
              
                
                  r1
                  2
                
                
                
                  
                
                
                p
                
                
                  
                
                
                wallchamberratio
              
              
                
                  r2
                  2
                
                
                
                  
                
                -
                
                  
                
                
                
                  r1
                  2
                
              
            
            
            
              (
              
                1
                +
                
                  
                    r2
                    2
                  
                  
                    r
                    2
                  
                
              
              )
            
          
          +
          
            
              (
              
                
                  
                    3
                    +
                    μ
                  
                  8
                
                
                ρ
                
                
                  ω
                  2
                
                
                
                  (
                  
                    
                      
                        r2
                        2
                      
                      
                      
                        
                      
                      +
                      
                        
                      
                      
                      
                        r1
                        2
                      
                    
                    -
                    
                      
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                      
                      
                        r
                        2
                      
                    
                    -
                    
                      r
                      2
                    
                  
                  )
                
              
              )
            
            
            
              (
              
                1
                -
                μ
              
              )
            
          
        
        )
      
    
    
    
      
    
    ;
  





  
    &IndentingNewLine;
  
  
  
    
      
        minmaxr
        
        
          
        
        =
        
          
        
        
        
          Solve
          
          
            [
            
              
                0
                ==
                
                  D
                  
                  
                    [
                    
                      maxtstressformula
                      ,
                      r
                    
                    ]
                  
                
              
              ,
              r
            
            ]
          
        
      
      ;
    
    
    
      &IndentingNewLine;
    
  




Null




  
    &IndentingNewLine;
  
  
  
    
      
        maxr
        
        
          
        
        =
        
          
            minmaxr
            
            
              [
              
                [
                4
                ]
              
              ]
            
          
          
          
            [
            
              [
              1
              ]
            
            ]
          
        
      
      ;
    
    
    
      &IndentingNewLine;
    
    
    
      (*
      
      
        
          
            /.
            
              {
              
                
                  r1
                  
                  
                    
                  
                  
                  rInner
                
                ,
                
                  p
                  
                  chamberPressure
                
                ,
                
                  μ
                  
                  .3
                
                ,
                
                  ρ
                  
                  density
                
                ,
                
                  radialelongation
                  
                  
                    
                  
                  
                  linterference
                
                ,
                
                  r2
                  
                  
                    
                  
                  
                  
                    
                  
                  
                  rOuter
                
                
                
                  
                
                ,
                
                  wallthickness
                  
                  
                    
                  
                  ->
                  
                    
                  
                  
                  thicknessOfChamberWall
                
                ,
                
                  
                
                
                
                  ω
                  ->
                  
                    
                  
                  
                  
                    rotationalVelocityNominal
                    /
                    rInjector
                  
                
              
              
              
                
              
              }
            
          
          /.
          
            Join
            
            
              [
              
                geometry
                ,
                fuel
                ,
                oxidizer
                ,
                superalloy
                ,
                velocity
              
              ]
            
          
        
        ]
      
      
      *)
    
  





  





  
    samaxtstress
    =
    
      
        maxtstressformula
        
        
          
        
        /.
        
          {
          
            
              r1
              
              
                
              
              
              rInner
            
            ,
            
              
            
            
            
              p
              
              chamberPressure
            
            ,
            
              μ
              
              .3
            
            ,
            maxr
            ,
            
              ρ
              
              density
            
            ,
            
              radialelongation
              
              
                
              
              
              linterference
            
            ,
            
              r2
              
              
                
              
              
              
                
              
              
              rOuter
            
            
            
              
            
            ,
            
              wallthickness
              
              
                
              
              ->
              
                
              
              
              thicknessOfChamberWall
            
            ,
            
              
            
            
            
              ω
              ->
              
                
              
              
              
                rotationalVelocityNominal
                /
                rInjector
              
            
          
          
          
            
          
          }
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            superalloy
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    samaxtstress
    =
    
      
        maxtstressformula
        
        
          
        
        /.
        
          {
          
            
              r1
              
              
                
              
              
              rInner
            
            ,
            
              
            
            
            
              p
              
              chamberPressure
            
            ,
            
              μ
              
              .3
            
            ,
            
              r
              
              
                rInner
                
                
                  
                
                +
                
                  
                
                
                linterference
              
            
            ,
            
              ρ
              
              density
            
            ,
            
              radialelongation
              
              
                
              
              
              linterference
            
            ,
            
              r2
              
              
                
              
              
              
                
              
              
              rOuter
            
            
            
              
            
            ,
            
              wallthickness
              
              
                
              
              ->
              
                
              
              
              thicknessOfChamberWall
            
            ,
            
              
            
            
            
              ω
              ->
              
                
              
              
              
                rotationalVelocityNominal
                /
                rInjector
              
            
          
          
          
            
          
          }
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            superalloy
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    1.3620354151308376`*^8
    /
    6894.7
  
  
  
    &IndentingNewLine;
  




19754.817687946357`




  
    samaxtstress
    /
    6894.6
  
  ;





  
    it
    
    
      
    
    
    seems
    
    
      
    
    
    to
    
    
      
    
    
    take
    
    
      
    
    
    that
    
    
      
    
    
    much
    
    
      
    
    
    psi
    
    
      
    
    
    to
    
    
      
    
    
    do
    
    
      
    
    
    that
  
  ,
  
    
  
  
  
    for
    
    
      
    
    
    steel
  





  
    
      with
      
      
        
      
      
      impellers
      
      
        
      
      
      to
      
      
        
      
      
      pre
      
      
        
      
      
      pressurize
      
      
        
      
      
      itwe
      
      
        
      
      
      get
      
      
        
      
      
      a
      
      
        
      
      
      bit
      
      
        
      
      
      more
    
    ,
    
      
    
    
    
      that
      
      
        
      
      
      can
      
      
        
      
      
      be
      
      
        
      
      
      added
      
      
        
      
      
      as
      
      
        
      
      
      it
      
      
        
      
      
      is
      
      
        
      
      
      
        designed
        .
        
          &IndentingNewLine;
        
        
        note
      
      
      
        
      
      
      that
      
      
        
      
      
      is
      
      
        
      
      
      not
      
      
        
      
      
      too
      
      
        
      
      
      bad
      
      
        
      
      
      a
      
      
        
      
      
      model
      
      
        
      
      
      for
      
      
        
      
      
      the
      
      
        
      
      
      strength
      
      
        
      
      
      of
      
      
        
      
      
      this
    
    ,
    
      
        
          
            though
            
            
              
            
            
            a
            
            
              
            
            
            bit
            
            
              
            
            
            
              conservative
              !
            
            
            
              
            
            
            The
            
            
              
            
            
            engine
            
            
              
            
            
            can
            
            
              
            
            
            be
            
            
              
            
            
            thought
            
            
              
            
            
            of
            
            
              
            
            
            as
            
            
              
            
            
            two
            
            
              
            
            
            disks
            
            
              
            
            
            distorted
            
            
              
            
            
            to
            
            
              
            
            
            meet
            
            
              
            
            
            in
            
            
              
            
            
            the
            
            
              
            
            
            
              middle
              .
              
                
              
              
              It
            
          
          ;
        
        '
      
      
      s
      
      
        
      
      
      conservative
      
      
        
      
      
      bvecause
      
      
        
      
      
      the
      
      
        
      
      
      disks
      
      
        
      
      
      are
      
      
        
      
      
      trimmed
      
      
        
      
      
      a
      
      
        
      
      
      bit
      
      
        
      
      
      at
      
      
        
      
      
      the
      
      
        
      
      
      edges
    
    ,
    
      this
      
      
        
      
      
      makes
      
      
        
      
      
      the
      
      
        
      
      
      edges
      
      
        
      
      
      lighter
      
      
        
      
      
      and
      
      
        
      
      
      thus
      
      
        
      
      
      this
      
      
        
      
      
      model
      
      
        
      
      
      is
      
      
        
      
      
      
        conservative
        
        
          
        
        .
        
          
        
        
        That
      
      
      
        
      
      
      is
      
      
        
      
      
      lighter
      
      
        
      
      
      on
      
      
        
      
      
      the
      
      
        
      
      
      
        outside
        .
        
          &IndentingNewLine;
        
        
        Note
      
      
      
        
      
      
      that
      
      
        
      
      
      the
      
      
        
      
      
      result
      
      
        
      
      
      is
      
      
        
      
      
      for
      
      
        
      
      
      some
      
      
        
      
      
      steel
    
    ,
    
      
    
    
    
      for
      
      
        
      
      
      aluminum
      
      
        
      
      
      the
      
      
        
      
      
      answer
      
      
        
      
      
      is
      
      
        
      
      
      similar
    
  
  
  
    
  
  
  
    &IndentingNewLine;
  





  





  
    ω
    
    
      
    
    =.
  
  ;





  
    radialelongation
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    modulusElasticity
    
    
      
    
    =.
  
  ;





  
    μ
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    ρ
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    p
    =
    
      
    
    .
  
  ;





  
    ω
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r1
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r2
    
    
      
    
    =.
  
  ;





  
    
      pinterference
      
      
        
      
      =.
    
    ;
  
  
  
    
  
  
  
    &IndentingNewLine;
  





  
    ros
    
    
      
    
    =
    
      
        
          
            
              
                
                  rotationsolution
                  
                  
                    
                  
                  [
                  
                    [
                    1
                    ]
                  
                  ]
                
                /.
                
                  {
                  
                    
                      r1
                      
                      
                        
                      
                      
                      rInner
                    
                    ,
                    
                      radialelongation
                      
                      
                        
                      
                      
                      
                        
                      
                      
                      linterference
                    
                    ,
                    
                      ρ
                      
                      density
                    
                    ,
                    
                      p
                      
                      chamberPressure
                    
                    ,
                    
                      μ
                      
                      .3
                    
                    ,
                    
                      r
                      
                      
                        rInner
                        
                        
                          
                        
                        +
                        
                          
                        
                        
                        linterference
                      
                    
                    ,
                    
                      r2
                      
                      
                        
                      
                      
                      
                        
                      
                      
                      rOuter
                    
                  
                  }
                
              
              /.
              geometry
            
            /.
            fuel
          
          /.
          oxidizer
        
        /.
        aluminum
      
      /.
      velocity
    
  
  ;





  
    wextreme
    
    
      
    
    =
    
      
    
    
    
      
        
          ω
          
          
            
          
          *
          r2
        
        
        
          
        
        /.
        
          {
          
            
              r2
              
              
                
              
              
              
                
              
              
              rInjector
            
            
            
              
            
            ,
            
              ros
              
              
                [
                
                  [
                  1
                  ]
                
                ]
              
            
          
          }
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            aluminum
            ,
            velocity
          
          ]
        
      
    
  
  ;





  





  
    almaxstress
    
    
      
    
    =
    
      
        maxtstressformula
        /.
        
          {
          
            
              r1
              
              
                
              
              
              rInner
            
            ,
            
              p
              
              
                
              
              
              chamberPressure
            
            ,
            
              μ
              
              .3
            
            ,
            
              r
              
              
                rInner
                
                
                  
                
                +
                
                  
                
                
                linterference
              
            
            ,
            
              radialelongation
              
              
                
              
              
              linterference
            
            ,
            
              ρ
              
              density
            
            ,
            
              r2
              
              
                
              
              
              
                
              
              
              rOuter
            
            ,
            
              
            
            
            
              ω
              ->
              
                
              
              
              
                rotationalVelocityNominal
                /
                rInjector
              
            
          
          
          
            
          
          }
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            aluminum
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    
      almaxstress
      /
      6894
    
    
    
      
    
    
    psi
  
  ;





  
    
  
  
  
    not
    
    
      
    
    
    bad
    
    
      
    
    
    for
    
    
      
    
    
    aluminum
  





  



    The stresses on the center of the rotor will show us the speed where the rotor fails by flying apart, again ignoring shear effects. We use the interferencePressure formula, but use the outer edge and a failure stress !


    Now, and more interestingly, we look at the tangential pressure components integrated over the area of the chamber wall + the tangential stresses integrated along the length of the rotor.  .... how close is this to a solution... ...rigid ia an Pyrex... how close are we to integrating real torsion to this ....




  
    &IndentingNewLine;
  
  
  
    
      
        stressVelocity
        
        
          
        
        =
        
          
        
        
        44444444444444444444444444.
      
      ;
    
    
    
      

    
    
    
      
        stressPressure
        
        
          
        
        =
        
          
        
        
        5555555555555555555555555.
      
      ;
    
  





  Null
  2


Chemistry




  
    TLox
    
    
      
    
    =
    
      
    
    
    90
  
  ;





  
    
      TPropane
      
      
        
      
      =
      
        
      
      
      90
    
    ;
  
  
  
    

  





  
    
      
        TChamber
        
        
          
        
        =
        
          
        
        
        3200
      
      ;
    
    
    
      
    
    
    
      (*
      
      
        
      
      
      
        actualy
        
        
          
        
        
        is
        
        
          
        
        
        f
        
        
          (
          
            
              Pressure
              
              
                
              
              &
            
            
            
              
            
            
            fulemixratio
          
          )
        
      
      
      
        
      
      
      *)
    
  
  
  
    

  





  
    molWeightPropane
    
    
      
    
    =
    
      
    
    
    44
  
  ;





  
    molWeightO2
    
    
      
    
    =
    
      
    
    
    32
  
  ;





  
    molWeightStoich
    
    
      
    
    =
    
      
    
    
    
      molWeightPropane
      
      
        
      
      +
      
        
      
      
      
        (
        
          5
          
          
            
          
          
          molWeightO2
        
        )
      
    
  
  ;





  
    O2WeightStoich
    
    
      
    
    =
    
      
    
    
    
      5
      
      
        
      
      
      
        molWeightO2
        /
        molWeightStoich
      
    
  
  ;





  
    propaneWeightStoich
    
    
      
    
    =
    
      
    
    
    
      molWeightPropane
      /
      molWeightStoich
    
  
  ;





  
    
      volStoich
      
      
        
      
      =
      
        
      
      
      
        
          
            (
            
              O2WeightStoich
              /
              densityOxidizer
            
            )
          
          
          
            
          
          +
          
            
          
          
          
            (
            
              propaneWeightStoich
              /
              densityFuel
            
            )
          
        
        /.
        
          Join
          
          
            [
            
              geometry
              ,
              fuel
              ,
              oxidizer
              ,
              velocity
            
            ]
          
        
      
    
    ;
  
  ;





  
    volStoichO2Fraction
    
    
      
    
    =
    
      
    
    
    
      
        (
        
          O2WeightStoich
          /
          densityOxidizer
        
        )
      
      /
      volStoich
    
  
  ;





  
    volStoichPropaneFraction
    
    
      
    
    =
    
      
    
    
    
      
        (
        
          propaneWeightStoich
          /
          densityFuel
        
        )
      
      /
      volStoich
    
  
  ;





  
    ratioFuelRichness
    
    
      
    
    =
    
      
    
    
    2.0
  
  ;





  
    molWeightRich
    
    
      
    
    =
    
      
        (
        
          
        
        
        
          ratioFuelRichness
          
          
            
          
          *
          
            
          
          
          molWeightPropane
        
        )
      
      
      
        
      
      +
      
        
      
      
      
        (
        
          5
          
          
            
          
          
          molWeightO2
        
        )
      
    
  
  ;





  
    
  
  
  
    
      Print
      
      
        [
        Fuel  analisys
        ]
      
    
    ;
  





  Print
  
  
    [
    
      molWeightRich
      
      
        
      
      ,
       mol weight rich
    
    ]
  





  
    O2WeightRich
    
    
      
    
    =
    
      
    
    
    
      5
      
      
        
      
      
      
        molWeightO2
        /
        molWeightRich
      
    
  
  ;





  
    Print
    
    
      [
      
        O2WeightRich
        
        
          
        
        ,
         O2 weight rich
      
      ]
    
  
  ;





  
    propaneWeightRich
    
    
      
    
    =
    
      
    
    
    
      ratioFuelRichness
      
      
        
      
      
      
        molWeightPropane
        /
        molWeightRich
      
    
  
  ;





  Print
  
  
    [
    
      propaneWeightRich
      
      
        
      
      ,
       propane weight rich
    
    ]
  





  
    volRich
    
    
      
    
    =
    
      
    
    
    
      
        
          (
          
            O2WeightRich
            /
            densityOxidizer
          
          )
        
        
        
          
        
        +
        
          
        
        
        
          (
          
            propaneWeightRich
            /
            densityFuel
          
          )
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    volRichO2Fraction
    
    
      
    
    =
    
      
    
    
    
      
        
          (
          
            O2WeightRich
            /
            densityOxidizer
          
          )
        
        /
        volRich
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  Print
  
  
    [
    
      volRichO2Fraction
      
      
        
      
      ,
      
        
      
      
       vol rich O2 fraction 
    
    ]
  





  
    volRichPropaneFraction
    
    
      
    
    =
    
      
    
    
    
      
        
          (
          
            propaneWeightRich
            /
            densityFuel
          
          )
        
        /
        volRich
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    Print
    
    
      [
      
        volRichPropaneFraction
        
        
          
        
        ,
        
          
        
        
         vol rich propane fraction 
      
      ]
    
  
  
  
    
  
  
  
    

  





  
    
      flowRateInnerLox
      
      
        
      
      =
      
        
      
      
      
        
          volRichO2Fraction
          
          
            
          
          
          
            nominalFuelFlowVol
            
            
              
            
            /
            areaTubesInnerLOX
          
        
        /.
        
          Join
          
          
            [
            
              geometry
              ,
              fuel
              ,
              oxidizer
              ,
              velocity
            
            ]
          
        
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  
    flowRateOuterLox
    
    
      
    
    =
    
      
    
    
    
      
        volRichO2Fraction
        
        
          
        
        
        
          nominalFuelFlowVol
          
          
            
          
          /
          areaTubesOuterLOX
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    flowRateInnerPropane
    
    
      
    
    =
    
      
    
    
    
      
        volRichPropaneFraction
        
        
          
        
        
        
          nominalFuelFlowVol
          
          
            
          
          /
          areaTubesInnerPropane
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    
      flowRateOuterPropane
      
      
        
      
      =
      
        
      
      
      
        
          volRichO2Fraction
          
          
            
          
          
          
            nominalFuelFlowVol
            
            
              
            
            /
            areaTubesOuterPropane
          
        
        /.
        
          Join
          
          
            [
            
              geometry
              ,
              fuel
              ,
              oxidizer
              ,
              velocity
            
            ]
          
        
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  Print
  
  
    [
    
      flowRateInnerLox 
      ,
      flowRateInnerLox
    
    ]
  





  Print
  
  
    [
    
      flowRateOuterLox 
      ,
      flowRateOuterLox
    
    ]
  





  Print
  
  
    [
    
      flowRateInnerPropane 
      ,
      flowRateInnerPropane
    
    ]
  





  Print
  
  
    [
    
      flowRateOuterPropane 
      ,
      flowRateOuterPropane
    
    ]
  





  
    localnominalFuelFlowMass
    =
    
      
    
    
    
      nominalFuelFlowMass
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    Print
    
    
      [
      
        nominalFuelFlowMass 
        ,
        localnominalFuelFlowMass
      
      ]
    
  
  
  
    

  




Null



Fuel  analisys




  248.`
  
  
  
   mol weight rich





  0.6451612903225806`
  
  
  
   O2 weight rich





  0.3548387096774194`
  
  
  
   propane weight rich





  0.5275056518462697`
  
  
  
   vol rich O2 fraction 





  0.47249434815373026`
  
  
  
   vol rich propane fraction 





  flowRateInnerLox 
  
  
  
  47.955059258751795`





  flowRateOuterLox 
  
  
  
  2.997191203671987`





  flowRateInnerPropane 
  
  
  
  42.95403165033912`





  flowRateOuterPropane 
  
  
  
  2.997191203671987`





  nominalFuelFlowMass 
  
  
  
  2.5703939893007397`


Pressure




  
    

  
  
  
    
      pressureFuelInjector
      
      
        
      
      =
      
        
      
      
      
        
          
            (
            
              rotationalVelocity
              ^
              2
            
            )
          
          
          
            
          
          
          
            densityFuel
            /
            2
          
        
        
        
          
        
        /.
        
          Join
          
          
            [
            
              geometry
              ,
              fuel
              ,
              oxidizer
              ,
              aluminum
              ,
              velocity
            
            ]
          
        
      
    
    ;
  





  
    
      Print
      
      
        [
        
          fuel pressure injector 
          ,
          
            
          
          
          
            pressureFuelInjector
            /
            
              (
              
                100000
                /
                15
              
              )
            
          
          ,
          
            
          
          
          psi
        
        ]
      
    
    ;
  
  
  
    

  
  
  
    (*
    
    
      
    
    
    
      
        
          
            v
            ^
            2
          
          
          
            
          
          
          density
        
        
        
          
        
        =
        
          
        
        
        pressure
      
      ,
      
        
      
      
      
        this
        
        
          
        
        
        is
        
        
          
        
        
        equilivent
        
        
          
        
        
        to
        
        
          
        
        
        the
        
        
          
        
        
        standard
        
        
          
        
        
        form
        
        
          
        
        
        in
        
        
          
        
        
        thetextbooks
        
        
          

        
        
        
          
        
        
        for
        
        
          
        
        
        centrefugal
        
        
          
        
        
        pumps
      
      ,
      
        
      
      
      
        that
        
        
          
        
        
        is
        
        
          
        
        
        expressed
        
        
          
        
        
        in
        
        
          
        
        
        terms
        
        
          
        
        
        of
        
        
          
        
        
        head
      
      
      
        
      
      ,
      
        
      
      
      
        this
        
        
          
        
        
        form
        
        
          
        
        
        is
        
        
          
        
        
        more
        
        
          
        
        
        convinent
        
        
          
        
        
        conceptually
        
        
          
        
        
        here
      
      ,
      
        
      
      
      
        as
        
        
          
        
        
        it
        
        
          
        
        
        shows
        
        
          
        
        
        thatpressure
        
        
          
        
        
        is
        
        
          
        
        
        related
        
        
          
        
        
        only
        
        
          
        
        
        to
        
        
          
        
        
        velocity
        
        
          
        
        
        and
        
        
          
        
        
        density
      
    
    
    
      
    
    
    *)
  





  
    pressureOxidizerInjector
    
    
      
    
    =
    
      
    
    
    
      
        
          (
          
            rotationalVelocity
            ^
            2
          
          )
        
        
        
          
        
        
        
          densityOxidizer
          /
          2
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            aluminum
            ,
            velocity
          
          ]
        
      
    
  
  
  
    
  
  ;





  
    Print
    
    
      [
      
        oxidizer pressure injector 
        ,
        
          pressureOxidizerInjector
          /
          
            (
            
              100000
              /
              15
            
            )
          
        
        
        
          
        
        ,
        psi
      
      ]
    
  
  ;





  
    oxidizerPressureDrop
    
    
      
    
    =
    
      
    
    
    
      
        pressureOxidizerInjector
        
        
          
        
        -
        
          
        
        
        chamberPressure
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            aluminum
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    
      Print
      
      
        [
        
          Oxidizer pressure drop 
          ,
          
            
          
          
          
            oxidizerPressureDrop
            
            
              
            
            /
            
              (
              
                100000
                /
                15
              
              )
            
          
          ,
          
            
          
          
          psi
        
        ]
      
    
    ;
  
  
  
    

  





  
    fuelPressureDrop
    
    
      
    
    =
    
      
    
    
    
      
        pressureFuelInjector
        
        
          
        
        -
        
          
        
        
        chamberPressure
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            aluminum
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    Print
    
    
      [
      
        fuel pressure drop 
        
        
          
        
        ,
        
          
        
        
        
          fuelPressureDrop
          /
          
            (
            
              100000
              /
              15
            
            )
          
        
        ,
        
          
        
        
        psi
      
      ]
    
  
  
  
    
  





  
    Print
    [
    
      fuel pressure drop ratio 
      
      
        
      
      ,
      
        
      
      
      
        fuelPressureDrop
        /
        pressureFuelInjector
      
    
    
    
      
    
    ]
  
  
  
    
  





  fuel pressure injector 
  
  
  
  
    0.0525`
    
    
      
    
    
    
      rotationalVelocity
      2
    
  
  
  
  
  psi





  oxidizer pressure injector 
  
  
  
  
    
      171
      
      
        
      
      
      
        rotationalVelocity
        2
      
    
    2000
  
  
  
  
  psi





  Oxidizer pressure drop 
  
  
  
  
    
      3
      
      
        
      
      
      
        (
        
          
            -
            7.`*^7
          
          +
          
            570
            
            
              
            
            
            
              rotationalVelocity
              2
            
          
        
        )
      
    
    20000
  
  
  
  
  psi





  fuel pressure drop 
  
  
  
  
    
      3
      
      
        
      
      
      
        (
        
          
            -
            7.`*^7
          
          +
          
            350.`
            
            
              
            
            
            
              rotationalVelocity
              2
            
          
        
        )
      
    
    20000
  
  
  
  
  psi





  fuel pressure drop ratio 
  
  
  
  
    
      0.002857142857142857`
      
      
        
      
      
      
        (
        
          
            -
            7.`*^7
          
          +
          
            350.`
            
            
              
            
            
            
              rotationalVelocity
              2
            
          
        
        )
      
    
    
      rotationalVelocity
      2
    
  


Thermal




  
    velocityhotgas
    
    
      
    
    =
    
      
    
    
    3333333333333333333333333
  
  ;





  Cold
  
  
    
  
  
  Cooling
  
  
    
  
  
  side





  Cold
  
  
    
  
  
  Cooling
  
  
    
  
  
  side
  
  
    
  
  
  analisys
  
  
    
  
  
  of
  
  
    
  
  
  boundary
  
  
    
  
  
  layer
  
  
    
  
  
  dominated
  
  
    
  
  
  by
  
  
    
  
  
  fuel
  
  
    
  
  
  speed





  results
  
  
    
  
  
  in
  
  
    
  
  
  a
  
  
    
  
  
  badness
  
  
    
  
  
  factor
  
  
    
  
  
  of
  
  
    
  
  
  about
  
  
    
  
  
  200





  200
  
  
    
  
  
  a
  
  
    
  
  
  about
  
  
    
  
  
  badness
  
  
    
  
  
  factor
  
  
    
  
  
  in
  
  
    
  
  
  of
  
  
    
  
  
  results


Note for the first cut this is the same equation as the hot side cooling, the parameters are different as is the geometry.We will have to do this a few times,first we split it into to pies top and bottom as the geometries are different,then for a first approximation,we first calculate how much heat we transfer assuming the fuel input temperature throaty this gives us an upper bound,then use that as input temperature, ,this gives us a lower bound for heat transfer We will have to do this a few times,first we split it into to pieces top and bottom as the geometries are different,then for a first approximation,we first calculate how much heat we transfer assuming the fuel input temperature throaty this gives us an upper bound.Then perhaps a third try with incremental steps,this can also generate an upper and lowerbound if done correctly,the precision required of the computation in;t too high given the availability of upper and lower bounds,because the formula is at best a crude approximation,and given that the roughness factor has an uncertainty of over a factor of 3?.t is quite possible there is a better formulation for this.Note salty the the various fluid property parameters may be off quite a bit,They are in red in the online version to indicate this.Better data are available and I will generate them as time permits.. Note that as part of an optimization program these will have to be generated on the fly as a function of fuel mix and pressure.I have this in the works. .

Cooling Cold sideFor the amount of heat transferred from cold tubes we will start with
the approximation of constant temperature of the metal wall. I will use Q = π∫DqⅆL
and h g = 0.026 ( c p μ 0.2 Pr 0.6 ) ( ρμ ) 0.8 ( ρ am ρ ' ) ( ` am μ 0 )
equations (8-20) & (8-23) from Sutton 7th ed. My intuition fails me here without a good reference.




  
    

  
  
  
    

  
  
  
    
      
        
          ρlocal
          
          
            
          
          =.
        
        ;
      
      
      
        

      
      
      
        

      
      
      
        

      
      
      
        
          
            c
            p
          
          
          
            
          
          =
          
            
          
          .
        
        
        
          
        
        ;
      
      
      
        

      
      
      
        
          
            ρ
            am
          
          =.
        
        ;
      
    
    
    
      
    
    
    
      

    
    
    
      
        
          ρ
          '
        
        =.
      
      ;
    
    
    
      

    
    
    
      
        
          μ
          am
        
        =.
      
      ;
    
    
    
      

    
    
    
      
        
          μ
          0
        
        =.
      
      ;
    
    
    
      

    
    
    
      
        μlocal
        =.
      
      ;
    
    
    
      

    
    
    
      

    
    
    
      

    
    
    
      
        Pr
        =.
      
      ;
    
    
    
      
    
  





  Null
  8





  
    TEngineWall
    =
    300.
  
  ;
  
    thicknessToCoolantEngine
    =
    0.0025
  
  ;





  
    
      LOXcharisterics
      
      
        
      
      =
      
        {
        
          
            ρlocal
            ->
            1249.8
          
          ,
          
            

          
          
          
            
              c
              p
            
            ->
            51.535
          
          ,
          
            

          
          
          
            
              ρ
              am
            
            ->
            1230
          
          ,
          
            

          
          
          
            
              ρ
              
            
            ->
            1216.7
          
          ,
          
            

          
          
          
            
              μ
              am
            
            ->
            .000300
          
          ,
          
            

          
          
          
            
              μ
              0
            
            ->
            .00027349
          
          ,
          
            

          
          
          
            μlocal
            ->
            .00033697
          
          ,
          
            &IndentingNewLine;
          
          
          
            thermalConductivity
            
            
              
            
            
            .17
          
        
        }
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  
    propanecharisterics
    =
    
      {
      
        
          ρlocal
          ->
          730.80
        
        ,
        
          

        
        
        
          
            c
            p
          
          ->
          85.078
        
        ,
        
          

        
        
        
          
            ρ
            am
          
          ->
          728.10
        
        ,
        
          

        
        
        
          
            ρ
            
          
          ->
          722.15
        
        ,
        
          

        
        
        
          
            μ
            am
          
          ->
          .00300
        
        ,
        
          

        
        
        
          
            μ
            0
          
          ->
          .002766
        
        ,
        
          μlocal
          ->
          .004365
        
        ,
        
          &IndentingNewLine;
        
        
        
          thermalConductivity
          
          
            
          
          
          .21
        
      
      }
    
  
  ;





  
    Pr
    
    
      
    
    =
    
      
        c
        p
      
      
      
        μlocal
        
        
          
        
        /
        thermalConductivity
      
    
  
  ;





  
    {
    
      
        ρlocal
        
        730.8`
      
      ,
      
        
          c
          p
        
        
        85.078`
      
      ,
      
        
          ρ
          am
        
        
        728.1`
      
      ,
      
        
          ρ
          
        
        
        722.15`
      
      ,
      
        
          μ
          am
        
        
        0.003`
      
      ,
      
        
          μ
          0
        
        
        0.002766`
      
      ,
      
        μlocal
        
        0.004365`
      
      ,
      
        0.24`
        
        0.21`
      
    
    }
  
  ;





  
    {
    
      
        ρlocal
        
        730.8`
      
      ,
      
        
          c
          p
        
        
        85.078`
      
      ,
      
        
          ρ
          am
        
        
        728.1`
      
      ,
      
        
          ρ
          
        
        
        722.15`
      
      ,
      
        
          μ
          am
        
        
        0.003`
      
      ,
      
        
          μ
          0
        
        
        0.002766`
      
      ,
      
        μlocal
        
        0.004365`
      
      ,
      
        0.24`
        
        0.21`
      
    
    }
  
  ;





  
    Qabstract
    =
    
      π
      
      
        2
      
      *
      tubeDiameter
      *
      Numberoftubes
      
      
        
      
      
      
        
          
          arBot
          arTop
        
        
        
          
        
        
        
          
            (
            
              
                
                  (
                  tubeDiameter
                  )
                
                
                  -
                  .2
                
              
              
              .026
              
              r
              
              
                (
                
                  TFluid
                  -
                  TEngineWall
                
                )
              
              
              
                (
                
                  
                    
                      c
                      p
                    
                    
                    
                      μlocal
                      0.2
                    
                  
                  
                    Pr
                    0.6
                  
                
                )
              
              *
              
                
                  (
                  
                    ρlocal
                    
                    
                      
                    
                    
                    fuelfeedvelocity
                  
                  )
                
                ^
                0.8
              
              
              
                (
                
                  
                    ρ
                    am
                  
                  
                    ρ
                    '
                  
                
                )
              
              
              
                (
                
                  
                    μ
                    am
                  
                  
                    μ
                    0
                  
                
                )
              
            
            )
          
          
          
            
            r
          
        
      
    
  
  ;





  
    QinnerLOX
    =
    
      
        
          
            
              
                
                  Qabstract
                  /.
                  
                    fuelfeedvelocity
                    ->
                    flowRateInnerLox
                  
                
                /.
                
                  arTop
                  
                  rCenter
                
              
              /.
              
                arBot
                
                rBot
              
            
            /.
            LOXcharisterics
          
          /.
          geometry
        
        /.
        
          tubeDiameter
          
          
            2
            
            
              
            
            
            rTubesInner
          
        
      
      /.
      
        Numberoftubes
        ->
        nTubesInner
      
    
  
  ;





  
    Qouterlox
    =
    
      
        
          
            
              
                
                  Qabstract
                  /.
                  
                    fuelfeedvelocity
                    ->
                    flowRateOuterLox
                  
                
                /.
                
                  arTop
                  
                  rTop
                
              
              /.
              
                arBot
                
                rCenter
              
            
            /.
            LOXcharisterics
          
          /.
          geometry
        
        /.
        
          tubeDiameter
          
          
            2
            
            
              
            
            
            rTubesOuter
          
        
      
      /.
      
        Numberoftubes
        ->
        nTubesOuter
      
    
  
  ;





  
    Qinnerpropane
    =
    
      
        
          
            
              
                
                  Qabstract
                  /.
                  
                    fuelfeedvelocity
                    ->
                    flowRateInnerPropane
                  
                
                /.
                
                  arTop
                  
                  rCenter
                
              
              /.
              
                arBot
                
                rBot
              
            
            /.
            propanecharisterics
          
          /.
          geometry
        
        /.
        
          tubeDiameter
          
          
            2
            
            
              
            
            
            rTubesInner
          
        
      
      /.
      
        Numberoftubes
        ->
        nTubesInner
      
    
  
  ;





  
    Qouterpropane
    =
    
      
        
          
            
              
                
                  Qabstract
                  /.
                  
                    fuelfeedvelocity
                    ->
                    flowRateOuterPropane
                  
                
                /.
                
                  arTop
                  
                  rTop
                
              
              /.
              
                arBot
                
                rCenter
              
            
            /.
            propanecharisterics
          
          /.
          geometry
        
        /.
        
          tubeDiameter
          
          
            2
            
            
              
            
            
            rTubesOuter
          
        
      
      /.
      
        Numberoftubes
        ->
        nTubesOuter
      
    
  
  ;





  
    Q
    =
    
      QinnerLOX
      +
      Qouterlox
      +
      Qinnerpropane
      +
      Qouterpropane
    
  
  ;





  
    fuelfeedvelocity
    =
    flowRateInnerLox
  
  ;





  
    qPerKey
    =
    
      Q
      /
      
        (
        nominalFuelFlowMass
        )
      
    
  
  ;





  
    localqPerKeycold
    =
    
      
        qPerKey
        /.
        
          TFluid
          
          100
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  
    Print
    
    
      [
      
        Q = 
        ,
        
          
            Q
            /.
            
              TFluid
              
              100
            
          
          /.
          
            Join
            
            
              [
              
                geometry
                ,
                fuel
                ,
                oxidizer
                ,
                velocity
              
              ]
            
          
        
      
      ]
    
  
  /.
  
    tubeDiameter
    
    
      2
      
      
        
      
      
      rTubesInner
    
  





  Print
  
  
    [
    
      coldQ per kilogram of fuel = 
      ,
      localqPerKeycold
    
    ]
  





  Print
  
  
    [
    
      cf kcal 
      ,
      cf
      ,
       
      ,
      
        cf
        *
        4186.8
      
      ,
       Watts
    
    ]
  





  Print
  
  
    [
    
      fuelfeedvelocity  = 
      ,
      flowRateInnerLox
    
    ]
  





  Print
  
  
    [
    
      nominalFuelFlowMass = 
      ,
      
        nominalFuelFlowMass
        /.
        
          Join
          
          
            [
            
              geometry
              ,
              fuel
              ,
              oxidizer
              ,
              velocity
            
            ]
          
        
      
    
    ]
  





  Print
  
  
    [
    
      aprox degrees fuel temperature rise 
      ,
      
        localqPerKeycold
        /
        
          (
          
            cf
            *
            4186.8
          
          )
        
      
    
    ]
  




Null




  
    Syntax
    
    ::
    
    sntxf
  
  
  
    :
    
      
    
  
  
  \"\!\(π \@2 * tubeDiameter * Numberoftubes\\ \)\" cannot be followed by \"\!\(\(∫\_arBot\%arTop\)\\ \(\(\(\((\(&LeftSkeleton; 1 &RightSkeleton;\))\)\) \(\(ⅆ r\)\)\)\)\)\".\!\(\"\"\)





  
    Qabstract
    =
    
      π
      
      
        2
      
      *
      tubeDiameter
      *
      Numberoftubes
      
      
        
      
      
System`Convert`MathMLDump`ToSymbolicMathML[ErrorBox[RowBox[{\(∫\_arBot\%arTop\), " ", RowBox[{RowBox[{"(", RowBox[{\(\((tubeDiameter)\)\^\(-.2\)\), ".026", "r", \((TFluid - TEngineWall)\), FormBox[\((\(c\_p μlocal\^0.2\)\/Pr\^0.6)\), "TraditionalForm"], "*", FormBox[\(\((ρlocal\ fuelfeedvelocity)\)^0.8\), "TraditionalForm"], FormBox[\((ρ\_am\/\(ρ '\))\), "TraditionalForm"], FormBox[\((μ\_am\/μ\_0)\), "TraditionalForm"]}], ")"}], \(ⅆ r\)}]}]]]    
  
  ;





  
    &IndentingNewLine;
  
  
  
    Cold
    
    
      
    
    
    Cooling
    
    
      
    
    
    side
    
    
      
    
    
    analisys
    
    
      
    
    
    of
    
    
      
    
    
    boundary
    
    
      
    
    
    layer
    
    
      
    
    
    dominated
    
    
      
    
    
    by
    
    
      
    
    
    convection
  





  analisys
  
  
    
  
  
  boundary
  
  
    
  
  
  by
  
  
    
  
  
  Cold
  
  
    
  
  
  convection
  
  
    
  
  
  Cooling
  
  
    
  
  
  dominated
  
  
    
  
  
  layer
  
  
    
  
  
  of
  
  
    
  
  
  side





  
    
  
  
  
    One
    
    
      
    
    
    of
    
    
      
    
    
    the
    
    
      
    
    
    uses
    
    
      
    
    
    for
    
    
      
    
    
    this
    
    
      
    
    
    calculation
    
    
      
    
    
    will
    
    
      
    
    
    be
    
    
      
    
    
    to
    
    
      
    
    
    show
    
    
      
    
    
    what
    
    
      
    
    
    to
    
    
      
    
    
    optimize
    
    
      
    
    
    for
    
    
      
    
    
    in
    
    
      
    
    
    the
    
    
      
    
    
    design
  





  
    which
    
    
      
    
    
    dimensions
    
    
      
    
    
    should
    
    
      
    
    
    be
    
    
      
    
    
    large
    
    
      
    
    
    and
    
    
      
    
    
    which
    
    
      
    
    
    small
  
  ,
  
    
  
  
  
    
      (
      natural
      )
    
    
    convection
    
    
      
    
    
    in
    
    
      
    
    
    the
    
    
      
    
    
    engine
    
    
      
    
    
    is
    
    
      
    
    
    in
    
    
      
    
    
    the
    
    
      
    
    
    direction
    
    
      
    
    
    opposed
    
    
      
    
    
    to
    
    
      
    
    
    fule
    
    
      
    
    
    flow
  
  ,
  
    
  
  
  
    os
    
    
      
    
    
    it
    
    
      
    
    
    may
    
    
      
    
    
    be
    
    
      
    
    
    that
    
    
      
    
    
    for
    
    
      
    
    
    the
    
    
      
    
    
    vertical
    
    
      
    
    
    component
    
    
      
    
    
    fuel
    
    
      
    
    
    flow
    
    
      
    
    
    wants
    
    
      
    
    
    to
    
    
      
    
    
    be
    
    
      
    
    
    minimized
  
  ,
  
    or
    
    
      
    
    
    at
    
    
      
    
    
    least
    
    
      
    
    
    
      slow
      .
    
  





  
    thicknessToCoolantEngine
    =
    0.0025
  
  ;





  
    
      LOXcharisterics
      
      
        
      
      =
      
        {
        
          
            ρlocal
            ->
            1249.8
          
          ,
          
            

          
          
          
            
              c
              p
            
            ->
            51.535
          
          ,
          
            

          
          
          
            
              ρ
              am
            
            ->
            1230
          
          ,
          
            

          
          
          
            
              ρ
              
            
            ->
            1216.7
          
          ,
          
            

          
          
          
            
              μ
              am
            
            ->
            .000300
          
          ,
          
            

          
          
          
            
              μ
              0
            
            ->
            .00027349
          
          ,
          
            

          
          
          
            μlocal
            ->
            .00033697
          
          ,
          
            &IndentingNewLine;
          
          
          
            thermalConductivity
            
            
              
            
            
            .17
          
        
        }
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  
    
      propanecharisterics
      =
      
        {
        
          
            ρlocal
            ->
            730.80
          
          ,
          
            

          
          
          
            
              c
              p
            
            ->
            85.078
          
          ,
          
            

          
          
          
            
              ρ
              am
            
            ->
            728.10
          
          ,
          
            

          
          
          
            
              ρ
              
            
            ->
            722.15
          
          ,
          
            

          
          
          
            
              μ
              am
            
            ->
            .00300
          
          ,
          
            

          
          
          
            
              μ
              0
            
            ->
            .002766
          
          ,
          
            

          
          
          
            μlocal
            ->
            .004365
          
          ,
          
            &IndentingNewLine;
          
          
          
            thermalConductivity
            
            
              
            
            
            .21
          
        
        }
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  
    μ
    
    
      
    
    =.
  
  ;





  
    
      ν
      
      
        
      
      =
      
        
      
      
      
        μ
        ρ
      
    
    ;
  
  
  
    

  





  
    Pr
    
    
      
    
    =
    
      
        c
        p
      
      
      
        μ
        /
        thermalConductivity
      
    
  
  ;





  
    Gr
    
    
      
    
    =
    
      
    
    
    
      
        geffective
        
        
          
        
        
        β
        
        
          (
          
            TEngineWall
            
            
              
            
            -
            TFluid
          
          )
        
        
        
          L
          3
        
      
      
        ν
        2
      
    
  
  ;





  
    Ra
    
    
      
    
    =
    
      
    
    
    
      Gr
      
      
        
      
      
      Pr
    
  
  ;





  
    Gz
    
    
      
    
    =
    
      
    
    
    
      Ren
      
      
        
      
      
      Pr
      
      
        
      
      
      
        D
        L
      
    
  
  ;





  
    Ren
    
    
      
    
    =
    
      
    
    
    
      
        V
        
        
          
        
        
        D
      
      μ
    
  
  ;





  
    Pr
    
    
      
    
    =
    
      
        c
        p
      
      
      
        μ
        /
        thermalConductivity
      
    
  
  ;




Null




  Now
  
  
    
  
  
  for
  
  
    
  
  
  full
  
  
    
  
  
  angled
  
  
    
  
  
  
    case
    !
  
  
  
    
  
  
  formula
  
  
    
  
  
  for
  
  
    
  
  
  a
  
  
    
  
  
  parallelaped
  
  
    
  
  
  at
  
  
    
  
  
  angle
  
  
    
  
  
  ϕ





  
    μ
    
    
      
    
    =.
  
  ;





  
    ϕ
    
    
      
    
    =.
  
  ;





  
    
      ν
      
      
        
      
      =
      
        
      
      
      
        μ
        ρ
      
    
    ;
  
  
  
    

  





  
    Pr
    
    
      
    
    =
    
      
        c
        p
      
      
      
        μ
        /
        thermalConductivity
      
    
  
  ;





  
    GrL
    
    
      
    
    =
    
      
    
    
    
      
        geffective
        
        
          
        
        
        β
        
        
          (
          
            TEngineWall
            
            
              
            
            -
            TFluid
          
          )
        
        
        
          L
          3
        
      
      
        ν
        2
      
    
  
  ;





  
    GrD
    
    
      
    
    =
    
      
    
    
    
      
        geffective
        
        
          
        
        
        β
        
        
          (
          
            TEngineWall
            
            
              
            
            -
            TFluid
          
          )
        
        
        
          D
          3
        
      
      
        ν
        2
      
    
  
  ;





  
    RaL
    
    
      
    
    =
    
      
    
    
    
      GrL
      
      
        
      
      
      Pr
    
  
  ;





  RaD
  
  
    
  
  =
  
    
  
  
  
    GrD
    
    
      
    
    
    Pr
  





  
    GzD
    
    
      
    
    =
    
      
    
    
    
      RenD
      
      
        
      
      
      Pr
      
      
        
      
      
      
        D
        L
      
    
  
  ;





  
    RenD
    
    
      
    
    =
    
      
    
    
    
      
        V
        
        
          
        
        
        D
      
      μ
    
  
  ;





  
    RenL
    
    
      
    
    =
    
      
    
    
    
      
        V
        
        
          
        
        
        L
      
      μ
    
  
  ;





  
    Pr
    
    
      
    
    =
    
      
        c
        p
      
      
      
        μ
        /
        thermalConductivity
      
    
  
  ;





  
    
  
  
  
    
      Nu
      
      avL
    
    
    
      
    
    =
    
      
        1
        
        
          
        
        +
        
          
            Max
            
            
              [
              
                0
                ,
                
                  (
                  
                    1
                    -
                    
                      1798
                      
                        Ra
                        
                        
                          
                        
                        
                        
                          Cos
                          
                          
                            [
                            ϕ
                            ]
                          
                        
                      
                    
                  
                  )
                
              
              ]
            
          
          
          
            
          
          
          
            Max
            
            
              [
              
                0
                ,
                
                  (
                  
                    1
                    -
                    
                      
                        1798
                        
                        
                          
                            Sin
                            
                            
                              [
                              
                                1.8
                                
                                ϕ
                              
                              ]
                            
                          
                          1.6
                        
                      
                      
                        Ra
                        
                        
                          
                        
                        
                        
                          Cos
                          
                          
                            [
                            ϕ
                            ]
                          
                        
                      
                    
                  
                  )
                
              
              ]
            
          
        
        +
        
          
            Max
            
            
              [
              
                0
                ,
                
                  
                    
                      (
                      
                        
                          Ra
                          
                          
                            
                          
                          
                          
                            Cos
                            
                            
                              [
                              ϕ
                              ]
                            
                          
                        
                        5830
                      
                      )
                    
                    
                      1
                      3
                    
                  
                  -
                  1
                
              
              ]
            
          
          
          
            
          
          
          for
          
          
            
          
          
          
            H
            L
          
        
      
      
      
        
      
      
      12
    
  





  
    4.166666666666667`
    
    
      
    
    
    
      D
      3
    
    
    
      
    
    
    geffective
    
    
      
    
    
    
      (
      
        
          300.`
          
          
        
        -
        TFluid
      
      )
    
    
    
      
    
    
    β
    
    
      
    
    
    
      ρ
      2
    
    
    
      
    
    
    
      c
      p
    
  
  μ





  
    1
    +
    
      
        Max
        
        
          [
          
            0
            ,
            
              1
              -
              
                
                  431.52`
                  
                  
                    
                  
                  
                  μ
                  
                  
                    
                  
                  
                  
                    Sec
                    
                    
                      [
                      ϕ
                      ]
                    
                  
                
                
                  geffective
                  
                  
                    
                  
                  
                  
                    L
                    3
                  
                  
                  
                    
                  
                  
                  
                    (
                    
                      
                        300.`
                        
                        
                      
                      -
                      TFluid
                    
                    )
                  
                  
                  
                    
                  
                  
                  β
                  
                  
                    
                  
                  
                  
                    ρ
                    2
                  
                  
                  
                    
                  
                  
                  
                    c
                    p
                  
                
              
            
          
          ]
        
      
      
      
        
      
      
      
        Max
        
        
          [
          
            0
            ,
            
              1
              -
              
                
                  431.52`
                  
                  
                    
                  
                  
                  μ
                  
                  
                    
                  
                  
                  
                    Sec
                    
                    
                      [
                      ϕ
                      ]
                    
                  
                  
                  
                    
                  
                  
                  
                    
                      Sin
                      
                      
                        [
                        
                          1.8`
                          
                          
                            
                          
                          
                          ϕ
                        
                        ]
                      
                    
                    1.6`
                  
                
                
                  geffective
                  
                  
                    
                  
                  
                  
                    L
                    3
                  
                  
                  
                    
                  
                  
                  
                    (
                    
                      
                        300.`
                        
                        
                      
                      -
                      TFluid
                    
                    )
                  
                  
                  
                    
                  
                  
                  β
                  
                  
                    
                  
                  
                  
                    ρ
                    2
                  
                  
                  
                    
                  
                  
                  
                    c
                    p
                  
                
              
            
          
          ]
        
      
    
    +
    
      
        for
        
        
          
        
        
        H
        
        
          
        
        
        
          Max
          
          
            [
            
              0
              ,
              
                
                  -
                  1
                
                +
                
                  0.08940738673291768`
                  
                  
                    
                  
                  
                  
                    
                      (
                      
                        
                          geffective
                          
                          
                            
                          
                          
                          
                            L
                            3
                          
                          
                          
                            
                          
                          
                          
                            (
                            
                              
                                300.`
                                
                                
                              
                              -
                              TFluid
                            
                            )
                          
                          
                          
                            
                          
                          
                          β
                          
                          
                            
                          
                          
                          
                            ρ
                            2
                          
                          
                          
                            
                          
                          
                          
                            Cos
                            
                            
                              [
                              ϕ
                              ]
                            
                          
                          
                          
                            
                          
                          
                          
                            c
                            p
                          
                        
                        μ
                      
                      )
                    
                    
                      1
                      /
                      3
                    
                  
                
              
            
            ]
          
        
      
      L
    
  
  
  12





  
    &IndentingNewLine;
  
  
  
    
      Nu
      
      avL
    
    
    
      
    
    =
    
      1
      
      
        
      
      +
      
        
          Max
          
          
            [
            
              0
              ,
              
                (
                
                  1
                  -
                  
                    1798
                    
                      RaL
                      
                      
                        
                      
                      
                      
                        Cos
                        
                        
                          [
                          ϕ
                          ]
                        
                      
                    
                  
                
                )
              
            
            ]
          
        
        *
        
          
        
        
        
          Max
          
          
            [
            
              0
              ,
              
                (
                
                  1
                  -
                  
                    
                      1798
                      
                      
                        
                      
                      
                      
                        
                          Sin
                          
                          
                            [
                            
                              1.8
                              
                              ϕ
                            
                            ]
                          
                        
                        1.6
                      
                    
                    
                      RaL
                      
                      
                        
                      
                      
                      
                        Cos
                        
                        
                          [
                          ϕ
                          ]
                        
                      
                    
                  
                
                )
              
            
            ]
          
        
      
      +
      
        Max
        
        
          [
          
            0
            ,
            
              
                
                  (
                  
                    
                      RaL
                      
                      
                        
                      
                      
                      
                        Cos
                        
                        
                          [
                          ϕ
                          ]
                        
                      
                    
                    5830
                  
                  )
                
                
                  1
                  3
                
              
              -
              1
            
          
          ]
        
      
    
  





  
    nuavllocalLOX
    =
    
      
        
          
            
              
                
                  
                    
                      
                        Nu
                        
                        avL
                      
                      
                      
                        
                      
                      /.
                      
                        ϕ
                        
                        
                          
                        
                        ->
                        
                          π
                          4
                        
                      
                    
                    /.
                    
                      μ
                      
                      
                        
                      
                      
                      μlocal
                    
                  
                  /.
                  
                    ρ
                    
                    
                      
                    
                    
                    ρlocal
                  
                
                /.
                LOXcharisterics
              
              /.
              
                L
                
                
                  
                
                
                lTube
              
            
            
            
              
            
            /.
            
              geffective
              
              
                
              
              
              
                
              
              
              
                10
                7
              
            
          
          /.
          
            β
            
            
              
            
            
            1
          
        
        
        
          
        
        /.
        
          
        
        
        
          TFluid
          
          
            
          
          
          
            
          
          
          100
        
      
      
      
        
      
      /.
      geometry
    
  
  ;





  
    nuavllocalpropane
    =
    
      
        
          
            
              
                
                  
                    
                      
                        Nu
                        
                        avL
                      
                      
                      
                        
                      
                      /.
                      
                        ϕ
                        
                        
                          
                        
                        ->
                        
                          π
                          4
                        
                      
                    
                    /.
                    
                      μ
                      
                      
                        
                      
                      
                      μlocal
                    
                  
                  /.
                  
                    ρ
                    
                    
                      
                    
                    
                    ρlocal
                  
                
                /.
                propanecharisterics
              
              /.
              
                L
                
                
                  
                
                
                lTube
              
            
            
            
              
            
            /.
            
              geffective
              
              
                
              
              
              
                
              
              
              
                10
                7
              
            
          
          /.
          
            β
            
            
              
            
            
            1
          
        
        
        
          
        
        /.
        
          
        
        
        
          TFluid
          
          
            
          
          
          
            
          
          
          100
        
      
      
      
        
      
      /.
      geometry
    
  
  ;





  
    nuavllocalLOX25
    =
    
      
        
          
            
              
                
                  
                    
                      
                        Nu
                        
                        avL
                      
                      
                      
                        
                      
                      /.
                      
                        ϕ
                        
                        
                          
                        
                        ->
                        
                          π
                          4
                        
                      
                    
                    /.
                    
                      μ
                      
                      
                        
                      
                      
                      μlocal
                    
                  
                  /.
                  
                    ρ
                    
                    
                      
                    
                    
                    ρlocal
                  
                
                /.
                LOXcharisterics
              
              /.
              
                L
                
                
                  
                
                
                lTube
              
            
            
            
              
            
            /.
            
              geffective
              
              
                
              
              
              
                
              
              
              
                2.5
                
                
                  
                
                *
                
                  10
                  6
                
              
            
          
          /.
          
            β
            
            
              
            
            
            1
          
        
        
        
          
        
        /.
        
          
        
        
        
          TFluid
          
          
            
          
          
          
            
          
          
          100
        
      
      
      
        
      
      /.
      geometry
    
  
  ;





  
    nuavllocalpropane25
    =
    
      
        
          
            
              
                
                  
                    
                      
                        Nu
                        
                        avL
                      
                      
                      
                        
                      
                      /.
                      
                        ϕ
                        
                        
                          
                        
                        ->
                        
                          π
                          4
                        
                      
                    
                    /.
                    
                      μ
                      
                      
                        
                      
                      
                      μlocal
                    
                  
                  /.
                  
                    ρ
                    
                    
                      
                    
                    
                    ρlocal
                  
                
                /.
                propanecharisterics
              
              /.
              
                L
                
                
                  
                
                
                lTube
              
            
            
            
              
            
            /.
            
              geffective
              
              
                
              
              
              
                
              
              
              
                2.5
                
                
                  
                
                *
                
                  10
                  6
                
              
            
          
          /.
          
            β
            
            
              
            
            
            1
          
        
        
        
          
        
        /.
        
          
        
        
        
          TFluid
          
          
            
          
          
          
            
          
          
          100
        
      
      
      
        
      
      /.
      geometry
    
  
  ;





  
    rallocal
    
    
      
    
    =
    
      
        
          
            
              
                
                  
                    RaL
                    
                    
                      
                    
                    /.
                    
                      μ
                      
                      
                        
                      
                      
                      μlocal
                    
                  
                  /.
                  
                    ρ
                    
                    
                      
                    
                    
                    ρlocal
                  
                
                /.
                LOXcharisterics
              
              /.
              
                L
                
                
                  
                
                
                lTube
              
            
            
            
              
            
            /.
            
              geffective
              
              
                
              
              
              
                
              
              
              
                10
                7
              
            
          
          /.
          
            β
            
            
              
            
            
            1
          
        
        
        
          
        
        /.
        
          
        
        
        
          TFluid
          
          
            
          
          
          
            
          
          
          100
        
      
      
      
        
      
      /.
      geometry
    
  
  ;





  
    radlocal
    
    
      
    
    =
    
      
        
          
            
              
                
                  
                    
                      RaD
                      
                      
                        
                      
                      /.
                      
                        μ
                        
                        
                          
                        
                        
                        μlocal
                      
                    
                    /.
                    
                      ρ
                      
                      
                        
                      
                      
                      ρlocal
                    
                  
                  /.
                  LOXcharisterics
                
                /.
                
                  L
                  
                  
                    
                  
                  
                  lTube
                
              
              
              
                
              
              /.
              
                geffective
                
                
                  
                
                
                
                  
                
                
                
                  10
                  7
                
              
            
            /.
            
              β
              
              
                
              
              
              1
            
          
          
          
            
          
          /.
          
            
          
          
          
            TFluid
            
            
              
            
            
            
              
            
            
            100
          
        
        
        
          
        
        /.
        
          D
          ->
          
            2
            
            
              
            
            
            rTubesOuter
          
        
      
      /.
      geometry
    
  
  ;





  
    
      gzdlocal
      
      
        
      
      =
      
        
          
            
              
                
                  
                    
                      
                        
                          
                            GzD
                            
                            
                              
                            
                            /.
                            
                              μ
                              
                              
                                
                              
                              
                              μlocal
                            
                          
                          /.
                          
                            ρ
                            
                            
                              
                            
                            
                            ρlocal
                          
                        
                        /.
                        LOXcharisterics
                      
                      /.
                      
                        L
                        
                        
                          
                        
                        
                        lTube
                      
                    
                    
                    
                      
                    
                    /.
                    
                      geffective
                      
                      
                        
                      
                      
                      
                        
                      
                      
                      
                        10
                        7
                      
                    
                  
                  /.
                  
                    β
                    
                    
                      
                    
                    
                    1
                  
                
                
                
                  
                
                /.
                
                  
                
                
                
                  TFluid
                  
                  
                    
                  
                  
                  
                    
                  
                  
                  100
                
              
              
              
                
              
              /.
              
                D
                ->
                
                  2
                  
                  
                    
                  
                  
                  rTubesOuter
                
              
            
            
            
              
            
            /.
            
              
            
            
            geometry
          
          
          
            
          
          /.
          
            ρ
            
            
              
            
            
            ρlocal
          
        
        /.
        
          
        
        
        
          V
          
          
            
          
          ->
          flowRateInnerLox
        
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  
    rendlocal
    
    
      
    
    =
    
      
        
          
            
              
                
                  
                    
                      
                        RenD
                        
                        
                          
                        
                        /.
                        
                          μ
                          
                          
                            
                          
                          
                          μlocal
                        
                      
                      /.
                      LOXcharisterics
                    
                    /.
                    
                      L
                      
                      
                        
                      
                      
                      lTube
                    
                  
                  /.
                  
                    
                  
                  
                  
                    geffective
                    
                    
                      
                    
                    
                    
                      
                    
                    
                    
                      10
                      7
                    
                  
                
                /.
                
                  β
                  
                  
                    
                  
                  
                  1
                
              
              
              
                
              
              /.
              
                
              
              
              
                TFluid
                
                
                  
                
                
                
                  
                
                
                100
              
            
            
            
              
            
            /.
            
              D
              ->
              
                2
                
                
                  
                
                
                rTubesOuter
              
            
          
          /.
          
            
          
          
          geometry
        
        
        
          
        
        /.
        
          ρ
          
          
            
          
          
          ρlocal
        
      
      
      
        
      
      /.
      
        
      
      
      
        V
        
        
          
        
        ->
        flowRateInnerLox
      
    
  
  ;





  
    prlocal
    
    
      
    
    =
    
      
        
          
            
              
                
                  
                    
                      
                        Pr
                        
                        
                          
                        
                        /.
                        
                          μ
                          
                          
                            
                          
                          
                          μlocal
                        
                      
                      /.
                      LOXcharisterics
                    
                    /.
                    
                      L
                      
                      
                        
                      
                      
                      lTube
                    
                  
                  /.
                  
                    
                  
                  
                  
                    geffective
                    
                    
                      
                    
                    
                    
                      
                    
                    
                    
                      10
                      7
                    
                  
                
                /.
                
                  β
                  
                  
                    
                  
                  
                  1
                
              
              
              
                
              
              /.
              
                
              
              
              
                TFluid
                
                
                  
                
                
                
                  
                
                
                100
              
            
            
            
              
            
            /.
            
              D
              ->
              
                2
                
                
                  
                
                
                rTubesOuter
              
            
          
          
          
            
          
          /.
          
            
          
          
          geometry
        
        
        
          
        
        /.
        
          ρ
          
          
            
          
          
          ρlocal
        
      
      
      
        
      
      /.
      
        
      
      
      
        V
        
        
          
        
        ->
        flowRateOuterLox
      
    
  
  ;





  
    grllocal
    
    
      
    
    =
    
      
    
    
    
      
        
          
            
              
                
                  
                    
                      
                        
                          GrL
                          /.
                          
                            μ
                            
                            
                              
                            
                            
                            μlocal
                          
                        
                        /.
                        
                          ρ
                          
                          
                            
                          
                          
                          ρlocal
                        
                      
                      /.
                      LOXcharisterics
                    
                    /.
                    
                      L
                      
                      
                        
                      
                      
                      lTube
                    
                  
                  
                  
                    
                  
                  /.
                  
                    geffective
                    
                    
                      
                    
                    
                    
                      
                    
                    
                    
                      10
                      7
                    
                  
                
                /.
                
                  β
                  
                  
                    
                  
                  
                  1
                
              
              
              
                
              
              /.
              
                
              
              
              
                TFluid
                
                
                  
                
                
                
                  
                
                
                100
              
            
            
            
              
            
            /.
            
              D
              ->
              
                2
                
                
                  
                
                
                rTubesOuter
              
            
          
          
          
            
          
          /.
          
            
          
          
          geometry
        
        
        
          
        
        /.
        
          ρ
          
          
            
          
          
          ρlocal
        
      
      /.
      
        
      
      
      
        V
        
        
          
        
        ->
        flowRateInnerLox
      
    
  
  ;





  
    
      grdlocal
      
      
        
      
      =
      
        
      
      
      
        
          
            
              
                
                  
                    
                      
                        
                          
                            GrD
                            /.
                            
                              μ
                              
                              
                                
                              
                              
                              μlocal
                            
                          
                          /.
                          
                            ρ
                            
                            
                              
                            
                            
                            ρlocal
                          
                        
                        /.
                        LOXcharisterics
                      
                      /.
                      
                        L
                        
                        
                          
                        
                        
                        lTube
                      
                    
                    
                    
                      
                    
                    /.
                    
                      geffective
                      
                      
                        
                      
                      
                      
                        
                      
                      
                      
                        10
                        7
                      
                    
                  
                  /.
                  
                    β
                    
                    
                      
                    
                    
                    1
                  
                
                
                
                  
                
                /.
                
                  
                
                
                
                  TFluid
                  
                  
                    
                  
                  
                  
                    
                  
                  
                  100
                
              
              
              
                
              
              /.
              
                D
                ->
                
                  2
                  
                  
                    
                  
                  
                  rTubesOuter
                
              
            
            
            
              
            
            /.
            
              
            
            
            geometry
          
          
          
            
          
          /.
          
            ρ
            
            
              
            
            
            ρlocal
          
        
        /.
        
          
        
        
        
          V
          
          
            
          
          ->
          flowRateOuterLox
        
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  
    localhpermsqLOXouter
    
    
      
    
    =
    
      
    
    
    
      
        
          
            nuavllocalLOX
            
            
              
            
            *
            
              thermalConductivity
              
              
                
              
              /
              D
            
          
          /.
          LOXcharisterics
        
        /.
        
          D
          ->
          
            2
            *
            
              
            
            
            rTubesOuter
          
        
      
      /.
      geometry
    
  
  ;





  
    Print
    
    
      [
      
        hpermsqLOXouter = 
        ,
        localhpermsqLOXouter
      
      ]
    
  
  ;





  
    localhLOXouter
    
    
      
    
    =
    
      
    
    
    
      
        
          localhpermsqLOXouter
          
          
            
          
          *
          2
          
          
            
          
          
          nTubesOuter
          
          
            
          
          
          Pi
          
          
            
          
          
          rTubesOuter
          
          
            
          
          *
          lTube
          
          
            
          
          *
          
            (
            
              TEngineWall
              -
              TFluid
            
            )
          
        
        /.
        
          TFluid
          
          
            
          
          ->
          
            
          
          
          100
        
      
      /.
      
        D
        ->
        
          2
          *
          
            
          
          
          
            rTubesOuter
            /
            geometry
          
        
      
    
  
  ;





  
    
      Print
      
      
        [
        
          hLOXouter = 
          ,
          
            localhLOXouter
            /.
            geometry
          
        
        ]
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  
    localhpermsqLOXinner
    
    
      
    
    =
    
      
    
    
    
      
        
          
            nuavllocalLOX25
            
            
              
            
            *
            
              thermalConductivity
              
              
                
              
              /
              D
            
          
          /.
          LOXcharisterics
        
        /.
        
          D
          ->
          
            2
            *
            
              
            
            
            rTubesInner
          
        
      
      /.
      geometry
    
  
  ;





  
    Print
    
    
      [
      
        hpermsqLOXinner = 
        ,
        localhpermsqLOXinner
      
      ]
    
  
  ;





  
    localhLOXinner
    
    
      
    
    =
    
      
    
    
    
      
        
          localhpermsqLOXinner
          
          
            
          
          *
          2
          
          
            
          
          
          nTubesInner
          
          
            
          
          
          Pi
          
          
            
          
          
          rTubesInner
          
          
            
          
          *
          lTube
          
          
            
          
          *
          
            (
            
              TEngineWall
              -
              TFluid
            
            )
          
        
        /.
        
          TFluid
          
          
            
          
          ->
          
            
          
          
          100
        
      
      /.
      
        D
        ->
        
          2
          *
          
            
          
          
          
            rTubesOuter
            /
            geometry
          
        
      
    
  
  ;





  
    
      Print
      
      
        [
        
          hLOXinner = 
          ,
          
            localhLOXinner
            /.
            geometry
          
        
        ]
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  
    localhpermsqpropaneouter
    
    
      
    
    =
    
      
    
    
    
      
        
          
            nuavllocalpropane
            
            
              
            
            *
            
              thermalConductivity
              
              
                
              
              /
              D
            
          
          /.
          propanecharisterics
        
        /.
        
          D
          ->
          
            2
            *
            
              
            
            
            rTubesOuter
          
        
      
      /.
      geometry
    
  
  ;





  
    Print
    
    
      [
      
        hpermsqpropaneouter = 
        ,
        localhpermsqpropaneouter
      
      ]
    
  
  ;





  
    localhpropaneouter
    
    
      
    
    =
    
      
    
    
    
      
        
          localhpermsqpropaneouter
          
          
            
          
          *
          2
          
          
            
          
          
          nTubesOuter
          
          
            
          
          
          Pi
          
          
            
          
          
          rTubesOuter
          
          
            
          
          *
          lTube
          
          
            
          
          *
          
            (
            
              TEngineWall
              -
              TFluid
            
            )
          
        
        /.
        
          TFluid
          
          
            
          
          ->
          
            
          
          
          100
        
      
      /.
      
        D
        ->
        
          2
          *
          
            
          
          
          
            rTubesOuter
            /
            geometry
          
        
      
    
  
  ;





  
    
      Print
      
      
        [
        
          hpropaneouter = 
          ,
          
            localhpropaneouter
            /.
            geometry
          
        
        ]
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  
    localhpermsqpropaneinner
    
    
      
    
    =
    
      
    
    
    
      
        
          
            nuavllocalpropane25
            
            
              
            
            *
            
              thermalConductivity
              
              
                
              
              /
              D
            
          
          /.
          propanecharisterics
        
        /.
        
          D
          ->
          
            2
            *
            
              
            
            
            rTubesInner
          
        
      
      /.
      geometry
    
  
  ;





  
    Print
    
    
      [
      
        hpermsqpropaneinner = 
        ,
        localhpermsqpropaneinner
      
      ]
    
  
  ;





  
    localhpropaneinner
    
    
      
    
    =
    
      
    
    
    
      
        
          localhpermsqpropaneinner
          
          
            
          
          *
          2
          
          
            
          
          
          nTubesInner
          
          
            
          
          
          Pi
          
          
            
          
          
          rTubesInner
          
          
            
          
          *
          lTube
          
          
            
          
          *
          
            (
            
              TEngineWall
              -
              TFluid
            
            )
          
        
        /.
        
          TFluid
          
          
            
          
          ->
          
            
          
          
          100
        
      
      /.
      
        D
        ->
        
          2
          *
          
            
          
          
          
            rTubesOuter
            /
            geometry
          
        
      
    
  
  ;





  
    Print
    
    
      [
      
        hpropaneinner = 
        ,
        
          localhpropaneinner
          /.
          geometry
        
      
      ]
    
  
  ;





  
    localconvectionQ
    
    
      
    
    =
    
      
    
    
    
      
        localhpropaneinner
        
        
          
        
        +
        localhpropaneouter
        
        
          
        
        +
        localhLOXinner
        +
        localhLOXouter
      
      /.
      geometry
    
  
  ;





  
    
      Print
      [
      
        convectionQ = 
        ,
        localconvectionQ
      
      
      
        
      
      ]
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  
    Print
    
    
      [
      
        
          
            "
            
System`Convert`MathMLDump`ToSymbolicMathML[$Failed]              ] = 
            
            "
          
          
"
StyleBox[Nu
StyleBox[\"avL\",\nFontSize->6]LOX] = "          
        
        ,
        
          
        
        
        nuavllocalLOX
      
      ]
    
  
  ;





  
    
      Print
      
      
        [
        
          
            
              "
              
                Nu
System`Convert`MathMLDump`ToSymbolicMathML[$Failed]                propane = 
              
              "
            
            
"Nu
StyleBox[\"avL\",\nFontSize->6]propane = "            
          
          ,
          
            
          
          
          nuavllocalpropane
        
        ]
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  
  
  
    (*
    
    
      
        
          
            Print
            
            
              [
              
                heat LOX =
                ,
                localhpermsqpropaneinner
              
              ]
            
          
          ;
          
            
          
          
          
            
              
                nuavllocalLOX
                *
                nTubesOuter
                
                
                  
                
                *
                thermalConductivity
              
              /.
              LOXcharisterics
            
            /.
            geometry
          
        
        ]
      
      ;
      
        &IndentingNewLine;
      
      
      
        Print
        
        
          [
          
            heat propane =
            ,
            
              
            
            
            
              
                
                  nuavllocalpropane
                  *
                  nTubesOuter
                  
                  
                    
                  
                  *
                  thermalConductivity
                
                /.
                propanecharisterics
              
              /.
              geometry
            
          
          ]
        
      
      ;
      
        &IndentingNewLine;
      
      
      
        Print
        
        
          [
          
            heat LOX.25 =
            ,
            
              
            
            
            
              
                
                  nuavllocalLOX25
                  *
                  nTubesOuter
                  
                  
                    
                  
                  *
                  thermalConductivity
                
                /.
                LOXcharisterics
              
              /.
              geometry
            
          
          ]
        
      
      ;
      
        &IndentingNewLine;
      
      
      
        Print
        
        
          [
          
            heat propane.25 =
            ,
            
              
            
            
            
              
                
                  nuavllocalpropane25
                  *
                  nTubesOuter
                  
                  
                    
                  
                  *
                  thermalConductivity
                
                /.
                propanecharisterics
              
              /.
              geometry
            
          
          ]
        
      
      ;
    
    
    *)
  





  
    Print
    
    
      [
      
        GrL = 
        ,
        grllocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        GrD = 
        ,
        grdlocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        RaD = 
        ,
        radlocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        for a double check D = 
        ,
        
          
            2
            
            
              
            
            
            rTubesInner
          
          /.
          geometry
        
        ,
         L = 
        ,
        
          
        
        
        
          lTube
          /.
          geometry
        
        ,
        
          
            "
            
               Gz = Ren  Pr 
              
                D
                L
              
               = 
            
            "
          
          
" Gz = Ren  Pr DL = "          
        
        ,
        
          
            
              
                
                  Ren
                  
                  
                    
                  
                  *
                  
                    
                  
                  
                  Pr
                  
                  
                    
                  
                  *
                  2
                  *
                  
                    rTubesInner
                    /
                    lTube
                  
                
                /.
                
                  V
                  
                  
                    
                  
                  ->
                  flowRateInnerLox
                
              
              
              
                
              
              /.
              
                
              
              
              
                D
                ->
                
                  2
                  *
                  
                    
                  
                  
                  rTubesInner
                
              
            
            /.
            LOXcharisterics
          
          /.
          geometry
        
        ,
        
          
        
        
         Gz again =  
        ,
        
          
            renlocal
            *
            prlocal
            *
            2
            
            
              
            
            
            
              rTubesInner
              /
              lTube
            
          
          /.
          geometry
        
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        GzD = 
        ,
        gzdlocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        RenD = 
        ,
        rendlocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        Pr = 
        ,
        prlocal
      
      ]
    
  
  ;





  
    
      Print
      
      
        [
        
          V = 
          ,
          flowRateInnerLox
        
        ]
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    (*
    
    
      Ren
      
      
        
      
      =
      
        
      
      
      
        
          V
          
          
            
          
          
          D
        
        μ
      
    
    
    *)
  





  
    
      Print
      
      
        [
        
          doublecheck Ren = 
          ,
          
            
              
                
                  flowRateInnerLox
                  *
                  2
                  *
                  
                    
                  
                  
                  
                    rTubesInner
                    /
                    μlocal
                  
                
                /.
                geometry
              
              /.
              LOXcharisterics
            
            /.
            geometry
          
        
        ]
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    (*
    
    
      Ra
      
      
        
      
      =
      
        
      
      
      
        Gr
        
        
          
        
        
        Pr
      
    
    
    *)
  





  
    Print
    
    
      [
      
        doublecheck RaD = 
        ,
        
          grdlocal
          *
          prlocal
        
      
      ]
    
  
  ;





  1
  +
  
    
      Max
      
      
        [
        
          0
          ,
          
            1
            -
            
              
                431.52`
                
                
                  
                
                
                μ
                
                
                  
                
                
                
                  Sec
                  
                  
                    [
                    ϕ
                    ]
                  
                
              
              
                geffective
                
                
                  
                
                
                
                  L
                  3
                
                
                
                  
                
                
                
                  (
                  
                    
                      300.`
                      
                      
                    
                    -
                    TFluid
                  
                  )
                
                
                
                  
                
                
                β
                
                
                  
                
                
                
                  ρ
                  2
                
                
                
                  
                
                
                
                  c
                  p
                
              
            
          
        
        ]
      
    
    
    
      
    
    
    
      Max
      
      
        [
        
          0
          ,
          
            1
            -
            
              
                431.52`
                
                
                  
                
                
                μ
                
                
                  
                
                
                
                  Sec
                  
                  
                    [
                    ϕ
                    ]
                  
                
                
                
                  
                
                
                
                  
                    Sin
                    
                    
                      [
                      
                        1.8`
                        
                        
                          
                        
                        
                        ϕ
                      
                      ]
                    
                  
                  1.6`
                
              
              
                geffective
                
                
                  
                
                
                
                  L
                  3
                
                
                
                  
                
                
                
                  (
                  
                    
                      300.`
                      
                      
                    
                    -
                    TFluid
                  
                  )
                
                
                
                  
                
                
                β
                
                
                  
                
                
                
                  ρ
                  2
                
                
                
                  
                
                
                
                  c
                  p
                
              
            
          
        
        ]
      
    
  
  +
  
    Max
    
    
      [
      
        0
        ,
        
          
            -
            1
          
          +
          
            0.08940738673291768`
            
            
              
            
            
            
              
                (
                
                  
                    geffective
                    
                    
                      
                    
                    
                    
                      L
                      3
                    
                    
                    
                      
                    
                    
                    
                      (
                      
                        
                          300.`
                          
                          
                        
                        -
                        TFluid
                      
                      )
                    
                    
                    
                      
                    
                    
                    β
                    
                    
                      
                    
                    
                    
                      ρ
                      2
                    
                    
                    
                      
                    
                    
                    
                      Cos
                      
                      
                        [
                        ϕ
                        ]
                      
                    
                    
                    
                      
                    
                    
                    
                      c
                      p
                    
                  
                  μ
                
                )
              
              
                1
                /
                3
              
            
          
        
      
      ]
    
  





  hpermsqLOXouter = 
  
  
  
  528414.6944727737`





  hLOXouter = 
  
  
  
  676133.1735394327`





  hpermsqLOXinner = 
  
  
  
  332895.1998990098`





  hLOXinner = 
  
  
  
  26622.259268870323`





  hpermsqpropaneouter = 
  
  
  
  185972.2318680521`





  hpropaneouter = 
  
  
  
  237960.8225100865`





  hpermsqpropaneinner = 
  
  
  
  117169.96639224577`





  hpropaneinner = 
  
  
  
  9370.304001876562`





  convectionQ = 
  
  
  
  950086.5593202661`





  \!\(\* StyleBox[\(Nu\* StyleBox[\"avL\",\nFontSize->6]LOX\)]\) = 
  
  
  
  13210.367361819344`





  Nu\!\(\* StyleBox[\"avL\",\nFontSize->6]\)propane = 
  
  
  
  4649.305796701303`





  GrL = 
  
  
  
  2.6263181266296422`*^17





  GrD = 
  
  
  
  5.942679542057504`*^15





  RaD = 
  
  
  
  4.2999617090696494`*^14





  for a double check D = 
  
  
  
  0.006`
  
  
  
   L = 
  
  
  
  0.021213203435596427`
  
  
  
   Gz = Ren  Pr \!\(D\/L\) = 
  
  
  
  17.475182282601985`
  
  
  
   Gz again =  
  
  
  
  17.47518228260198`





  GzD = 
  
  
  
  17.475182282601978`





  RenD = 
  
  
  
  853.8752872733797`





  Pr = 
  
  
  
  0.07235728729166667`





  V = 
  
  
  
  47.955059258751795`





  doublecheck Ren = 
  
  
  
  853.8752872733796`





  doublecheck RaD = 
  
  
  
  4.2999617090696494`*^14





  



Cooling Hot side

For the amount of heat transferred from the combustion chamber we will start with
the approximation of constant temperature of the metal wall. I will use Q = π∫DqⅆL
and h g = D - .2 0.026 ( c p μ 0.2 Pr 0.6 ) ( ρμ ) 0.8 ( ρ am ρ ' ) ( μ am μ 0 )
equations (8-20) & (8-23) from Sutton 7th ed. My intuition fails me here without a good reference.
It is quite possible that there is a better formulation for this. Note also that the various fluid property parameters
may be off quite a bit, they are in red to indicate this, though the fact that they are raised to fractional power ameliorates this.




  
    
      TEngineWall
      
      
        
      
      =
      
        
      
      
      300.
    
    ;
  
  
  
    
  
  
  
    (*
    
    
      
    
    
    Kelvin
    
    
      
    
    
    *)
  





  
    
      
        thicknessToCoolantEngine
        
        
          
        
        =
        
          
        
        
        .0025
      
      ;
    
    
    
      
    
    
    
      (*
      
      
        
      
      
      
        .1
        
        
          
        
        
        inch
      
      
      
        
      
      
      *)
    
  
  
  
    

  
  
  
    (*
    
    
      
    
    
    
      
        these
        
        
          
        
        
        are
        
        
          
        
        
        approximations
      
      ,
      
        
      
      
      
        
          
            
              
                rather
                
                
                  
                
                
                thery
                
                
                  
                
                
                are
                
                
                  
                
                
                precice
                
                
                  
                
                
                data
                
                
                  
                
                
                used
                
                
                  
                
                
                in
                
                
                  
                
                
                an
                
                
                  
                
                
                approximate
                
                
                  
                
                
                way
              
              
              
                &IndentingNewLine;
              
              
              
                
                  in
                  
                  
                    
                  
                  
                  particular
                  
                  
                    
                  
                  
                  I
                  
                  
                    
                  
                  
                  
                    haven
                    '
                  
                  
                  t
                  
                  
                    
                  
                  
                  taken
                  
                  
                    
                  
                  
                  into
                  
                  
                    
                  
                  
                  account
                  
                  
                    
                  
                  
                  the
                  
                  
                    
                  
                  
                  velocitys
                  
                  
                    
                  
                  
                  both
                  
                  
                    
                  
                  
                  through
                  
                  
                    
                  
                  
                  acceleration
                  
                  
                    
                  
                  
                  near
                  
                  
                    
                  
                  
                  the
                  
                  
                    
                  
                  
                  nozzles
                  
                  
                    
                  
                  
                  and
                  
                  
                    
                  
                  
                  the
                  
                  
                    
                  
                  
                  velocit
                  
                  
                    
                  
                  
                  of
                  
                  
                    
                  
                  
                  rotation
                  
                  
                    
                  
                  
                  in
                  
                  
                    
                  
                  
                  determining
                  
                  
                    
                  
                  
                  the
                  
                  
                    
                  
                  
                  static
                  
                  
                    
                  
                  
                  temperature
                  
                  
                    
                  
                  
                  zzz
                  
                  
                    
                  
                  
                  we
                  
                  
                    
                  
                  
                  need
                  
                  
                    
                  
                  
                  to
                  
                  
                    
                  
                  
                  asses
                  
                  
                    
                  
                  
                  the
                  
                  
                    
                  
                  
                  affect
                  
                  
                    
                  
                  
                  of
                  
                  
                    
                  
                  
                  this
                  
                  
                    
                  
                  
                  and
                  
                  
                    
                  
                  
                  set
                  
                  
                    
                  
                  
                  up
                  
                  
                    
                  
                  
                  the
                  
                  
                    
                  
                  
                  falues
                  
                  
                    
                  
                  
                  as
                  
                  
                    
                  
                  
                  functions
                  
                  
                    
                  
                  
                  of
                  
                  
                    
                  
                  
                  T
                
                
                
                  
                
                &
              
            
            
            
              
            
            
            P
          
          
          
            
          
          &
        
        
        
          
        
        
        v
      
    
    
    
      
    
    
    *)
  





  
    
      ρlocal
      =
      46.827
    
    ;
  
  
  
    

  
  
  
    (*
    
    
      
        Pr
        
        
          
        
        =
        
          
        
        
        .558
      
      ;
    
    
    *)
  





  
    
      c
      p
    
    
    
      
    
    =
    
      2.37
      
      
        
      
      
      
        10
        3
      
    
  
  
  
    
  
  ;





  
    μlocal
    =
    
      1.273
      
      
        
      
      
      
        10
        
          -
          4
        
      
    
  
  ;





  
    
      ρ
      '
    
    =
    575
  
  ;





  
    
      
        ρ
        am
      
      =
      83
    
    ;
  
  
  
    
  





  
    
      μ
      am
    
    =
    
      6.609
      
      
        
      
      
      
        10
        
          -
          5
        
      
    
  
  ;





  
    
      μ
      0
    
    =
    
      1.415
      
      
        
      
      
      
        10
        
          -
          5
        
      
    
  
  ;





  
    thermalConductivity
    
    
      
    
    =
    
      
    
    
    .24
  
  ;





  
    Pr
    
    
      
    
    =
    
      
    
    
    
      
        
          c
          p
        
        
        μlocal
      
      thermalConductivity
    
  
  
  
    
  
  ;





  
    
  
  
  
    
      rATr
      
      
        
      
      =
      
        
      
      
      
        combustionChamberHeight
        /
        2
      
    
    ;
  
  
  
    
  





  
    Q
    
    
      
    
    =
    
      2
      
      π
      
      
        2
      
      
      
        
          
          rBot
          rTop
        
        
        
          
            (
            
              
                
                  (
                  
                    2
                    *
                    rATr
                  
                  )
                
                
                  -
                  .2
                
              
              
              0.026
              
              r
              
              
                (
                
                  TChamber
                  
                  
                    
                  
                  -
                  TEngineWall
                
                )
              
              *
              
                (
                
                  
                    
                      c
                      p
                    
                    
                    
                      μlocal
                      0.2
                    
                  
                  
                    Pr
                    0.6
                  
                
                )
              
              *
              
                (
                
                  
                    (
                    
                      
                    
                    
                    
                      ρlocal
                      
                      
                        
                      
                      
                      rotationalVelocityNominal
                      
                      
                        
                      
                      
                      
                        
                          (
                          
                            rTop
                            
                            
                              
                            
                            -
                            r
                          
                          )
                        
                        /
                        rTop
                      
                    
                    )
                  
                  ^
                  0.8
                
                )
              
              *
              
                (
                
                  
                    ρ
                    am
                  
                  
                    ρ
                    '
                  
                
                )
              
              *
              
                (
                
                  
                    μ
                    am
                  
                  
                    μ
                    0
                  
                
                )
              
            
            )
          
          
          
            
            r
          
        
      
    
  
  
  
    
  
  ;





  
    
  
  
  
    
      localq
      
      
        
      
      =
      
        
      
      
      
        Q
        
        
          
        
        /.
        
          Join
          
          
            [
            
              geometry
              ,
              fuel
              ,
              oxidizer
              ,
              velocity
            
            ]
          
        
      
    
    ;
  
  
  
    

  





  
    
  
  
  
    
      
        Print
        
        
          [
          
            Q 
            ,
            localq
          
          ]
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            aluminum
            ,
            velocity
          
          ]
        
      
    
    ;
  
  
  
    

  
  
  
    
  





  
    Print
    
    
      [
      
        nominalFuelFlowMass = 
        ,
        
          nominalFuelFlowMass
          /.
          
            Join
            
            
              [
              
                geometry
                ,
                fuel
                ,
                oxidizer
                ,
                velocity
              
              ]
            
          
        
      
      ]
    
  
  
  
    

  
  
  
    

  
  
  
    
  
  
  
    (*
    
    
      
    
    
    
      
        aprox
        
        
          
        
        
        for
        
        
          
        
        
        now
      
      ,
      
        
      
      
      
        this
        
        
          
        
        
        calculation
        
        
          
        
        
        makes
        
        
          
        
        
        a
        
        
          
        
        
        lot
        
        
          
        
        
        more
        
        
          
        
        
        sense
        
        
          
        
        
        with
        
        
          
        
        
        numbers
        
        
          
        
        
        here
      
    
    
    
      
    
    
    *)
  





  
    qPerKey
    
    
      
    
    =
    
      
    
    
    
      Q
      /
      
        (
        nominalFuelFlowMass
        )
      
    
  
  
  
    
  
  
  
    (*
    
    
      
    
    
    
      watts
      
      
        
      
      
      per
      
      
        
      
      
      kg
    
    
    
      
    
    
    *)
  
  
  
    
  
  ;





  
    localqPerKeyhot
    
    
      
    
    =
    
      
    
    
    
      qPerKey
      
      
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
          
          ]
        
      
    
  
  ;





  Print
  
  
    [
    
      Hot Q per kilogram of fuel = 
      ,
      localqPerKeyhot
    
    ]
  





  Print
  
  
    [
    
      cf kcal 
      ,
      cf
      
      
        
      
      ,
       
      ,
      
        cf
        
        
          
        
        *
        4186.8
      
      ,
       Watts
    
    ]
  





  
    
      Print
      
      
        [
        
          hot aprox degrees fuel temperature rise 
          ,
          
            localqPerKeyhot
            /
            
              (
              
                cf
                
                
                  
                
                *
                4186.8
              
              )
            
          
        
        ]
      
    
    
    
      

    
    
    
      (*
      
      
        
      
      
      
        seems
        
        
          
        
        
        to
        
        
          
        
        
        be
        
        
          
        
        
        about
        
        
          
        
        
        5.000
        
        
          
        
        
        or
        
        
          
        
        
        about
        
        
          
        
        
        2.500
        
        
          
        
        
        C
        
        
          
        
        
        for
        
        
          
        
        
        propane
        
        
          
        
        
        5.000
        
        
          
        
        
        C
        
        
          
        
        
        for
        
        
          
        
        
        oxygen
      
      
      *)
    
  
  
  
    

  
  
  
    

  
  
  
    

  
  
  
    

  




Null




  Q 
  
  
  
  226822.0533069916`





  nominalFuelFlowMass = 
  
  
  
  2.5703939893007397`





  Hot Q per kilogram of fuel = 
  
  
  
  88244.08018814937`





  cf kcal 
  
  
  
  2.`
  
  
  
   
  
  
  
  8373.6`
  
  
  
   Watts





  hot aprox degrees fuel temperature rise 
  
  
  
  10.538368227303593`


Combined Hot & cold thermal balance and temperatures distribution




  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  



Print [ badness ratio = , - localqPerKeyhot / localqPerKeycold ] ; Print [ badness ratio = , localqPerKeyhot / localconvectionQ ] ;
Print["goodness ratio = ",localconvectionQ/localqPerKeyhot ];




  badness ratio = 
  
  
  
  182.41583839231004`





  badness ratio = 
  
  
  
  0.09288004268925042`





  goodness ratio = 
  
  
  
  10.766575585518504`



Propulsion

Control

Startup

Legend:

text color black -- normal or certain
red -- incomplete or a problem
blue -- probably ok assumptions or design variables
magenta -- not completely certain, but not totally bogus
green -- assumptions or design variables too hard to read
cyan too hard to read
yellow -- unreadable



results



results




  
    &IndentingNewLine;
  
  
  
    Show
    
    
      [
      
        g1
        ,
        g2
        ,
        
          AspectRatio
          ->
          
            
          
          
          Automatic
        
      
      ]
    
  


[Graphics:Images/index_gr_2.gif]




  
  
  Graphics
  
  





  





  
    ω
    
    
      
    
    =.
  
  ;





  
    radialelongation
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    modulusElasticity
    
    
      
    
    =.
  
  ;





  
    μ
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    ρ
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    p
    =
    
      
    
    .
  
  ;





  
    ω
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r1
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r2
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    thicknessOfChamberWall
    
    
      
    
    =.
  
  ;





  
    pinterference
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    
      chFROMthrust
      =
      
        Chop
        
        
          [
          
            
              Solve
              
              
                [
                
                  
                    THRUST
                    
                    nominalThrust
                  
                  ,
                  combustionChamberHeight
                
                ]
              
            
            ,
            
              10
              ^
              
                -
                8
              
            
          
          ]
        
      
    
    ;
  
  
  
    

  
  
  
    (*
    
    
      
        Print
        
        
          [
          
            chFROMthrust
            ,
            chFROMthrust
          
          ]
        
      
      ;
    
    
    *)
  
  
  
    
  





  
    ω
    =.
  
  ;





  
    radialelongation
    =.
  
  ;





  
    modulusElasticity
    =.
  
  ;





  
    μ
    =.
  
  ;





  
    ρ
    =.
  
  ;





  
    r
    =.
  
  ;





  
    p
    =.
  
  ;





  
    ω
    =.
  
  ;





  
    r1
    =.
  
  ;





  
    r2
    =.
  
  ;





  
    pinterference
    =.
  
  ;





  
    
      metal
      
      
        
      
      =
      
        
      
      
      superalloy
    
    ;
  
  
  
    (*
    
    
      
    
    
    
      {
      
        aluminum
        ,
        superalloy
        ,
        copper
        ,
        titanium
        ,
        tungsten
        ,
        graphite
        ,
        brass
        ,
        silver
      
      }
    
    
    *)
  





  
    omega
    =
    
      rotationalVelocityNominal
      
      
        
      
      
      rInjector
    
  
  ;





  
    geo
    
    
      
    
    =
    
      {
      
        
      
      
      
        
          rTubesInner
          
          .001
        
        ,
        
          rTubesOuter
          
          .001
        
        ,
        
          lStar
          
          .275
        
      
      }
    
  
  ;





  
    nnozvect
    
    
      
    
    =
    
      
    
    
    
      {
      
        2
        ,
        3
        ,
        5
        ,
        7
        ,
        11
        ,
        13
        ,
        17
        ,
        19
        ,
        23
        ,
        29
      
      }
    
  
  ;





  
    
      groosvec
      
      
        
      
      =
      
        {
        
          
        
        
        
          
            {
            
              
                metalv
                
                
                  
                
                
                aluminum
              
              ,
              
                rB1v
                
                
                  
                
                ->
                
                  
                
                
                
                  {
                  
                    .0025
                    ,
                    .005
                    ,
                    .01
                    ,
                    .015
                  
                  }
                
              
              ,
              
                thrustvectv
                
                
                  
                
                
                
                  {
                  
                    400
                    ,
                    500
                    ,
                    1000
                  
                  }
                
              
              ,
              
                tcwvv
                
                
                  
                
                ->
                
                  
                
                
                
                  {
                  
                    .005
                    ,
                    .006
                    ,
                    .0065
                    ,
                    .007
                    ,
                    .0075
                    ,
                    .008
                    ,
                    .0085
                    ,
                    .009
                    ,
                    .01
                  
                  }
                
              
            
            }
          
          ,
          
            {
            
              
                metalv
                
                
                  
                
                
                superalloy
              
              ,
              
                rB1v
                
                
                  
                
                ->
                
                  
                
                
                
                  {
                  
                    .0025
                    ,
                    .005
                    ,
                    .01
                    ,
                    .015
                  
                  }
                
              
              ,
              
                thrustvectv
                
                
                  
                
                ->
                
                  {
                  
                    100
                    ,
                    1000
                    ,
                    10000
                    ,
                    50000
                    ,
                    100000
                    ,
                    500000
                  
                  }
                
              
              ,
              
                tcwvv
                
                
                  
                
                ->
                
                  
                
                
                
                  {
                  
                    .001
                    ,
                    .005
                    ,
                    .0075
                    ,
                    .01
                    ,
                    .025
                    ,
                    .03
                    ,
                    .04
                    ,
                    .045
                    ,
                    .05
                    ,
                    .055
                    ,
                    .06
                    ,
                    
                      
                    
                    
                    .075
                    ,
                    .1
                  
                  }
                
              
            
            }
          
        
        }
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    (*
    
    
      
        rB1
        
        
          
        
        =
        
          
        
        
        
          {
          
            .0025
            ,
            .005
            ,
            .01
            ,
            .015
            ,
            .02
            ,
            .025
            ,
            .03
            ,
            .04
            ,
            .05
          
          }
        
      
      ;
    
    
    *)
  
  
  
    &IndentingNewLine;
  





  
    lgroosvec
    
    
      
    
    =
    
      
    
    
    
      Length
      
      
        [
        groosvec
        ]
      
    
  
  ;





  For
  
  
    [
    
      
        groosvi
        
        
          
        
        =
        
          
        
        
        1
      
      ,
      
        groosvi
        <
        
          lgroosvec
          +
          1
        
      
      ,
      
        ++
        groosvi
      
      ,
      
        (
        
          &IndentingNewLine;
        
        
        
          (*
          
          
            
              Print
              
              
                
              
              [
              
                groosvi = 
                ,
                groosvi
                ,
                 
                ,
                
                  groosvec
                  
                  
                    [
                    
                      [
                      groosvi
                      ]
                    
                    ]
                  
                
              
              ]
            
            ;
          
          
          *)
        
        
        
          

        
        
        
          (*
          
          
            
              rB1
              
              
                
              
              =
              
                
              
              
              
                {
                
                  .0025
                  ,
                  .005
                  ,
                  .01
                  ,
                  .015
                  ,
                  .02
                  ,
                  .025
                  ,
                  .03
                  ,
                  .04
                  ,
                  .05
                  ,
                  .075
                
                }
              
            
            ;
          
          
          *)
        
        
        
          &IndentingNewLine;
        
        
        
          
            rB1
            
            
              
            
            =
            
              
            
            
            
              rB1v
              /.
              
                groosvec
                
                
                  [
                  
                    [
                    groosvi
                    ]
                  
                  ]
                
              
            
          
          ;
          
            &IndentingNewLine;
          
          
          
            len
            
            
              
            
            =
            
              
            
            
            
              Length
              
              
                [
                rB1
                ]
              
            
          
          ;
          
            &IndentingNewLine;
          
          
          
            (*
            
            
              
                thrustvect
                
                
                  
                
                =
                
                  {
                  
                    100
                    ,
                    1000
                    ,
                    10000
                    ,
                    50000
                    ,
                    100000
                    ,
                    500000
                  
                  }
                
              
              ;
            
            
            *)
          
          
          
            

          
          
          
            thrustvect
            
            
              
            
            =
            
              
            
            
            
              thrustvectv
              
              
                
              
              /.
              
                groosvec
                
                
                  [
                  
                    [
                    groosvi
                    ]
                  
                  ]
                
              
            
          
          ;
          
            &IndentingNewLine;
          
          
          
            ltv
            
            
              
            
            =
            
              
            
            
            
              Length
              
              
                [
                thrustvect
                ]
              
            
          
          ;
          
            &IndentingNewLine;
          
          
          
            (*
            
            
              
                tcwv
                
                
                  
                
                =
                
                  
                
                
                
                  {
                  
                    .001
                    ,
                    .005
                    ,
                    .0075
                    ,
                    .01
                    ,
                    .025
                    ,
                    .05
                    ,
                    
                      
                    
                    
                    .075
                    ,
                    .01
                  
                  }
                
              
              ;
            
            
            *)
          
          
          
            &IndentingNewLine;
          
          
          
            tcwv
            
            
              
            
            =
            
              
            
            
            
              tcwvv
              /.
              
                groosvec
                
                
                  [
                  
                    [
                    groosvi
                    ]
                  
                  ]
                
              
            
          
          ;
          
            &IndentingNewLine;
          
          
          
            ltcwv
            
            
              
            
            =
            
              
            
            
            
              Length
              
              
                [
                tcwv
                ]
              
            
          
          ;
          
            &IndentingNewLine;
          
          
          
            metal
            
            
              
            
            =
            
              
            
            
            
              metalv
              /.
              
                groosvec
                
                
                  [
                  
                    [
                    groosvi
                    ]
                  
                  ]
                
              
            
          
          ;
          
            &IndentingNewLine;
          
          
          
            (*
            
            
              
                Print
                
                
                  [
                  
                    len = 
                    ,
                    len
                    ,
                     ltv = 
                    ,
                    ltv
                    ,
                     ltcwv = 
                    ,
                    ltcwv
                  
                  ]
                
              
              ;
            
            
            *)
          
          
          
            &IndentingNewLine;
          
          
          
            (*
            
            
              
                Print
                
                
                  [
                  
                    metal = 
                    ,
                    metal
                    ,
                    tcwv = 
                    ,
                    tcwv
                    ,
                     rB1 = 
                    ,
                    rB1
                  
                  ]
                
              
              ;
            
            
            *)
          
          
          
            &IndentingNewLine;
          
          
          
            For
            
            
              [
              
                
                  j
                  =
                  1
                
                ,
                
                  j
                  <
                  
                    ltv
                    +
                    1
                  
                
                ,
                
                  ++
                  j
                
                ,
                
                  (
                  
                    &IndentingNewLine;
                  
                  
                  
                    &IndentingNewLine;
                  
                  
                  
                    
                      th
                      
                      
                        
                      
                      =
                      
                        
                      
                      
                      
                        thrustvect
                        
                        
                          [
                          
                            [
                            j
                            ]
                          
                          ]
                        
                      
                    
                    ;
                    
                      &IndentingNewLine;
                    
                    
                    
                      almaxtstress
                      
                      
                        
                      
                      =
                      
                        {
                        }
                      
                    
                    ;
                    
                      &IndentingNewLine;
                    
                    
                    
                      
                        For
                        
                        
                          [
                          
                            
                              i
                              =
                              1
                            
                            ,
                            
                              i
                              <
                              
                                len
                                +
                                1
                              
                            
                            ,
                            
                              ++
                              i
                            
                            ,
                            
                              (
                              
                                &IndentingNewLine;
                              
                              
                              
                                (*
                                
                                
                                  
                                    Print
                                    
                                    
                                      [
                                      
                                        i = 
                                        ,
                                        i
                                      
                                      ]
                                    
                                  
                                  ;
                                
                                
                                *)
                              
                              
                              
                                &IndentingNewLine;
                              
                              
                              
                                For
                                
                                
                                  [
                                  
                                    
                                      k
                                      =
                                      
                                        
                                      
                                      
                                      0
                                    
                                    ,
                                    
                                      k
                                      
                                      
                                        
                                      
                                      <
                                      ltcwv
                                    
                                    
                                    
                                      
                                    
                                    ,
                                    
                                      
                                        ++
                                        k
                                      
                                      
                                      
                                        (
                                        
                                          &IndentingNewLine;
                                        
                                        
                                        
                                          
                                            tc
                                            
                                            
                                              
                                            
                                            =
                                            
                                              
                                            
                                            
                                            
                                              tcwv
                                              
                                              
                                                [
                                                
                                                  [
                                                  k
                                                  ]
                                                
                                                ]
                                              
                                            
                                          
                                          ;
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            (*
                                            
                                            
                                              
                                                Print
                                                
                                                
                                                  
                                                
                                                [
                                                
                                                  groosvi = 
                                                  ,
                                                  groosvi
                                                  ,
                                                   i j k = 
                                                  ,
                                                  i
                                                  ,
                                                   
                                                  ,
                                                  j
                                                  ,
                                                   
                                                  ,
                                                  k
                                                
                                                ]
                                              
                                              ;
                                            
                                            
                                            *)
                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            rb
                                            
                                            
                                              
                                            
                                            =
                                            
                                              
                                            
                                            
                                            
                                              rB1
                                              
                                              
                                                [
                                                
                                                  [
                                                  i
                                                  ]
                                                
                                                ]
                                              
                                            
                                          
                                          ;
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            (*
                                            
                                            
                                              
                                                Print
                                                
                                                
                                                  [
                                                  
                                                    rb = 
                                                    ,
                                                    rb
                                                  
                                                  ]
                                                
                                              
                                              ;
                                            
                                            
                                            *)
                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            stuff
                                            
                                            
                                              
                                            
                                            =
                                            
                                            
                                            
                                              {
                                              
                                                
                                                  r1
                                                  
                                                  rInner
                                                
                                                ,
                                                
                                                  p
                                                  
                                                  chamberPressure
                                                
                                                ,
                                                
                                                  μ
                                                  
                                                  .3
                                                
                                                ,
                                                
                                                  ρ
                                                  
                                                  density
                                                
                                                ,
                                                
                                                  radialelongation
                                                  
                                                  linterference
                                                
                                                ,
                                                
                                                  rBot
                                                  
                                                  rb
                                                
                                                ,
                                                
                                                  r2
                                                  
                                                  rOuter
                                                
                                                ,
                                                
                                                  wallthickness
                                                  
                                                  thicknessOfChamberWall
                                                
                                                ,
                                                
                                                  ω
                                                  
                                                  
                                                    rotationalVelocityNominal
                                                    rInjector
                                                  
                                                
                                              
                                              }
                                            
                                          
                                          
                                          
                                          ;
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            ch
                                            =
                                            
                                              Chop
                                              
                                              
                                                [
                                                
                                                  
                                                    
                                                      
                                                        
                                                          
                                                            
                                                              
                                                                chFROMthrust
                                                                
                                                                
                                                                  [
                                                                  
                                                                    [
                                                                    3
                                                                    ]
                                                                  
                                                                  ]
                                                                
                                                              
                                                              
                                                              
                                                                [
                                                                
                                                                  [
                                                                  1
                                                                  ]
                                                                
                                                                ]
                                                              
                                                            
                                                            /.
                                                            
                                                              {
                                                              
                                                                
                                                                  r1
                                                                  
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  rInner
                                                                
                                                                ,
                                                                
                                                                  p
                                                                  
                                                                  chamberPressure
                                                                
                                                                ,
                                                                
                                                                  μ
                                                                  
                                                                  .3
                                                                
                                                                ,
                                                                
                                                                  ρ
                                                                  
                                                                  density
                                                                
                                                                ,
                                                                
                                                                  r
                                                                  
                                                                  
                                                                    rInner
                                                                    
                                                                    
                                                                      
                                                                    
                                                                    +
                                                                    
                                                                      
                                                                    
                                                                    
                                                                    linterference
                                                                  
                                                                
                                                                ,
                                                                
                                                                  radialelongation
                                                                  
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  linterference
                                                                
                                                                ,
                                                                
                                                                  r2
                                                                  
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  rOuter
                                                                
                                                                
                                                                
                                                                  
                                                                
                                                                ,
                                                                
                                                                  wallthickness
                                                                  
                                                                  
                                                                    
                                                                  
                                                                  ->
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  thicknessOfChamberWall
                                                                
                                                                ,
                                                                
                                                                  
                                                                
                                                                
                                                                
                                                                  ω
                                                                  ->
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  
                                                                    rotationalVelocityNominal
                                                                    /
                                                                    rInjector
                                                                  
                                                                
                                                              
                                                              
                                                              
                                                                
                                                              
                                                              }
                                                            
                                                          
                                                          /.
                                                          geo
                                                        
                                                        /.
                                                        
                                                          Join
                                                          
                                                          
                                                            [
                                                            
                                                              fuel
                                                              ,
                                                              oxidizer
                                                              ,
                                                              velocity
                                                            
                                                            ]
                                                          
                                                        
                                                      
                                                      /.
                                                      
                                                        THRUST
                                                        
                                                        
                                                          th
                                                          *
                                                          
                                                            32
                                                            /
                                                            2.2
                                                          
                                                        
                                                      
                                                    
                                                    
                                                    
                                                      
                                                    
                                                    /.
                                                    
                                                      rBot
                                                      
                                                      
                                                        
                                                      
                                                      ->
                                                      rb
                                                    
                                                  
                                                  ,
                                                  
                                                    10
                                                    ^
                                                    
                                                      -
                                                      8
                                                    
                                                  
                                                
                                                ]
                                              
                                            
                                          
                                          ;
                                          
                                            

                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            (*
                                            
                                            
                                              
                                                Print
                                                
                                                
                                                  [
                                                  
                                                    ch =
                                                    ,
                                                    ch
                                                  
                                                  ]
                                                
                                              
                                              ;
                                            
                                            
                                            *)
                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            maxrvalue1
                                            
                                            
                                              
                                            
                                            =
                                            
                                              Chop
                                              [
                                              
                                                
                                              
                                              
                                              
                                                
                                                  
                                                    
                                                      
                                                        
                                                          maxr
                                                          
                                                          
                                                            
                                                          
                                                          /.
                                                          
                                                          
                                                          stuff
                                                        
                                                        /.
                                                        
                                                          Join
                                                          [
                                                          
                                                          
                                                          
                                                            fuel
                                                            ,
                                                            oxidizer
                                                            ,
                                                            metal
                                                            ,
                                                            velocity
                                                          
                                                          ]
                                                        
                                                      
                                                      /.
                                                      
                                                      
                                                      
                                                        thicknessOfChamberWall
                                                        
                                                        
                                                          
                                                        
                                                        
                                                        
                                                          
                                                        
                                                        
                                                        tc
                                                      
                                                    
                                                    /.
                                                    
                                                      THRUST
                                                      
                                                      
                                                        th
                                                        *
                                                        
                                                          32
                                                          /
                                                          2.2
                                                        
                                                      
                                                    
                                                  
                                                  /.
                                                  ch
                                                
                                                /.
                                                
                                                  rBot
                                                  
                                                  rb
                                                
                                              
                                              ]
                                            
                                          
                                          ;
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            (*
                                            
                                            
                                              
                                                Print
                                                [
                                                
                                                  maxrvalue1 = 
                                                  ,
                                                  maxrvalue1
                                                
                                                
                                                
                                                  
                                                
                                                ]
                                              
                                              ;
                                            
                                            
                                            *)
                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            enginediameter
                                            =
                                            
                                              2
                                              
                                              
                                                
                                              
                                              
                                              
                                                (
                                                
                                                  rBot
                                                  +
                                                  thicknessOfChamberWall
                                                  +
                                                  combustionChamberHeight
                                                
                                                )
                                              
                                            
                                          
                                          ;
                                          
                                            

                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            

                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            an
                                            
                                            
                                              
                                            
                                            =
                                            
                                              
                                            
                                            
                                            
                                              
                                                aNozzles
                                                /.
                                                
                                                  rBot
                                                  
                                                  
                                                    
                                                  
                                                  ->
                                                  rb
                                                
                                              
                                              /.
                                              ch
                                            
                                          
                                          
                                          
                                            
                                          
                                          ;
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            maxnoz
                                            
                                            
                                              
                                            
                                            =
                                            
                                              
                                            
                                            
                                            0
                                          
                                          ;
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            minnoz
                                            
                                            
                                              
                                            
                                            =
                                            
                                              
                                            
                                            
                                            0
                                          
                                          ;
                                          
                                            &IndentingNewLine;
                                          
                                          
                                          
                                            
                                              For
                                              
                                              
                                                [
                                                
                                                  
                                                    in
                                                    
                                                    
                                                      
                                                    
                                                    =
                                                    1
                                                  
                                                  ,
                                                  
                                                    in
                                                    
                                                    
                                                      
                                                    
                                                    <
                                                    
                                                      
                                                        Length
                                                        
                                                        
                                                          [
                                                          nnozvect
                                                          ]
                                                        
                                                      
                                                      +
                                                      1
                                                    
                                                  
                                                  ,
                                                  
                                                    ++
                                                    in
                                                  
                                                  ,
                                                  
                                                    (
                                                    
                                                      &IndentingNewLine;
                                                    
                                                    
                                                    
                                                      
                                                        franoz
                                                        =
                                                        
                                                          
                                                        
                                                        
                                                        
                                                          
                                                            
                                                              nnozvect
                                                              
                                                              
                                                                [
                                                                
                                                                  [
                                                                  in
                                                                  ]
                                                                
                                                                ]
                                                              
                                                            
                                                            
                                                            
                                                              
                                                                
                                                                  an
                                                                  /
                                                                  
                                                                    (
                                                                    
                                                                      
                                                                    
                                                                    
                                                                    
                                                                      
                                                                        nnozvect
                                                                        
                                                                        
                                                                          [
                                                                          
                                                                            [
                                                                            in
                                                                            ]
                                                                          
                                                                          ]
                                                                        
                                                                      
                                                                      *
                                                                      Pi
                                                                    
                                                                    )
                                                                  
                                                                
                                                              
                                                              /
                                                              
                                                                (
                                                                
                                                                  
                                                                
                                                                
                                                                
                                                                  
                                                                    (
                                                                    
                                                                      
                                                                        combustionChamberHeight
                                                                        /
                                                                        2
                                                                      
                                                                      +
                                                                      
                                                                        2
                                                                        
                                                                        rb
                                                                      
                                                                    
                                                                    )
                                                                  
                                                                  *
                                                                  Pi
                                                                
                                                                )
                                                              
                                                            
                                                          
                                                          /.
                                                          ch
                                                        
                                                      
                                                      ;
                                                      
                                                        &IndentingNewLine;
                                                      
                                                      
                                                      
                                                        fitnoz
                                                        
                                                        
                                                          
                                                        
                                                        =
                                                        
                                                          
                                                        
                                                        
                                                        
                                                          
                                                            
                                                              combustionChamberHeight
                                                              /
                                                              4
                                                            
                                                            -
                                                            
                                                              
                                                                an
                                                                /
                                                                
                                                                  (
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  
                                                                    
                                                                      nnozvect
                                                                      
                                                                      
                                                                        [
                                                                        
                                                                          [
                                                                          in
                                                                          ]
                                                                        
                                                                        ]
                                                                      
                                                                    
                                                                    *
                                                                    Pi
                                                                  
                                                                  )
                                                                
                                                              
                                                            
                                                          
                                                          /.
                                                          ch
                                                        
                                                      
                                                      ;
                                                      
                                                        &IndentingNewLine;
                                                      
                                                      
                                                      
                                                        If
                                                        [
                                                        
                                                          
                                                            (
                                                            
                                                              
                                                                
                                                                  
                                                                    
                                                                      an
                                                                      /
                                                                      
                                                                        (
                                                                        
                                                                          
                                                                        
                                                                        
                                                                        
                                                                          
                                                                            nnozvect
                                                                            
                                                                            
                                                                              [
                                                                              
                                                                                [
                                                                                in
                                                                                ]
                                                                              
                                                                              ]
                                                                            
                                                                          
                                                                          *
                                                                          Pi
                                                                        
                                                                        )
                                                                      
                                                                    
                                                                  
                                                                  <
                                                                  
                                                                    combustionChamberHeight
                                                                    /
                                                                    4
                                                                  
                                                                
                                                                &&
                                                                
                                                                  
                                                                    
                                                                      nnozvect
                                                                      
                                                                      
                                                                        [
                                                                        
                                                                          [
                                                                          in
                                                                          ]
                                                                        
                                                                        ]
                                                                      
                                                                    
                                                                    
                                                                    
                                                                      
                                                                        an
                                                                        /
                                                                        
                                                                          (
                                                                          
                                                                            
                                                                          
                                                                          
                                                                          
                                                                            
                                                                              nnozvect
                                                                              
                                                                              
                                                                                [
                                                                                
                                                                                  [
                                                                                  in
                                                                                  ]
                                                                                
                                                                                ]
                                                                              
                                                                            
                                                                            *
                                                                            Pi
                                                                          
                                                                          )
                                                                        
                                                                      
                                                                    
                                                                  
                                                                  <
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  
                                                                    
                                                                      (
                                                                      
                                                                        
                                                                          combustionChamberHeight
                                                                          /
                                                                          2
                                                                        
                                                                        +
                                                                        rb
                                                                      
                                                                      )
                                                                    
                                                                    *
                                                                    Pi
                                                                  
                                                                
                                                              
                                                              /.
                                                              ch
                                                            
                                                            )
                                                          
                                                          ,
                                                          
                                                            &IndentingNewLine;
                                                          
                                                          
                                                          
                                                            (
                                                            
                                                              
                                                                maxnoz
                                                                
                                                                
                                                                  
                                                                
                                                                =
                                                                
                                                                  nnozvect
                                                                  
                                                                  
                                                                    [
                                                                    
                                                                      [
                                                                      in
                                                                      ]
                                                                    
                                                                    ]
                                                                  
                                                                
                                                              
                                                              ;
                                                              
                                                                &IndentingNewLine;
                                                              
                                                              
                                                              
                                                                If
                                                                
                                                                
                                                                  [
                                                                  
                                                                    
                                                                      minnoz
                                                                      
                                                                      
                                                                        
                                                                      
                                                                      ==
                                                                      
                                                                        
                                                                      
                                                                      
                                                                      0
                                                                    
                                                                    ,
                                                                    
                                                                      minnoz
                                                                      
                                                                      
                                                                        
                                                                      
                                                                      =
                                                                      
                                                                        
                                                                      
                                                                      
                                                                      
                                                                        nnozvect
                                                                        
                                                                        
                                                                          [
                                                                          
                                                                            [
                                                                            in
                                                                            ]
                                                                          
                                                                          ]
                                                                        
                                                                      
                                                                    
                                                                    ,
                                                                  
                                                                  ]
                                                                
                                                              
                                                              ;
                                                            
                                                            
                                                            
                                                              &IndentingNewLine;
                                                            
                                                            
                                                            
                                                              (*
                                                              
                                                              
                                                                
                                                                  Print
                                                                  [
                                                                  
                                                                    
                                                                  
                                                                  
                                                                  
                                                                    
                                                                      nnozvect
                                                                      
                                                                      
                                                                        [
                                                                        
                                                                          [
                                                                          in
                                                                          ]
                                                                        
                                                                        ]
                                                                      
                                                                    
                                                                    ,
                                                                     nozzles radius = 
                                                                    ,
                                                                    
                                                                      
                                                                        
                                                                          an
                                                                          /
                                                                          
                                                                            (
                                                                            
                                                                              
                                                                            
                                                                            
                                                                            
                                                                              
                                                                                nnozvect
                                                                                
                                                                                
                                                                                  [
                                                                                  
                                                                                    [
                                                                                    in
                                                                                    ]
                                                                                  
                                                                                  ]
                                                                                
                                                                              
                                                                              *
                                                                              Pi
                                                                            
                                                                            )
                                                                          
                                                                        
                                                                        
                                                                        
                                                                          
                                                                        
                                                                      
                                                                    
                                                                    ,
                                                                    
                                                                      
                                                                    
                                                                    
                                                                     fraction nozzle = 
                                                                    ,
                                                                    franoz
                                                                    
                                                                    
                                                                      
                                                                    
                                                                    ,
                                                                     minnoz = 
                                                                    ,
                                                                    minnoz
                                                                    ,
                                                                     maxnoz = 
                                                                    ,
                                                                    maxnoz
                                                                  
                                                                  ]
                                                                
                                                                ;
                                                              
                                                              
                                                              *)
                                                            
                                                            
                                                            
                                                              &IndentingNewLine;
                                                            
                                                            
                                                            
                                                              
                                                            
                                                            )
                                                          
                                                          
                                                          
                                                            &IndentingNewLine;
                                                          
                                                          ,
                                                        
                                                        
                                                        
                                                          (*
                                                          
                                                          
                                                            
                                                              Print
                                                              [
                                                              
                                                                
                                                              
                                                              
                                                              
                                                                
                                                                  nnozvect
                                                                  
                                                                  
                                                                    [
                                                                    
                                                                      [
                                                                      in
                                                                      ]
                                                                    
                                                                    ]
                                                                  
                                                                
                                                                ,
                                                                 fraction nozzle = 
                                                                ,
                                                                franoz
                                                                ,
                                                                 nozlefit = 
                                                                ,
                                                                
                                                                  fitnoz
                                                                  .
                                                                   radius = 
                                                                
                                                                ,
                                                                
                                                                  
                                                                    
                                                                      an
                                                                      /
                                                                      
                                                                        (
                                                                        
                                                                          
                                                                        
                                                                        
                                                                        
                                                                          
                                                                            nnozvect
                                                                            
                                                                            
                                                                              [
                                                                              
                                                                                [
                                                                                in
                                                                                ]
                                                                              
                                                                              ]
                                                                            
                                                                          
                                                                          *
                                                                          Pi
                                                                        
                                                                        )
                                                                      
                                                                    
                                                                    
                                                                    
                                                                      
                                                                    
                                                                  
                                                                
                                                              
                                                              ]
                                                            
                                                            ;
                                                          
                                                          
                                                          *)
                                                        
                                                        
                                                        
                                                          &IndentingNewLine;
                                                        
                                                        ]
                                                      
                                                    
                                                    
                                                    
                                                      &IndentingNewLine;
                                                    
                                                    )
                                                  
                                                
                                                ]
                                              
                                            
                                            
                                            
                                              &IndentingNewLine;
                                            
                                            
                                            
                                              AppendTo
                                              
                                              
                                                [
                                                
                                                  almaxtstress
                                                  ,
                                                  
                                                    
                                                      
                                                        
                                                          
                                                            
                                                              
                                                                
                                                                  
                                                                    
                                                                      
                                                                        
                                                                          {
                                                                          
                                                                            rBot
                                                                            ,
                                                                            thicknessOfChamberWall
                                                                            ,
                                                                            
                                                                              (*
                                                                              
                                                                              
                                                                                combustionChamberHeight
                                                                                ,
                                                                                maxtstressformula
                                                                                ,
                                                                              
                                                                              
                                                                              *)
                                                                            
                                                                            
                                                                            
                                                                              maxtstressformula
                                                                              6894.7
                                                                            
                                                                            ,
                                                                            
                                                                              nominalThrustlbf
                                                                              weightOfEnginelb
                                                                            
                                                                            ,
                                                                            weightOfEnginelb
                                                                            ,
                                                                            enginediameter
                                                                            ,
                                                                            r
                                                                            ,
                                                                            minnoz
                                                                            ,
                                                                            maxnoz
                                                                          
                                                                          }
                                                                        
                                                                        /.
                                                                        ch
                                                                      
                                                                      /.
                                                                      
                                                                      
                                                                      maxrvalue1
                                                                    
                                                                    /.
                                                                    
                                                                      rBot
                                                                      
                                                                      
                                                                        
                                                                      
                                                                      ->
                                                                      rb
                                                                    
                                                                  
                                                                  
                                                                  
                                                                    
                                                                  
                                                                  /.
                                                                  
                                                                  
                                                                  stuff
                                                                
                                                                
                                                                
                                                                  
                                                                
                                                                /.
                                                                
                                                                  
                                                                
                                                                
                                                                
                                                                  Join
                                                                  
                                                                  
                                                                    [
                                                                    
                                                                      geo
                                                                      ,
                                                                      fuel
                                                                      ,
                                                                      oxidizer
                                                                      ,
                                                                      metal
                                                                      ,
                                                                      velocity
                                                                    
                                                                    ]
                                                                  
                                                                
                                                              
                                                              /.
                                                              
                                                              
                                                              
                                                                thicknessOfChamberWall
                                                                
                                                                
                                                                  
                                                                
                                                                
                                                                
                                                                  
                                                                
                                                                
                                                                tc
                                                              
                                                            
                                                            /.
                                                            ch
                                                          
                                                          /.
                                                          
                                                          
                                                          maxrvalue1
                                                        
                                                        /.
                                                        
                                                          THRUST
                                                          
                                                          
                                                            th
                                                            *
                                                            
                                                              32
                                                              /
                                                              2.2
                                                            
                                                          
                                                        
                                                      
                                                      
                                                      
                                                        
                                                      
                                                      /.
                                                      
                                                        rBot
                                                        
                                                        
                                                          
                                                        
                                                        ->
                                                        rb
                                                      
                                                    
                                                    /.
                                                    ch
                                                  
                                                
                                                ]
                                              
                                            
                                          
                                          ;
                                        
                                        
                                        
                                          &IndentingNewLine;
                                        
                                        )
                                      
                                    
                                  
                                  ]
                                
                              
                              
                              
                                &IndentingNewLine;
                              
                              )
                            
                          
                          ]
                        
                      
                      
                      
                        &IndentingNewLine;
                      
                      
                      
                        (*
                        
                        
                          
                            Print
                            
                            
                              [
                              metal
                              ]
                            
                          
                          ;
                        
                        
                        *)
                      
                      
                      
                        &IndentingNewLine;
                      
                      
                      
                        Print
                        
                        
                          [
                          
                            
                              metalname
                              /.
                              metal
                            
                            ,
                             thrust = 
                            ,
                            th
                            
                            
                              
                            
                            ,
                            
                              
                            
                            
                             vol in^3 = 
                            ,
                            
                              
                                volumeOfCombustionChamberIn3
                                
                                
                                  
                                
                                /.
                                
                                  rBot
                                  
                                  
                                    
                                  
                                  ->
                                  rb
                                
                              
                              /.
                              ch
                            
                          
                          ]
                        
                      
                      
                      
                        &IndentingNewLine;
                      
                      
                      
                        (*
                        
                        
                          
                            Print
                            
                            
                              [
                              
                                
                                  
                                    
                                      
                                        {
                                        
                                          nominalFuelFlowMass
                                          ,
                                          volRichO2Fraction
                                          
                                          
                                            
                                          
                                          ,
                                          
                                            
                                          
                                          
                                          volRichPropaneFraction
                                        
                                        }
                                      
                                      /.
                                      fuel
                                    
                                    /.
                                    velocity
                                  
                                  /.
                                  
                                    rBot
                                    
                                    
                                      
                                    
                                    ->
                                    rb
                                  
                                
                                /.
                                ch
                              
                              ]
                            
                          
                          ;
                        
                        
                        *)
                      
                      
                      
                        &IndentingNewLine;
                      
                      
                      
                        Print
                        [
                        
                          &IndentingNewLine;
                        
                        
                        
                          TableForm
                          [
                          
                            
                          
                          
                          
                            almaxtstress
                            ,
                            
                              TableHeadings
                              
                              
                                {
                                
                                  None
                                  ,
                                  
                                    {
                                    
                                      rBot
                                      ,
                                      Wall
                                      ,
                                      stress lbf
                                      ,
                                      sp thrust
                                      ,
                                      weight
                                      ,
                                      dia
                                      ,
                                      r max stress
                                      ,
                                      min # noz
                                      ,
                                      max # noz
                                    
                                    }
                                  
                                
                                }
                              
                            
                          
                          ]
                        
                        ]
                      
                    
                    ;
                    
                      &IndentingNewLine;
                    
                    
                    
                      almaxtstress
                      
                      
                        
                      
                      =
                      
                        {
                        }
                      
                    
                    ;
                  
                  
                  
                    &IndentingNewLine;
                  
                  
                  
                    &IndentingNewLine;
                  
                  )
                
              
              ]
            
          
        
        
        
          &IndentingNewLine;
        
        )
      
    
    ]
  




Null




  aluminum
  
  
  
   thrust = 
  
  
  
  400
  
  
  
   vol in^3 = 
  
  
  
  0.6974145600000005`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.005` 30350.02675658955` 2292.771266436314` 0.17446136291725498` 0.05069141254838557` 0.014309892207546682` 2 29
0.0025` 0.006` 28281.819798717384` 1865.4285042395334` 0.2144279446201908` 0.052691412548385566` 0.015404369014760914` 2 29
0.0025` 0.0065` 27899.917111771454` 1696.2262554873` 0.23581759727276838` 0.05369141254838557` 0.015822891536686395` 2 29
0.0025` 0.007` 27812.98275643409` 1549.3514682602774` 0.258172537474114` 0.05469141254838557` 0.016189041837227688` 2 29
0.0025` 0.0075` 27958.98062202838` 1420.8907529351948` 0.28151354998524897` 0.05569141254838557` 0.01651645618222877` 2 29
0.0025` 0.008` 28294.289052121243` 1307.7818070877156` 0.3058614195671948` 0.05669141254838557` 0.01681428554897713` 2 29
0.0025` 0.0085` 28787.24565448052` 1207.5948138252047` 0.33123693098097284` 0.05769141254838557` 0.0170889242946856` 2 29
0.0025` 0.009` 29414.271968630266` 1118.3778676494333` 0.35766086898760413` 0.05869141254838557` 0.017344987607686647` 2 29
0.0025` 0.01` 31002.835799154236` 966.7973655144692` 0.4137371638235123` 0.06069141254838557` 0.017814244061119283` 2 29
0.005` 0.005` 29871.667658390157` 1950.3321432539967` 0.20509327161712423` 0.053106146577365634` 0.01576006935055686` 2 29
0.005` 0.006` 26934.495211477766` 1608.5281825096245` 0.2486745363552912` 0.055106146577365636` 0.016966830448280158` 2 29
0.005` 0.0065` 26197.31653771021` 1470.9483861600484` 0.27193340280566275` 0.05610614657736563` 0.01742482120018536` 2 29
0.005` 0.007` 25787.81260450732` 1350.4443409599837` 0.2961988049915882` 0.05710614657736563` 0.017823943289719864` 2 29
0.005` 0.0075` 25635.07431671533` 1244.2007504642515` 0.3214915276740888` 0.05810614657736563` 0.018179646613259114` 2 29
0.005` 0.008` 25689.255310996523` 1149.9792746241192` 0.34783235561418574` 0.05910614657736563` 0.01850227425035297` 2 29
0.005` 0.0085` 25914.185590250378` 1065.978546039266` 0.3752420735729008` 0.060106146577365634` 0.018799038900052325` 2 29
0.005` 0.009` 26282.938720250568` 990.7330145069368` 0.4037414663112545` 0.06110614657736563` 0.019075137097826295` 2 29
0.005` 0.01` 27374.638073702252` 861.8973008913445` 0.46409241517096506` 0.06310614657736563` 0.01957978161336164` 2 29
0.01` 0.005` 30503.967175632093` 1337.881064211502` 0.2989802387521983` 0.059036355239801754` 0.018717656858385865` 2 29
0.01` 0.006` 25849.5296380106` 1136.038676087302` 0.35210068848858533` 0.06103635523980175` 0.020218960756531852` 2 29
0.01` 0.0065` 24435.276428072837` 1051.8534950433182` 0.3802810960698733` 0.06203635523980175` 0.020775062945564006` 2 29
0.01` 0.007` 23421.952098902635` 976.6356082459049` 0.4095693384745858` 0.06303635523980175` 0.021253866561079825` 2 29
0.01` 0.0075` 22718.35861156758` 909.1194214236745` 0.4399862004637443` 0.06403635523980175` 0.02167620531423893` 2 29
0.01` 0.008` 22260.675534724134` 848.2619181611341` 0.4715524667983702` 0.06503635523980175` 0.02205588364054104` 2 29
0.01` 0.0085` 22002.752745602764` 793.1960873216282` 0.5042889222394846` 0.06603635523980175` 0.022402449844290427` 2 29
0.01` 0.009` 21910.331249389033` 743.1955548162969` 0.5382163515481091` 0.06703635523980175` 0.02272273699353261` 2 29
0.01` 0.01` 22123.955401269955` 656.0310144358812` 0.6097272708119732` 0.06903635523980176` 0.023303342828626464` 2 29
0.015` 0.005` 32684.466171482454` 909.1467899911656` 0.4399729553066861` 0.06601344432494906` 0.021655016983516757` 2 29
0.015` 0.006` 26358.5394370492` 791.2622092519667` 0.5055214255438121` 0.06801344432494906` 0.02355590612688179` 2 29
0.015` 0.0065` 24320.61430867128` 740.6109746857479` 0.5400946160293211` 0.06901344432494906` 0.024237771719465173` 2 29
0.015` 0.007` 22766.572829654622` 694.5712723056396` 0.5758948231074895` 0.07001344432494906` 0.024815847743246525` 2 29
0.015` 0.0075` 21581.714136128754` 652.5894086981076` 0.6129428315393378` 0.07101344432494905` 0.02531908960175518` 2 29
0.015` 0.008` 20686.427820623594` 614.1945651428437` 0.6512594260858886` 0.07201344432494905` 0.02576638912263367` 2 29
0.015` 0.0085` 20023.493964838155` 578.9839886563117` 0.6908653915081625` 0.07301344432494905` 0.02617065967876233` 2 29
0.015` 0.009` 19550.636733138308` 546.6112400089892` 0.7317815125671806` 0.07401344432494905` 0.026541055388969642` 2 29
0.015` 0.01` 19054.721003839582` 489.2204190514444` 0.817627360639536` 0.07601344432494905` 0.027205269255837744` 2 29



  aluminum
  
  
  
   thrust = 
  
  
  
  500
  
  
  
   vol in^3 = 
  
  
  
  0.8717682000000003`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.005` 31766.706673372173` 2500.2276956844144` 0.19998178600414623` 0.05366561529751494` 0.014732503081507097` 2 29
0.0025` 0.006` 29010.059456334282` 2045.6356986890366` 0.24442279743183476` 0.055665615297514945` 0.016028286655085412` 2 29
0.0025` 0.0065` 28365.962641947` 1864.7957973752684` 0.268125872389759` 0.05666561529751494` 0.016508297947128683` 2 29
0.0025` 0.007` 28045.628458401356` 1707.3876349133752` 0.29284503985843136` 0.05766561529751494` 0.016922158010240204` 2 29
0.0025` 0.0075` 27977.500421451314` 1569.3606336259406` 0.3186010845988736` 0.05866561529751494` 0.017287794471488326` 2 29
0.0025` 0.008` 28111.858948867623` 1447.5349999165571` 0.3454147913721068` 0.05966561529751494` 0.017617013980912127` 2 29
0.0025` 0.0085` 28412.919186366937` 1339.3803859756708` 0.3733069449391522` 0.06066561529751494` 0.017917950824798946` 2 29
0.0025` 0.009` 28854.196827448388` 1242.858750927818` 0.40229833006103116` 0.061665615297514936` 0.018196411811864818` 2 29
0.0025` 0.01` 30081.76789782313` 1078.3718984047046` 0.4636619340133752` 0.06366561529751494` 0.018701916691014876` 2 29
0.005` 0.005` 31629.46412411774` 2143.280301022989` 0.23328726520807844` 0.05603385860262498` 0.016121203847536094` 2 29
0.005` 0.006` 28018.07658979873` 1776.449045485727` 0.2814603668315672` 0.05803385860262497` 0.017544347299572726` 2 29
0.005` 0.0065` 27032.888116008504` 1628.1862859591972` 0.3070901679444132` 0.05903385860262497` 0.018067775099280522` 2 29
0.005` 0.007` 26406.888202225095` 1498.0083277943454` 0.33377651560602195` 0.06003385860262497` 0.018517413036198062` 2 29
0.005` 0.0075` 26059.021039188417` 1382.972094110929` 0.3615401945774148` 0.061033858602624974` 0.01891339430760497` 2 29
0.005` 0.008` 25932.972879846828` 1280.7311778486926` 0.39040198961961314` 0.062033858602624975` 0.0192689473912578` 2 29
0.005` 0.0085` 25988.216824575662` 1189.3924684668461` 0.4203826854936382` 0.06303385860262498` 0.019593168969328736` 2 29
0.005` 0.009` 26194.762987604587` 1107.4121896136105` 0.4515030669605111` 0.06403385860262498` 0.01989254237652623` 2 29
0.005` 0.01` 26976.133851446353` 966.6579831271122` 0.5172460257168868` 0.06603385860262498` 0.020434589903443663` 2 29
0.01` 0.005` 32780.75501291114` 1498.226874134065` 0.33372782762890085` 0.06182678804802683` 0.01891649953027311` 2 29
0.01` 0.006` 27437.02326017938` 1276.6094336530703` 0.39166246685897477` 0.06382678804802683` 0.020679845435457842` 2 29
0.01` 0.0065` 25786.155718028254` 1183.9322363936528` 0.42232146792711545` 0.06482678804802683` 0.02131284569920131` 2 29
0.01` 0.007` 24574.24699972961` 1100.9918469802399` 0.4541359696453538` 0.06582678804802683` 0.02185027409759078` 2 29
0.01` 0.0075` 23698.175776804856` 1026.4268859106064` 0.4871267567747111` 0.06682678804802683` 0.022318871197258314` 2 29
0.01` 0.008` 23086.643651865925` 959.1137223076339` 0.5213146140762087` 0.06782678804802683` 0.022736016226242554` 2 29
0.01` 0.0085` 22688.52006271174` 898.1170192101167` 0.5567203263108679` 0.06882678804802683` 0.023113560279124472` 2 29
0.01` 0.009` 22466.072529832963` 842.6521131714688` 0.5933646782397097` 0.06982678804802683` 0.023459892840552103` 2 29
0.01` 0.01` 22440.76053396488` 745.7650535702845` 0.670452440224028` 0.07182678804802684` 0.02408186238059449` 2 29
0.015` 0.005` 35373.83062482903` 1035.7952547886234` 0.4827208830011836` 0.06864841206148867` 0.021641277665268622` 2 29
0.015` 0.006` 28284.720681918134` 903.6659954436415` 0.5533017757899948` 0.07064841206148867` 0.023875244470927388` 2 29
0.015` 0.0065` 26000.340298097923` 846.7992868326114` 0.5904586928387863` 0.07164841206148867` 0.024650759033971945` 2 29
0.015` 0.007` 24246.06729192692` 795.0545866127226` 0.6288876366718631` 0.07264841206148867` 0.025299132386884363` 2 29
0.015` 0.0075` 22892.62884435802` 747.8207843697543` 0.6686093920502469` 0.07364841206148867` 0.025857196023905973` 2 29
0.015` 0.008` 21851.483409007207` 704.577895368365` 0.709644743734959` 0.07464841206148867` 0.02634848131690898` 2 29
0.015` 0.0085` 21059.55838610567` 664.8808176349384` 0.7520144764870202` 0.07564841206148867` 0.026788830603019766` 2 29
0.015` 0.009` 20470.543233711607` 628.3464356123093` 0.7957393750674523` 0.07664841206148866` 0.027189347056856824` 2 29
0.015` 0.01` 19769.98758912542` 563.483258647707` 0.8873378087575148` 0.07864841206148866` 0.027900953497460412` 2 29



  aluminum
  
  
  
   thrust = 
  
  
  
  1000
  
  
  
   vol in^3 = 
  
  
  
  1.7435364000000002`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.005` 38686.662591927656` 3220.379247756441` 0.31052243324964773` 0.06446679448495651` 0.015048940132696562` 2 29
0.0025` 0.006` 32902.037474305136` 2679.502946157153` 0.3732035456181022` 0.06646679448495652` 0.017685337841884557` 2 29
0.0025` 0.0065` 31277.802047632802` 2461.214776816955` 0.40630342764855426` 0.06746679448495652` 0.018513026440021466` 2 29
0.0025` 0.007` 30137.447403506874` 2269.6121959895668` 0.44060390659118454` 0.06846679448495652` 0.01918299385332613` 2 29
0.0025` 0.0075` 29352.4924065491` 2100.2854054004833` 0.47612576720701427` 0.06946679448495652` 0.019746393707275798` 2 29
0.0025` 0.008` 28840.067616482196` 1949.736592923491` 0.512889794257065` 0.07046679448495652` 0.020233596121110222` 2 29
0.0025` 0.0085` 28543.462663717404` 1815.1562085464002` 0.5509167725023583` 0.07146679448495652` 0.020664035169042184` 2 29
0.0025` 0.009` 28422.184025348663` 1694.2619964794135` 0.5902274867039142` 0.0724667944849565` 0.021050840005791254` 2 29
0.0025` 0.01` 28593.425640853406` 1486.3627804854887` 0.6727832620199031` 0.07446679448495651` 0.021728003046581637` 2 29
0.005` 0.005` 39552.759152449704` 2815.101695576275` 0.3552269538153546` 0.0667056740630978` 0.016165410200710245` 2 29
0.005` 0.006` 32864.85171338263` 2369.2219434249228` 0.42207949439908116` 0.0687056740630978` 0.019027126321526717` 2 29
0.005` 0.0065` 30915.68945784304` 2186.6409244577158` 0.4573224569315141` 0.0697056740630978` 0.019919447057335025` 2 29
0.005` 0.007` 29497.043199262363` 2025.0939080718335` 0.49380426063902216` 0.0707056740630978` 0.020639583995586828` 2 29
0.005` 0.0075` 28467.180654680844` 1881.305818636763` 0.5315456902826264` 0.0717056740630978` 0.021243624226471493` 2 29
0.005` 0.008` 27734.66583324737` 1752.6409168560533` 0.5705675306233484` 0.0727056740630978` 0.02176478874460372` 2 29
0.005` 0.0085` 27236.901923819118` 1636.9543989796416` 0.6108905664222088` 0.0737056740630978` 0.022224300431389243` 2 29
0.005` 0.009` 26929.17471769585` 1532.4834796906982` 0.6525355824402298` 0.0747056740630978` 0.022636478526384157` 2 29
0.005` 0.01` 26759.908800383517` 1351.5802173923767` 0.7398746941778375` 0.0767056740630978` 0.023356367310286962` 2 29
0.01` 0.005` 42463.868933528625` 2075.078044237184` 0.4819095854139832` 0.07209979618501382` 0.01818635635951149` 2 29
0.01` 0.006` 33762.92820254396` 1787.7472534460176` 0.5593631863074744` 0.07409979618501382` 0.02171361662970276` 2 29
0.01` 0.0065` 31135.72098477579` 1666.5419771596357` 0.6000448915810368` 0.07509979618501382` 0.02277807998301761` 2 29
0.01` 0.007` 29148.893471434476` 1557.4927102073834` 0.6420575797538393` 0.07609979618501382` 0.02362721865023755` 2 29
0.01` 0.0075` 27627.220221682273` 1458.9551372443632` 0.6854220355869026` 0.07709979618501382` 0.024332919063787827` 2 29
0.01` 0.008` 26458.60264279939` 1369.5646290144707` 0.7301590438412486` 0.07809979618501382` 0.024937098976852715` 2 29
0.01` 0.0085` 25566.682716439034` 1288.1794003782497` 0.7762893892778979` 0.07909979618501382` 0.025466251001374677` 2 29
0.01` 0.009` 24897.09450712195` 1213.836979287059` 0.8238338566578728` 0.08009979618501382` 0.02593810955888047` 2 29
0.01` 0.01` 24074.641166242433` 1083.1322451569988` 0.9232482962918821` 0.08209979618501383` 0.02675610546486803` 2 29
0.015` 0.005` 46771.2469992419` 1509.4338180432837` 0.6625000632994462` 0.0784460617526225` 0.01977319474672775` 2 29
0.015` 0.006` 35737.31282136502` 1327.2759866725758` 0.753422807344656` 0.0804460617526225` 0.02433835544588791` 2 29
0.015` 0.0065` 32400.857990469438` 1248.4368113969942` 0.8010016933744571` 0.0814460617526225` 0.025639500565344413` 2 29
0.015` 0.007` 29838.58872014362` 1176.4429509278086` 0.850019968423751` 0.08244606175262251` 0.026659402905463585` 2 29
0.015` 0.0075` 27830.968984159972` 1110.496121747679` 0.9004984172535588` 0.08344606175262251` 0.027495846729057995` 2 29
0.015` 0.008` 26240.12054582206` 1049.9152551912953` 0.9524578246249024` 0.08444606175262251` 0.028204277051307847` 2 29
0.015` 0.0085` 24973.183811699946` 994.1158528229935` 1.005918975298802` 0.08544606175262251` 0.02881908472754783` 2 29
0.015` 0.009` 23964.54141621567` 942.5935510627946` 1.0609026540362796` 0.08644606175262251` 0.02936298312692844` 2 29
0.015` 0.01` 22541.88315732067` 850.6868236705571` 1.1755207347460541` 0.08844606175262251` 0.03029648032649562` 2 29



  superalloy
  
  
  
   thrust = 
  
  
  
  100
  
  
  
   vol in^3 = 
  
  
  
  0.17435364`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.001` 103349.10861676613` 1984.4708611824578` 0.05039126648622822` 0.02849473346165951` 0.007202327929391729` 2 29
0.0025` 0.005` 61372.579669298844` 425.14915887080156` 0.23521156731345905` 0.03649473346165951` 0.011733347075273808` 2 29
0.0025` 0.0075` 86055.19526431525` 242.7327366309803` 0.41197574496112244` 0.04149473346165951` 0.012651025089264356` 2 29
0.0025` 0.01` 119137.9120321266` 155.02852656876107` 0.6450425751524267` 0.04649473346165951` 0.013450265898602471` 2 29
0.0025` 0.025` 454650.27259159216` 27.363637067871803` 3.65448495578141` 0.07649473346165951` 0.01733985894279328` 2 29
0.0025` 0.03` 616293.3684293281` 18.331520329115268` 5.455084914106866` 0.0864947334616595` 0.01844364448947272` 2 29
0.0025` 0.04` 1.0135635377193049`*^6 9.416277021038722` 10.619908460272645` 0.10649473346165951` 0.02047054937402841` 2 29
0.0025` 0.045` 1.2491505235991497`*^6 7.088873509965889` 14.106613675560029` 0.1164947334616595` 0.021411485432730623` 2 29
0.0025` 0.05` 1.5093603403077992`*^6 5.471107310889567` 18.27783560394846` 0.12649473346165951` 0.0223125425942047` 2 29
0.0025` 0.055` 1.7941887176317165`*^6 4.311308356843404` 23.19481505916146` 0.13649473346165952` 0.02317844515321622` 2 29
0.0025` 0.06` 2.103633024570098`*^6 3.457958999245644` 28.918792854922543` 0.1464947334616595` 0.024013040429010556` 2 29
0.0025` 0.075` 3.1796471976070628`*^6 1.940047698398869` 51.54512442272968` 0.1764947334616595` 0.026358402055376446` 2 29
0.0025` 0.1` 5.465237249110029`*^6 0.8999972296752402` 111.11145312756636` 0.22649473346165952` 0.029860260992967073` 2 29
0.005` 0.001` 116530.32595255654` 1281.0721458624184` 0.07805961617616777` 0.03125357655725637` 0.008083614265314083` 2 29
0.005` 0.005` 48797.67524969816` 340.37179720890896` 0.2937963744940457` 0.03925357655725637` 0.013577905406647332` 2 29
0.005` 0.0075` 66445.68150059547` 202.26697019952346` 0.4943960939413706` 0.04425357655725637` 0.014582080586166588` 2 29
0.005` 0.01` 91846.8381331458` 132.4907247224909` 0.7547698166000337` 0.04925357655725637` 0.015452776371283616` 2 29
0.005` 0.025` 359504.19909793226` 24.99405194017078` 4.000951916054821` 0.07925357655725637` 0.01970365687399833` 2 29
0.005` 0.03` 489782.0794849055` 16.925525887147096` 5.908235919330459` 0.08925357655725637` 0.020915875799917882` 2 29
0.005` 0.04` 811076.1156789513` 8.827618341154185` 11.328083763408976` 0.10925357655725637` 0.02314720852787494` 2 29
0.005` 0.045` 1.0020459654369939`*^6 6.683094054178221` 14.963129231658913` 0.11925357655725637` 0.02418498758556338` 2 29
0.005` 0.05` 1.2132175037827166`*^6 5.182266313615712` 19.296576815680694` 0.1292535765572564` 0.02517975342640198` 2 29
0.005` 0.055` 1.4445858397296756`*^6 4.100096924253092` 24.389667329197795` 0.13925357655725637` 0.02613650445644104` 2 29
0.005` 0.06` 1.696147966300252`*^6 3.2999334326346266` 30.303641585933818` 0.14925357655725635` 0.027059325568783613` 2 29
0.005` 0.075` 2.5719807555365595`*^6 1.8662539773519173` 53.583274952690495` 0.17925357655725638` 0.029655582427944804` 2 29
0.005` 0.1` 4.435480515231194`*^6 0.8732392916574975` 114.51614804252542` 0.22925357655725637` 0.03353842059533609` 2 29
0.01` 0.001` 158607.56340911248` 534.9536801281057` 0.18693207227970263` 0.03810466015935465` 0.008479844302356758` 2 29
0.01` 0.005` 34489.23493948981` 204.15426266136535` 0.4898256773892198` 0.04610466015935465` 0.017552102882718842` 2 29
0.01` 0.0075` 41894.7710986381` 132.25675765977743` 0.7561050321318474` 0.05110466015935465` 0.0187144493687492` 2 29
0.01` 0.01` 56250.60471316837` 91.67761129985199` 1.0907788562785277` 0.056104660159354655` 0.019705124288131405` 2 29
0.01` 0.025` 224103.32885284728` 20.145891084875014` 4.963791354708417` 0.08610466015935465` 0.024550638250979098` 2 29
0.01` 0.03` 307435.9025574249` 13.988004481299928` 7.148982553850799` 0.09610466015935465` 0.025945505821626434` 2 29
0.01` 0.04` 514080.2902339569` 7.5596701486966555` 13.228090383975381` 0.11610466015935465` 0.0285264222938099` 2 29
0.01` 0.045` 637333.9413512895` 5.798954209294292` 17.244488642404633` 0.12610466015935465` 0.029731822465172905` 2 29
0.01` 0.05` 773858.3509866446` 4.546741917943495` 21.993770881376584` 0.13610466015935466` 0.03088982345552796` 2 29
0.01` 0.055` 923647.4527133325` 3.6314541856857168` 27.53717791461474` 0.14610466015935464` 0.03200569497613219` 2 29
0.01` 0.06` 1.086697528691247`*^6 2.9467275370833343` 33.93595055584263` 0.15610466015935465` 0.03308377523474169` 2 29
0.01` 0.075` 1.6553934755293806`*^6 1.6984598459533848` 58.876870264700116` 0.18610466015935465` 0.0361249048685002` 2 29
0.01` 0.1` 2.8683197711151266`*^6 0.8112392906084731` 123.26819122012026` 0.23610466015935466` 0.04069064430443562` 2 29
0.015` 0.001` 220617.6229657703` + 39347.8160142561` 260.67452314614565` 0.38362015126401744` 0.04602083984793304` 0.007427768515184362` - 0.007427768515184362` 2 29
0.015` 0.005` 28633.59761070476` 124.12287045933492` 0.8056532984609147` 0.05402083984793304` 0.021756870456691422` 2 29
0.015` 0.0075` 29636.400296842166` 86.25569827134902` 1.1593436955946173` 0.059020839847933035` 0.023068753252653312` 2 29
0.015` 0.01` 37418.93101286789` 62.83817939131794` 1.5913891995065748` 0.06402083984793304` 0.02415843473185652` 2 29
0.015` 0.025` 145799.4789191735` 15.980043708782695` 6.2578051613863614` 0.09402083984793304` 0.029463132480193232` 2 29
0.015` 0.03` 200811.51253524135` 11.380255052677194` 8.787149280672326` 0.10402083984793303` 0.031001735967650896` 2 29
0.015` 0.04` 337841.7660490856` 6.379955466297658` 15.67409059957449` 0.12402083984793304` 0.033862932749201366` 2 29
0.015` 0.045` 419790.88932408264` 4.961752473303618` 20.154169426637747` 0.13402083984793303` 0.035204810952466546` 2 29
0.015` 0.05` 510676.0552834878` 3.935927077158205` 25.40697478374051` 0.14402083984793304` 0.03649683050744355` 2 29
0.015` 0.055` 610490.1203516846` 3.1752334347914206` 31.49374748460626` 0.15402083984793302` 0.03774428668530019` 2 29
0.015` 0.06` 719228.716124191` 2.5990411177830484` 38.47572834295859` 0.16402083984793303` 0.03895156656897802` 2 29
0.015` 0.075` 1.0989680948502847`*^6 1.52892742927212` 65.40532800017019` 0.19402083984793303` 0.04236667037172472` 2 29
0.015` 0.1` 1.9102174449387458`*^6 0.7467815589634584` 133.90796652611667` 0.24402083984793305` 0.047514981911065755` 2 29



  superalloy
  
  
  
   thrust = 
  
  
  
  1000
  
  
  
   vol in^3 = 
  
  
  
  1.7435364000000002`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.001` 166746.98742404146` + 91260.25892562118` 3273.952061017332` 0.3054412469586574` 0.05646679448495651` 0.013996272377974349` - 0.013996272377974349` 2 29
0.0025` 0.005` 57745.6287026938` 1092.9771992385497` 0.9149321693962835` 0.06446679448495651` 0.020278699172064138` 2 29
0.0025` 0.0075` 58840.342216501` 712.8241375904673` 1.4028705640920955` 0.06946679448495652` 0.021845486544423358` 2 29
0.0025` 0.01` 66754.20464142636` 504.4625194374991` 1.9823078255943576` 0.07446679448495651` 0.022963273430691544` 2 29
0.0025` 0.025` 164622.0551290476` 128.0558398269516` 7.809093293608096` 0.10446679448495652` 0.027745838453318006` 2 29
0.0025` 0.03` 210520.13318445222` 92.3328864423527` 10.830377328497601` 0.1144667944849565` 0.029083534897986547` 2 29
0.0025` 0.04` 320271.97833510605` 53.02529567784717` 18.858923598945225` 0.13446679448495652` 0.03156581698444192` 2 29
0.0025` 0.045` 384004.2212044671` 41.686350506386` 23.98866746195037` 0.1444667944849565` 0.0327306382967166` 2 29
0.0025` 0.05` 453603.4856983358` 33.395992123721555` 29.94371289510782` 0.1544667944849565` 0.03385333984714987` 2 29
0.0025` 0.055` 529055.7900147543` 27.184771651736106` 36.78530071214106` 0.16446679448495652` 0.03493860472339313` 2 29
0.0025` 0.06` 610352.3368130266` 22.43426504921076` 44.57467172677361` 0.1744667944849565` 0.035990204440104714` 2 29
0.0025` 0.075` 889258.3926008329` 13.469484300596323` 74.24189209350266` 0.2044667944849565` 0.03897184910626401` 2 29
0.0025` 0.1` 1.4706903444361703`*^6 6.740418864777106` 148.35873260423386` 0.2544667944849565` 0.04348450202178953` 2 29
0.005` 0.001` 178962.67850252122` + 99286.3866637421` 2547.7445930861268` 0.39250402207259033` 0.058705674063097804` 0.015198862663901054` - 0.015198862663901054` 2 29
0.005` 0.005` 54803.17351876331` 955.4284542561903` 1.0466508460630983` 0.0667056740630978` 0.021840714606290782` 2 29
0.005` 0.0075` 53628.98607811482` 638.503792991871` 1.566161408868453` 0.0717056740630978` 0.023505704239650545` 2 29
0.005` 0.01` 59761.815284321805` 458.7181343877156` 2.179987938202557` 0.0767056740630978` 0.024683842687704897` 2 29
0.005` 0.025` 146700.9912983857` 120.88583046630096` 8.272268107375638` 0.1067056740630978` 0.029699450021042486` 2 29
0.005` 0.03` 188217.77206820893` 87.68401563017868` 11.404587173763337` 0.1167056740630978` 0.031102685084860308` 2 29
0.005` 0.04` 287898.4447848038` 50.78975864352144` 19.689008703874915` 0.1367056740630978` 0.03370900876885304` 2 29
0.005` 0.045` 345929.43898438866` 40.05833648265783` 24.963592795045862` 0.1467056740630978` 0.03493308218689742` 2 29
0.005` 0.05` 409380.3322456407` 32.1804713215479` 31.07474685525828` 0.15670567406309782` 0.036113470828996` 2 29
0.005` 0.055` 478235.92838101706` 26.25794481177964` 38.0837116982357` 0.1667056740630978` 0.0372549981254729` 2 29
0.005` 0.06` 552486.6827637056` 21.71471170440876` 46.05172813770163` 0.17670567406309778` 0.03836154761388619` 2 29
0.005` 0.075` 807556.7970238314` 13.102297006183022` 76.32249517226606` 0.2067056740630978` 0.04150103877921572` 2 29
0.005` 0.1` 1.340256318156992`*^6 6.5932349617697845` 151.67061477384016` 0.2567056740630978` 0.04625728561969617` 2 29
0.01` 0.001` 204067.88991819188` + 115994.73472468236` 1534.486416625366` 0.6516838397300347` 0.06409979618501382` 0.017990740257240973` - 0.01799074025724097` 2 29
0.01` 0.005` 51271.95448062321` 704.2689119835289` 1.4199121713090577` 0.07209979618501382` 0.02512976506126836` 2 29
0.01` 0.0075` 45760.61702333796` 495.1605314283899` 2.019547069139981` 0.07709979618501382` 0.02701414930181125` 2 29
0.01` 0.01` 48605.88630047503` 367.6085195684359` 2.720285158717153` 0.08209979618501383` 0.028316182698392534` 2 29
0.01` 0.025` 115547.4438347722` 105.52345182785905` 9.476566418916104` 0.11209979618501383` 0.03376816605166596` 2 29
0.01` 0.03` 148946.21221140918` 77.61253302997184` 12.884516984052404` 0.12209979618501382` 0.03529148155027358` 2 29
0.01` 0.04` 229800.18173577503` 45.86809172278124` 21.801648214271182` 0.14209979618501384` 0.03812596288963766` 2 29
0.01` 0.045` 277099.5451894704` 36.45203519101719` 27.433310506800687` 0.15209979618501382` 0.039459574027642996` 2 29
0.01` 0.05` 328933.2384765045` 29.473579758059394` 33.928691669241694` 0.16209979618501383` 0.04074695833837388` 2 29
0.01` 0.055` 385283.6392113977` 24.184362708596684` 41.34903251531767` 0.1720997961850138` 0.04199315933658286` 2 29
0.01` 0.06` 446139.71326457` 20.09825075757008` 49.755573858752186` 0.18209979618501382` 0.04320222890729985` 2 29
0.01` 0.075` 655680.8067141235` 12.269214689796806` 81.50480901044219` 0.21209979618501382` 0.04663763938111811` 2 29
0.01` 0.1` 1.0946609148763786`*^6 6.2554727505469625` 159.86002015795893` 0.26209979618501383` 0.051853976158990504` 2 29
0.015` 0.001` 229265.69520450797` + 133124.42695560545` 963.5640341262127` 1.0378137462413992` 0.07044606175262251` 0.02124305928152141` - 0.021243059281521405` 2 29
0.015` 0.005` 50300.179051817344` 512.2926897601446` 1.9520091150787258` 0.0784460617526225` 0.02858317502818746` 2 29
0.015` 0.0075` 40805.00632654774` 376.8956534416365` 2.653254265122093` 0.08344606175262251` 0.03071967623004451` 2 29
0.015` 0.01` 40814.27357962628` 288.7179522760678` 3.4635878791624815` 0.08844606175262251` 0.032150907701343524` 2 29
0.015` 0.025` 91134.2510266928` 90.53761504651351` 11.045133003406953` 0.11844606175262251` 0.038002819151760556` 2 29
0.015` 0.03` 117745.12651519146` 67.60386489921692` 14.792053701231268` 0.12844606175262252` 0.039631921151153646` 2 29
0.015` 0.04` 182733.5059882023` 40.84475370591645` 24.482948463835346` 0.1484460617526225` 0.04266812693194821` 2 29
0.015` 0.045` 220932.35905134177` 32.73386266034793` 30.54940415606214` 0.1584460617526225` 0.04409917402905034` 2 29
0.015` 0.05` 262880.4256746175` 26.65847731949174` 37.51151980720352` 0.1684460617526225` 0.04548213505499434` 2 29
0.015` 0.055` 308557.69652124145` 22.01162660541115` 45.43053623098299` 0.1784460617526225` 0.04682221458026284` 2 29
0.015` 0.06` 357951.6758603831` 18.393275895882933` 54.36769424112405` 0.18844606175262252` 0.048123575304507865` 2 29
0.015` 0.075` 528364.798706978` 11.376509151742095` 87.90042592695224` 0.2184460617526225` 0.051827111677569336` 2 29
0.015` 0.1` 886305.4022201329` 5.886960246707086` 169.8669530780945` 0.26844606175262253` 0.05746456877811009` 2 29



  superalloy
  
  
  
   thrust = 
  
  
  
  10000
  
  
  
   vol in^3 = 
  
  
  
  17.435364`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.001` 212611.69920406764` + 165059.71414605604` 4333.554870198931` 2.3075743355110583` 0.1170812639592089` 0.0397708513849141` - 0.0397708513849141` 2 23
0.0025` 0.005` 89674.42345838952` 2134.927764292616` 4.683999228101937` 0.1250812639592089` 0.03175337404396605` 2 23
0.0025` 0.0075` 66971.53530503958` 1568.523868062301` 6.375420995253107` 0.13008126395920888` 0.03841223254142168` 2 23
0.0025` 0.01` 60418.31139397393` 1214.3865090037164` 8.234610583910403` 0.13508126395920889` 0.04129616938083881` 2 23
0.0025` 0.025` 78438.82533221524` 428.42041532853057` 23.341558063547446` 0.1650812639592089` 0.0488510692640533` 2 23
0.0025` 0.03` 91226.39339593498` 332.59739426703464` 30.06638107324209` 0.1750812639592089` 0.0505735749090927` 2 23
0.0025` 0.04` 122062.32627208359` 215.4372289689218` 46.41723274969607` 0.19508126395920888` 0.05368731170895187` 2 23
0.0025` 0.045` 139787.9720735542` 178.04447084735307` 56.16574304390242` 0.2050812639592089` 0.0551358204723797` 2 23
0.0025` 0.05` 158949.6388762506` 149.15437510141922` 67.04463072705975` 0.2150812639592089` 0.05653154542204859` 2 23
0.0025` 0.055` 179507.41837452055` 126.39806272382184` 79.11513661289162` 0.2250812639592089` 0.05788287741042935` 2 23
0.0025` 0.06` 201435.60341388587` 108.18003143813587` 92.43850151512144` 0.2350812639592089` 0.05919575033426762` 2 23
0.0025` 0.075` 275295.16448986233` 71.15505219195511` 140.5381584574345` 0.2650812639592089` 0.06294305856960401` 2 23
0.0025` 0.1` 424896.8895386749` 39.76502955851348` 251.4772429701127` 0.3150812639592089` 0.06869366068256504` 2 23
0.005` 0.001` 222939.9533635683` + 171926.22093652608` 3774.5097922538043` 2.6493506575403214` 0.11902867496457668` 0.0412765192412763` - 0.0412765192412763` 2 29
0.005` 0.005` 90690.7140480269` 1960.110132817417` 5.101754147674462` 0.12702867496457668` 0.032905735444953045` 2 29
0.005` 0.0075` 66335.94411354722` 1461.1662911361955` 6.843848000506533` 0.13202867496457668` 0.03980723595718326` 2 29
0.005` 0.01` 58937.204317984964` 1142.053133483902` 8.756160030395778` 0.13702867496457669` 0.04278531420175351` 2 29
0.005` 0.025` 74337.66312065876` 412.65531954623765` 24.233299623996505` 0.16702867496457668` 0.05054351544877002` 2 29
0.005` 0.03` 86384.62143899662` 321.53179962074046` 31.10112284942079` 0.1770286749645767` 0.05230738854621527` 2 29
0.005` 0.04` 115677.28857080753` 209.34788892472545` 47.767379223946534` 0.19702867496457668` 0.05549534117753581` 2 29
0.005` 0.045` 132583.6839808927` 173.34539308640638` 57.688294000495084` 0.20702867496457666` 0.05697849510385947` 2 29
0.005` 0.05` 150889.21245940172` 145.4558411472534` 68.74938758819879` 0.21702867496457667` 0.05840777612068424` 2 29
0.005` 0.055` 170552.0120159543` 123.4386540885061` 81.01190080078118` 0.22702867496457668` 0.05979178807053921` 2 29
0.005` 0.06` 191545.13927459845` 105.7786065199319` 94.53707445196581` 0.2370286749645767` 0.061136603474061045` 2 29
0.005` 0.075` 262352.13064824935` 69.7832001204516` 143.30096617436814` 0.26702867496457666` 0.06497614353869101` 2 29
0.005` 0.1` 406022.71751553705` 39.13233637797575` 255.54313709794604` 0.3170286749645767` 0.07087112389814863` 2 29
0.01` 0.001` 244333.2416068081` + 185604.80662015226` 2866.725523401293` 3.4883004732644487` 0.1234323786454386` 0.04450090388412788` - 0.044500903884127876` 3 29
0.01` 0.005` 93452.27318959533` 1634.8082433099119` 6.116925358630148` 0.1314323786454386` 0.035183670509270355` 3 29
0.01` 0.0075` 65637.97070635618` 1253.7045548051522` 7.976360907099186` 0.1364323786454386` 0.04266439169391823` 3 29
0.01` 0.01` 56522.54951662282` 998.8457687101236` 10.011555650792488` 0.1414323786454386` 0.04585268833526119` 3 29
0.01` 0.025` 66746.06721063469` 379.61681079320465` 26.342352908726898` 0.1714323786454386` 0.054032227556609955` 3 29
0.01` 0.03` 77339.33434244127` 298.1598453831082` 33.53905683426592` 0.1814323786454386` 0.05587713503572158` 3 29
0.01` 0.04` 103592.13089882319` 196.34959853405547` 50.929566827026505` 0.20143237864543861` 0.05920899671385814` 3 29
0.01` 0.045` 118878.34707600904` 163.27635687502257` 61.2458545216951` 0.2114323786454386` 0.06075903623393732` 3 29
0.01` 0.05` 135486.3664098827` 137.5052705594783` 72.7244851001873` 0.2214323786454386` 0.062253040552910345` 3 29
0.01` 0.055` 153370.35023776957` 117.05942138720746` 85.42669937622661` 0.23143237864543859` 0.06370007368316603` 3 29
0.01` 0.06` 172500.84364406025` 100.58971913469252` 99.41373816353655` 0.2414323786454386` 0.06510650253819304` 3 29
0.01` 0.075` 237202.97749769877` 66.80195856671844` 149.6962097303256` 0.27143237864543857` 0.06912415019494905` 3 29
0.01` 0.1` 368937.46763029887` 37.74829480977166` 264.9126285145831` 0.3214323786454386` 0.0752987553849777` 3 29
0.015` 0.001` 266496.80297111685` + 199158.30278425978` 2196.9721349878114` 4.551719086803748` 0.1284433825685633` 0.04799931441992645` - 0.04799931441992645` 3 29
0.015` 0.005` 97135.20905092587` 1353.4901557522776` 7.388306414716362` 0.1364433825685633` 0.03740430395370212` 3 29
0.015` 0.0075` 65663.54790856893` 1065.426203724681` 9.385915199983312` 0.14144338256856331` 0.04559689630498092` 3 29
0.015` 0.01` 54811.05343982206` 864.6339212625327` 11.565588342171525` 0.1464433825685633` 0.049025357777126535` 3 29
0.015` 0.025` 60021.6815072313` 346.07267949161684` 28.895664386712262` 0.1764433825685633` 0.05764611039705621` 3 29
0.015` 0.03` 69229.72303599227` 274.15360018817796` 36.47590253469602` 0.1864433825685633` 0.05956972331454295` 3 29
0.015` 0.04` 92578.91915206627` 182.78480465240125` 54.70914291271001` 0.20644338256856332` 0.06303928470177822` 3 29
0.015` 0.045` 106311.8782401757` 152.70759708372702` 65.48462677018725` 0.2164433825685633` 0.06465289237116141` 3 29
0.015` 0.05` 121288.27754851221` 129.11943591183228` 77.44767415827609` 0.2264433825685633` 0.06620831247070842` 3 29
0.015` 0.055` 137458.2327033037` 110.30280493696931` 90.65952589069998` 0.2364433825685633` 0.06771511660477515` 3 29
0.015` 0.06` 154789.73975140924` 95.07382326253386` 105.18142278118253` 0.2464433825685633` 0.06917999049460284` 3 29
0.015` 0.075` 213570.95036195716` 63.60522322638982` 157.21979253821718` 0.27644338256856327` 0.07336681666200286` 3 29
0.015` 0.1` 333652.20305788383` 36.249336111455264` 275.86712124197686` 0.3264433825685633` 0.07980804653872464` 3 29



  superalloy
  
  
  
   thrust = 
  
  
  
  50000
  
  
  
   vol in^3 = 
  
  
  
  87.17681999999998`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.001` 278683.4320180698` + 226198.35995892822` 4856.236815975474` 10.296038248282276` 0.1974952024011159` 0.07908981332211966` - 0.07908981332211966` 3 13
0.0025` 0.005` 148354.03139531345` + 53464.52796104396` 2975.346855971591` 16.804763417632753` 0.2054952024011159` 0.03845109331230173` - 0.038451093312301725` 3 13
0.0025` 0.0075` 102742.16479790177` 2357.3331016618154` 21.210409324313243` 0.2104952024011159` 0.04645730021002919` 3 13
0.0025` 0.01` 78336.40646871773` 1931.620260334959` 25.885004949849513` 0.2154952024011159` 0.05888071233513669` 3 13
0.0025` 0.025` 61471.92267010711` 833.2054571937904` 60.00920849510329` 0.2454952024011159` 0.07485922884180543` 3 13
0.0025` 0.03` 65138.06085537944` 676.7495854603111` 73.88257203880082` 0.2554952024011159` 0.07730148878573197` 3 13
0.0025` 0.04` 76433.65261111272` 472.836992172013` 105.74468755145654` 0.2754952024011159` 0.08135169825200025` 3 13
0.0025` 0.045` 83447.84643283278` 403.6948701088663` 123.85592114786171` 0.2854952024011159` 0.08314411887197844` 3 13
0.0025` 0.05` 91176.68865028942` 348.42656900767815` 143.5022597226166` 0.29549520240111593` 0.08483931149019606` 3 13
0.0025` 0.055` 99542.87464015651` 303.4994504769365` 164.74494408944446` 0.3054952024011159` 0.0864601010386409` 3 13
0.0025` 0.06` 108496.12100337823` 266.46029840654916` 187.6452150620691` 0.3154952024011159` 0.08802151055259942` 3 13
0.0025` 0.075` 138585.77743051498` 187.33330444329016` 266.90395575195816` 0.34549520240111586` 0.09243945042223127` 3 13
0.0025` 0.1` 198662.35361185682` 114.1892998101377` 437.8693982985701` 0.3954952024011159` 0.09919252813117638` 3 13
0.005` 0.001` 288256.29807620135` + 231826.02881225967` 4446.369341676335` 11.24512971321213` 0.19932929524494244` 0.0808187973227681` - 0.08081879732276809` 5 13
0.005` 0.005` 150890.84870258375` + 54752.964190586696` 2797.6893609868675` 17.871891246125635` 0.20732929524494245` 0.03927671011124281` - 0.039276710111242806` 5 13
0.005` 0.0075` 103698.3146640452` 2236.705138208954` 22.354309982958963` 0.21232929524494243` 0.047470102868574955` 5 13
0.005` 0.01` 78419.02234100585` 1844.4748943142129` 27.107986210129646` 0.21732929524494243` 0.060146076036549735` 5 13
0.005` 0.025` 59958.23493040658` 809.6492499262578` 61.75513656630199` 0.24732929524494246` 0.0764168153198885` 5 13
0.005` 0.03` 63334.729606970875` 659.4454933285651` 75.82127788549128` 0.2573292952449424` 0.07889680688420649` 5 13
0.005` 0.04` 74106.79485004702` 462.54905776161405` 108.09664220690888` 0.27732929524494243` 0.08300676619332469` 5 13
0.005` 0.045` 80867.72566105006` 395.4809285343884` 126.4283468365842` 0.28732929524494244` 0.08482498172669835` 5 13
0.005` 0.05` 88342.8292695136` 341.7532504933558` 146.30438753053528` 0.29732929524494245` 0.08654439857937908` 5 13
0.005` 0.055` 96452.40725587322` 297.99863206385675` 167.78600510248566` 0.30732929524494246` 0.08818827693266125` 5 13
0.005` 0.06` 105144.63346524817` 261.86999005582237` 190.93444036615884` 0.31732929524494247` 0.08977191660156654` 5 13
0.005` 0.075` 134415.90483124435` 184.50656971783954` 270.99306044475026` 0.34732929524494244` 0.09425296785435888` 5 13
0.005` 0.1` 192985.8901091537` 112.74560747735893` 443.4762570243883` 0.3973292952449424` 0.10110373546636131` 5 13
0.01` 0.001` 307906.96562149626` + 243036.41406504548` 3732.1330144195595` 13.397164518740043` 0.20331407466593046` 0.08442081376411309` - 0.08442081376411309` 5 17
0.01` 0.005` 156046.30539806475` + 57476.83403237656` 2464.99341116506` 20.284029877535424` 0.21131407466593047` 0.04105445383319374` - 0.04105445383319374` 5 17
0.01` 0.0075` 105924.52568169324` 2005.170807985191` 24.93553157710309` 0.21631407466593044` 0.049424981759973924` 5 17
0.01` 0.01` 78807.36461162294` 1674.295613145302` 29.86330466820667` 0.22131407466593045` 0.06269653498748458` 5 17
0.01` 0.025` 57116.30204651263` 761.4948237634425` 65.66032813314631` 0.2513140746659305` 0.07959478685538397` 5 17
0.01` 0.03` 59915.41859682177` 623.8313167647336` 80.14987169817994` 0.2613140746659305` 0.08215158009373436` 5 17
0.01` 0.04` 69645.49257065056` 441.1808538796139` 113.3322073256689` 0.28131407466593045` 0.08638131007953849` 5 17
0.01` 0.045` 75902.17863070937` 378.3651388262814` 132.14748101557134` 0.29131407466593046` 0.08825071117127008` 5 17
0.01` 0.05` 82871.67075747032` 327.81049923546493` 152.52714637454383` 0.30131407466593046` 0.09001800275318136` 5 17
0.01` 0.055` 90469.39497939756` 286.47968705481287` 174.5324442163099` 0.3113140746659305` 0.09170738359836414` 5 17
0.01` 0.06` 98640.38663075719` 252.23910718937637` 198.22461535459283` 0.3213140746659304` 0.09333474850485826` 5 17
0.01` 0.075` 126273.68739479163` 178.5492523169857` 280.03477668577983` 0.35131407466593045` 0.09793967669070505` 5 17
0.01` 0.1` 181815.73936638414` 109.6880137549462` 455.8383207822958` 0.4013140746659305` 0.10498197639689533` 5 17
0.015` 0.001` 328161.41592953546` + 254168.24675251468` 3145.2351295950316` 15.897062680473685` 0.20769542669610866` 0.0882114585754078` - 0.08821145857540778` 5 19
0.015` 0.005` 161286.4499875482` + 60395.3214330858` 2166.7817249827262` 23.075697668808147` 0.21569542669610867` 0.04299975737537226` - 0.04299975737537226` 5 19
0.015` 0.0075` 108563.82494243518` 1791.0412165612076` 27.91672214891838` 0.22069542669610864` 0.051275730590641666` 5 19
0.015` 0.01` 79486.7767438012` 1513.338676914989` 33.0395309144727` 0.22569542669610865` 0.06526798719230144` 5 19
0.015` 0.025` 54527.48882955198` 713.0374993792485` 70.12253919818896` 0.2556954266961087` 0.08285188144112011` 5 19
0.015` 0.03` 56755.77083696667` 587.6486995855289` 85.084847520747` 0.2656954266961087` 0.08548724349963231` 5 19
0.015` 0.04` 65459.18412550811` 419.1857375409241` 119.27886739018314` 0.28569542669610865` 0.08983704809416446` 5 19
0.015` 0.045` 71219.3266740872` 360.6643306899665` 138.63306056450836` 0.29569542669610865` 0.09175706140886827` 5 19
0.015` 0.05` 77690.6261193615` 313.33484744142146` 159.5736969835364` 0.30569542669610866` 0.09357142603183519` 5 19
0.015` 0.055` 84783.5261198036` 274.4809302010904` 182.16201746099065` 0.31569542669610867` 0.09530537058822772` 5 19
0.015` 0.06` 92439.85970167734` 242.17852625905144` 206.45926281059462` 0.3256954266961086` 0.09697544040553205` 5 19
0.015` 0.075` 118451.86932431396` 172.28490247293976` 290.21695622954155` 0.35569542669610865` 0.10170098955510504` 5 19
0.015` 0.1` 170982.81175400075` 106.4492448161267` 469.7074186516461` 0.4056954266961087` 0.10892946095300717` 5 19



  superalloy
  
  
  
   thrust = 
  
  
  
  100000
  
  
  
   vol in^3 = 
  
  
  
  174.35364000000007`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.001` 320714.3560593839` + 256912.09819699137` 5026.560122709375` 19.89432087924552` 0.24784899936255095` 0.10599867672980169` - 0.10599867672980169` 5 11
0.0025` 0.005` 154707.15564504534` + 77849.69210884268` 3330.125954675533` 30.028894210322264` 0.25584899936255096` 0.05834942964779853` - 0.05834942964779852` 5 11
0.0025` 0.0075` 144233.01719156792` + 28101.901490111115` 2718.642689303403` 36.78306104493011` 0.26084899936255096` 0.035057102558506574` - 0.035057102558506574` 5 11
0.0025` 0.01` 96137.70602233268` 2279.48616021373` 43.86953592673877` 0.26584899936255096` 0.06263295424375587` 5 11
0.0025` 0.025` 60362.49747983664` 1066.1487753193855` 93.79553990487219` 0.29584899936255094` 0.08997851527678626` 5 11
0.0025` 0.03` 61195.07731263437` 881.4996737105661` 113.44303688628963` 0.30584899936255094` 0.09309740036809744` 5 11
0.0025` 0.04` 67188.2209173344` 634.4625359921349` 157.61371921452536` 0.32584899936255096` 0.09795065923089075` 5 11
0.0025` 0.045` 71527.71123443685` 548.6685876162038` 182.25938618879067` 0.33584899936255097` 0.10000983686448499` 5 11
0.0025` 0.05` 76502.44603668165` 479.1713981388138` 208.6935914547856` 0.345848999362551` 0.101923160972649` 5 11
0.0025` 0.055` 82010.24743992747` 421.9808547342309` 236.97757582623348` 0.35584899936255093` 0.10372878993681817` 5 11
0.0025` 0.06` 87984.62069413853` 374.2899063828375` 267.1725801168582` 0.36584899936255094` 0.1054514320712951` 5 11
0.0025` 0.075` 108319.58024816486` 270.39003066188457` 369.8361206410281` 0.3958489993625509` 0.11026601685483112` 5 11
0.0025` 0.1` 149132.65335545156` 170.97576044224454` 584.8782291790417` 0.44584899936255096` 0.11754055956584397` 5 11
0.005` 0.001` 330061.8228248859` + 262021.80242259605` 4677.246955945027` 21.38009836596178` 0.2496493037286791` 0.10783147523795109` - 0.10783147523795106` 5 11
0.005` 0.005` 157080.78820272736` + 79357.52788049362` 3158.6482716400988` 31.659112189808937` 0.2576493037286791` 0.05934319122208691` - 0.059343191222086894` 5 11
0.005` 0.0075` 146009.10227254708` + 28594.98213557498` 2596.964205150805` 38.50649916608805` 0.2626493037286791` 0.035622282765610545` - 0.03562228276561054` 5 11
0.005` 0.01` 96705.62732006777` 2188.736525853748` 45.68845944625225` 0.2676493037286791` 0.06372028052770176` 5 11
0.005` 0.025` 59424.69253143692` 1039.1235610720157` 96.23494620489079` 0.2976493037286791` 0.09147858798548161` 5 11
0.005` 0.03` 60038.05784026897` 861.2716000228073` 116.10739283328499` 0.3076493037286791` 0.09463800619217913` 5 11
0.005` 0.04` 65666.62520044619` 622.0640229088812` 160.75515753568635` 0.3276493037286791` 0.09955073098592805` 5 11
0.005` 0.045` 69840.20267982007` 538.6394134959389` 185.65295723714053` 0.3376493037286791` 0.10163416224349792` 5 11
0.005` 0.05` 74653.4233140105` 470.9242951659266` 212.348356257062` 0.3476493037286791` 0.10356968567835709` 5 11
0.005` 0.055` 80001.55705139412` 415.1055318858215` 240.90259540917387` 0.3576493037286791` 0.10539606150066275` 5 11
0.005` 0.06` 85816.45639779433` 368.49118066325286` 271.3769155072001` 0.3676493037286791` 0.10713837993300548` 5 11
0.005` 0.075` 105664.60510134185` 266.7144835138095` 374.9327696139994` 0.3976493037286791` 0.11200773407843005` 5 11
0.005` 0.1` 145611.2271384103` 169.02076306745306` 591.6432879911438` 0.4476493037286791` 0.11936540505948895` 5 11
0.01` 0.001` 349172.49118223536` + 272206.7934511768` 4053.1877419928333` 24.671938820882986` 0.25350565087896476` 0.11161869684110305` - 0.11161869684110305` 5 13
0.01` 0.005` 161901.41009027176` + 82424.11983472583` 2835.7699448774197` 35.263791472450585` 0.26150565087896477` 0.061420680957682626` - 0.061420680957682626` 5 13
0.01` 0.0075` 149604.72308567213` + 29780.53193175065` 2363.3392739626674` 42.3130107055377` 0.2665056508789648` 0.036919319996391566` - 0.036919319996391566` 5 13
0.01` 0.01` 98019.57285836035` 2012.0054132858868` 49.70165554211209` 0.2715056508789648` 0.06586637483509802` 5 13
0.01` 0.025` 57665.32948187693` 984.3474198705007` 101.59014793085542` 0.30150565087896475` 0.09452658572413163` 5 13
0.01` 0.03` 57839.557593506055` 820.0166176678932` 121.94874816610123` 0.31150565087896476` 0.09776941614442324` 5 13
0.01` 0.04` 62739.89333864433` 596.5624365850099` 167.6270476774313` 0.3315056508789648` 0.10280274979836841` 5 13
0.01` 0.045` 66582.41885643917` 517.9489281383109` 193.06922858096243` 0.3415056508789648` 0.10493483817349251` 5 13
0.01` 0.05` 71073.34886885867` 453.8679163909695` 220.32841800136922` 0.3515056508789648` 0.10691468121896883` 5 13
0.01` 0.055` 76102.76129995367` 400.8564590835458` 249.4658567523748` 0.36150565087896475` 0.10878232495842735` 5 13
0.01` 0.06` 81599.14956248316` 356.45186800696024` 280.54278564770317` 0.37150565087896475` 0.11056367385473717` 5 13
0.01` 0.075` 100473.6349431416` 259.05197456587337` 386.0229213368586` 0.4015056508789647` 0.11554129549961882` 5 13
0.01` 0.1` 138682.04095669155` 164.92702747147996` 606.3287596527655` 0.45150565087896477` 0.12306279367872311` 5 13
0.015` 0.001` 368794.9263650986` + 282334.2836688006` 3523.86606578568` 28.377923034854074` 0.25768672058002184` 0.11556589906694435` - 0.11556589906694435` 5 13
0.015` 0.005` 166805.5428716422` + 85557.16548824379` 2543.6065812819593` 39.3142558821344` 0.26568672058002185` 0.06361742515994716` - 0.06361742515994716` 5 13
0.015` 0.0075` 153246.8570760059` + 31233.80448267484` 2146.5854064768296` 46.58561438937997` 0.27068672058002186` 0.03843796060064515` - 0.03843796060064515` 5 13
0.015` 0.01` 99568.02767810467` 1844.9619648650007` 54.201659386142` 0.27568672058002186` 0.0679699557238718` 5 13
0.015` 0.025` 56062.84956594195` 929.6701609417258` 107.56503134262508` 0.30568672058002183` 0.09763548475001968` 5 13
0.015` 0.03` 55798.66730028281` 778.4685247318085` 128.45734518868466` 0.31568672058002184` 0.1009648544570141` 5 13
0.015` 0.04` 59975.43216102687` 570.5606588309223` 175.26620255399285` 0.33568672058002186` 0.10612100677496444` 5 13
0.015` 0.045` 63489.74520754672` 496.75808791555824` 201.30522770068842` 0.3456867205800218` 0.10830193400237109` 5 13
0.015` 0.05` 67661.25313716028` 436.3338611154053` 229.18230490837655` 0.3556867205800218` 0.11032597146409102` 5 13
0.015` 0.055` 72374.73165735656` 386.16200057233164` 258.95867499078054` 0.36568672058002183` 0.11223456102446407` 5 13
0.015` 0.06` 77555.24811265324` 344.00247993452285` 290.69557876162395` 0.37568672058002184` 0.1140544888986271` 5 13
0.015` 0.075` 95462.74201623647` 251.07844447393796` 398.2819003420267` 0.40568672058002186` 0.11913861300426602` 5 13
0.015` 0.1` 131938.99219009816` 160.63768809302394` 622.5189193590166` 0.45568672058002185` 0.12682057350578366` 5 13



  superalloy
  
  
  
   thrust = 
  
  
  
  500000
  
  
  
   vol in^3 = 
  
  
  
  871.7682000000002`


rBot Wall stress lbf sp thrust weight dia r max stress min # noz max # noz
0.0025` 0.001` 466434.10508122056` + 341840.3125338378` 5319.413101774797` 93.99533189726844` 0.42116194020677555` 0.20846502446519818` - 0.20846502446519816` 0 0
0.0025` 0.005` 180593.8919266533` + 128824.89714766777` 4074.244955787645` 122.72212530808392` 0.42916194020677556` 0.12797391753650733` - 0.12797391753650733` 0 0
0.0025` 0.0075` 158709.51435772236` + 89922.39700610947` 3536.5699911331044` 141.3799249706923` 0.43416194020677557` 0.10691915064900012` - 0.10691915064900012` 0 0
0.0025` 0.01` 148901.83997594457` + 61150.81232399303` 3113.55562091914` 160.58810597139652` 0.43916194020677557` 0.08817037295819623` - 0.08817037295819623` 0 0
0.0025` 0.025` 71145.74930064706` 1737.1734060896986` 287.8238857717021` 0.46916194020677554` 0.1333897387273052` 0 0
0.0025` 0.03` 65234.514563929406` 1492.6001614596776` 334.9858943543385` 0.47916194020677555` 0.14108878993232804` 0 0
0.0025` 0.04` 60964.46897345739` 1144.6821472134582` 436.8024793757539` 0.49916194020677557` 0.1507942370848444` 0 0
0.0025` 0.045` 60803.245461742976` 1017.1294000597295` 491.5795374419797` 0.5091619402067755` 0.1543216770315157` 0 0
0.0025` 0.05` 61424.07998658759` 910.7179033739973` 549.0174269635162` 0.5191619402067755` 0.15737428187659463` 0 0
0.0025` 0.055` 62624.58766005277` 820.77898692632` 609.1773887540865` 0.5291619402067755` 0.16009707974818643` 0 0
0.0025` 0.06` 64274.83930966836` 743.9140426088309` 672.1206636274146` 0.5391619402067755` 0.16258022206792788` 0 0
0.0025` 0.075` 71174.04023359057` 569.3056956303841` 878.2627748811776` 0.5691619402067756` 0.1690962344473598` 0 0
0.0025` 0.1` 87013.34385014401` 389.64630855110033` 1283.2150312401263` 0.6191619402067756` 0.17825260277100854` 0 0
0.005` 0.001` 475416.81559023215` + 345863.85463782446` 5089.1002664583275` 98.24919412483227` 0.42290746170104015` 0.21056148466601274` - 0.21056148466601274` 0 0
0.005` 0.005` 182693.75326765917` + 130317.94346510395` 3930.464689955211` 127.21142140719691` 0.43090746170104016` 0.1292493757961077` - 0.1292493757961077` 0 0
0.005` 0.0075` 160230.95712589144` + 90950.2831118006` 3424.206700786919` 146.01922246256177` 0.43590746170104017` 0.10797628299209662` - 0.1079762829920966` 0 0
0.005` 0.01` 150130.92342483753` + 61832.47675447112` 3023.347477125991` 165.37960118143693` 0.44090746170104017` 0.08902965017790536` - 0.08902965017790536` 0 0
0.005` 0.025` 71005.37212637329` 1703.1440952488717` 293.57469012446506` 0.47090746170104014` 0.1347189895879387` 0 0
0.005` 0.03` 64935.64276647924` 1465.9573664117424` 341.0740390246555` 0.48090746170104015` 0.14248390933547303` 0 0
0.005` 0.04` 60449.16344166432` 1127.16275896466` 443.59166058614994` 0.5009074617010402` 0.15226842492928178` 0 0
0.005` 0.045` 60204.90151797017` 1002.5416136735715` 498.7324148749005` 0.5109074617010402` 0.15582315982796188` 0 0
0.005` 0.05` 60751.845176600655` 898.4035237702585` 556.542785920618` 0.5209074617010402` 0.15889872885840373` 0 0
0.005` 0.055` 61884.66837175251` 810.2624411282633` 617.0840145370266` 0.5309074617010402` 0.1616415225909849` 0 0
0.005` 0.06` 63471.542297554835` 734.843116828743` 680.4173415378484` 0.5409074617010401` 0.1641425379674034` 0 0
0.005` 0.075` 70195.44029785457` 563.2011228223039` 887.7823209840357` 0.5709074617010401` 0.17070413836133672` 0 0
0.005` 0.1` 85760.36392584392` 386.1157719849704` 1294.9483970301592` 0.6209074617010402` 0.17992266283681438` 0 0
0.01` 0.001` 493637.95961126685` + 353894.3700365489` 4660.852128513697` 107.2765207334406` 0.42655225493353544` 0.21483631741330236` - 0.2148363174133023` 7 7
0.01` 0.005` 186942.62751321864` + 133308.28703288612` 3656.7496486044147` 136.73345130171094` 0.43455225493353544` 0.1318558632830339` - 0.1318558632830339` 7 7
0.01` 0.0075` 163305.50063448475` + 93019.13442182376` 3208.081205780216` 155.85640385259472` 0.43955225493353545` 0.11014302996892503` - 0.11014302996892503` 7 7
0.01` 0.01` 152611.8164677141` + 63221.23443658406` 2848.4101171564353` 175.53652017608678` 0.44455225493353545` 0.09080345183651709` - 0.09080345183651709` 7 7
0.01` 0.025` 70769.31945229997` 1635.3425360121298` 305.7463430378794` 0.4745522549335354` 0.13739528095620124` 7 7
0.01` 0.03` 64379.76505816077` 1412.613102896356` 353.9539587837772` 0.48455225493353543` 0.14529740305481953` 7 7
0.01` 0.04` 59458.08773933604` 1091.8385893486743` 457.9431473458641` 0.5045522549335354` 0.1552448250570897` 7 7
0.01` 0.045` 59047.26179005323` 973.0519077630937` 513.8472017895` 0.5145522549335354` 0.15885530408644383` 7 7
0.01` 0.05` 59446.14271486651` 873.4551805305035` 572.4392174264962` 0.5245522549335354` 0.16197756365721433` 7 7
0.01` 0.055` 60443.439209122145` 788.9167483441203` 633.7804350705757` 0.5345522549335354` 0.1647608565586786` 7 7
0.01` 0.06` 61903.47302989698` 716.4020729214266` 697.9320955354623` 0.5445522549335354` 0.16729795185026985` 7 7
0.01` 0.075` 68276.67845770414` 550.7444102722558` 907.8621419921985` 0.5745522549335355` 0.17395111693598153` 7 7
0.01` 0.1` 83292.53803434847` 378.8825367197469` 1319.6702184504272` 0.6245522549335354` 0.18329367524710166` 7 7
0.015` 0.001` 512186.39696098794` + 361899.1827626346` 4273.311985988555` 117.00526468449134` 0.4303964194776103` 0.21921958647468087` - 0.21921958647468087` 7 7
0.015` 0.005` 191252.97788546444` + 136303.31091252432` 3401.626694800693` 146.9884984040837` 0.4383964194776103` 0.1345360757317307` - 0.13453607573173068` 7 7
0.015` 0.0075` 166419.05808707478` + 95105.05230650009` 3003.965020790616` 166.44667848642416` 0.4433964194776103` 0.11237956517544985` - 0.11237956517544984` 7 7
0.015` 0.01` 155120.28233204194` + 64644.136912978356` 2681.441634426067` 186.46685931205047` 0.44839641947761033` 0.0926510026853978` - 0.0926510026853978` 7 7
0.015` 0.025` 70592.77693328541` 1568.2897062206227` 318.8186455708723` 0.4783964194776103` 0.14009426454622692` 7 7
0.015` 0.03` 63879.85656849608` 1359.5123020473943` 367.77894488119864` 0.4883964194776103` 0.14814090399837895` 7 7
0.015` 0.04` 58520.32475502544` 1056.3420209478347` 473.33154422027064` 0.5083964194776103` 0.15825760562296617` 7 7
0.015` 0.045` 57942.50364684596` 943.3137738917823` 530.0463258764635` 0.5183964194776103` 0.16192536762386084` 7 7
0.015` 0.05` 58193.16508079612` 848.2218655183478` 589.4684166087259` 0.5283964194776103` 0.16509533191370476` 7 7
0.015` 0.055` 59054.94387176109` 767.2723864604069` 651.659057230781` 0.5383964194776103` 0.1679197973807689` 7 7
0.015` 0.06` 60388.24683922457` 697.6619367287576` 716.6794885563522` 0.5483964194776103` 0.17049341371806864` 7 7
0.015` 0.075` 66411.33605309646` 538.0208956861353` 929.3319348913999` 0.5783964194776103` 0.17723864741149994` 7 7
0.015` 0.1` 80878.9922312127` 371.45327991180955` 1346.0643021343362` 0.6283964194776104` 0.18670484057933415` 7 7



  
    Syntax
    
    ::
    
    sntxf
  
  
  
    :
    
      
    
  
  
  \"μ=.\" cannot be followed by \";\".
  
  





  
    μ
    =.
  
  ;





  
    (*
    
    
      TableForm
      
      
        [
        
          Chop
          
          
            [
            
              
                (
                
                  sa005maxtstress
                  =
                  
                    
                      
                        
                          
                            
                              {
                              
                                thicknessOfChamberWall
                                ,
                                combustionChamberHeight
                                ,
                                rBot
                                ,
                                maxtstressformula
                                ,
                                
                                  maxtstressformula
                                  6894.8
                                
                                ,
                                
                                  nominalThrustlbf
                                  weightOfEnginelb
                                
                                ,
                                weightOfEnginelb
                                ,
                                nominalThrustlbf
                                ,
                                volumeOfCombustionChamberIn3
                                ,
                                enginediameter
                                ,
                                r
                              
                              }
                            
                            /.
                            
                            
                            stuff
                          
                          /.
                          maxrvalue
                        
                        
                        
                          
                        
                        /.
                        
                          Join
                          [
                          
                          
                          
                            geometry
                            ,
                            fuel
                            ,
                            oxidizer
                            ,
                            metal
                            ,
                            velocity
                          
                          ]
                        
                      
                      /.
                      
                      
                      
                        thicknessOfChamberWall
                        
                        
                          
                        
                        
                        
                          
                        
                        
                        .005
                      
                    
                    /.
                    
                      THRUST
                      
                      
                        1000
                        *
                        
                          32
                          /
                          2.2
                        
                      
                    
                  
                
                )
              
              ,
              
                10
                ^
                
                  -
                  6
                
              
            
            ]
          
        
        ]
      
    
    
    *)
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  
  
  
    &IndentingNewLine;
  





  





  





  





  
    ω
    
    
      
    
    =.
  
  ;





  
    radialelongation
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    
      modulusElasticity
      
      
        
      
      =.
    
    ;
  
  
  
    

  
  
  
    (*
    
    
      
        μ
        
        
          
        
        =
        
          
        
        .
      
      ;
    
    
    *)
  





  
    ρ
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    p
    =
    
      
    
    .
  
  ;





  
    ω
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r1
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    r2
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    thicknessOfChamberWall
    
    
      
    
    =.
  
  ;





  
    pinterference
    
    
      
    
    =
    
      
    
    .
  
  ;





  
    
      chFROMthrust
      =
      
        Solve
        
        
          [
          
            
              THRUST
              
              nominalThrust
            
            ,
            combustionChamberHeight
          
          ]
        
      
    
    ;
  
  
  
    

  
  
  
    &IndentingNewLine;
  
  
  
    

  
  
  
    &IndentingNewLine;
  





  
    
      geometry
      
      
        
      
      =
      
        
      
      
      
        {
        
          
            thicknessOfChamberWall
            
            
              
            
            ->
            
              
            
            
            .01
          
          ,
          
            rBot
            
            
              
            
            
            
              {
              
                .001
                ,
                .0025
                ,
                .005
                ,
                .01
                ,
                .015
                ,
                .02
                ,
                .025
              
              }
            
          
          ,
          
            THRUST
            
            
              1000
              *
              
                32
                /
                2.2
              
            
          
          ,
          
            rTubesInner
            
            
              
            
            ->
            
              
            
            
            .001
          
          ,
          
            rTubesOuter
            
            
              
            
            ->
            
              
            
            
            .001
          
          ,
          
            
          
          
          
            lStar
            
            
              
            
            ->
            
              
            
            
            .275
          
        
        }
      
    
    ;
  
  
  
    

  





  Chop
  
  
    [
    
      
        chFROMthrust
        /.
        
          {
          
            
              r1
              
              
                
              
              
              rInner
            
            ,
            
              p
              
              chamberPressure
            
            ,
            
              μ
              
              .3
            
            ,
            
              ρ
              
              density
            
            ,
            
              r
              
              
                rInner
                
                
                  
                
                +
                
                  
                
                
                linterference
              
            
            ,
            
              radialelongation
              
              
                
              
              
              linterference
            
            ,
            
              r2
              
              
                
              
              
              
                
              
              
              rOuter
            
            
            
              
            
            ,
            
              wallthickness
              
              
                
              
              ->
              
                
              
              
              thicknessOfChamberWall
            
            ,
            
              
            
            
            
              ω
              ->
              
                
              
              
              
                rotationalVelocityNominal
                /
                rInjector
              
            
          
          
          
            
          
          }
        
      
      /.
      
        Join
        
        
          [
          
            geometry
            ,
            fuel
            ,
            oxidizer
            ,
            velocity
            ,
            aluminum
          
          ]
        
      
    
    ]
  





  {
  
    
      {
      
        combustionChamberHeight
        
        
          {
          
            
              
                -
                0.013824417039863798`
              
              -
              
                0.022760620626792547`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.014866698621239129`
              
              -
              
                0.022680149855586685`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.01667641851577445`
              
              -
              
                0.02237812398804479`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.020524949046253457`
              
              -
              
                0.021043351401422813`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.024611515438155627`
              
              -
              
                0.018452348094439918`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.028873790039330893`
              
              -
              
                0.013826932073298813`
                
                
                  
                
                
                
              
            
            ,
            
              -
              0.030696206486435652`
            
          
          }
        
      
      }
    
    ,
    
      {
      
        combustionChamberHeight
        
        
          {
          
            
              
                -
                0.013824417039863798`
              
              +
              
                0.022760620626792547`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.014866698621239129`
              
              +
              
                0.022680149855586685`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.01667641851577445`
              
              +
              
                0.02237812398804479`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.020524949046253457`
              
              +
              
                0.021043351401422813`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.024611515438155627`
              
              +
              
                0.018452348094439918`
                
                
                  
                
                
                
              
            
            ,
            
              
                -
                0.028873790039330893`
              
              +
              
                0.013826932073298813`
                
                
                  
                
                
                
              
            
            ,
            
              -
              0.03583800648441204`
            
          
          }
        
      
      }
    
    ,
    
      {
      
        combustionChamberHeight
        
        
          {
          
            0.0256488340797276`
            ,
            0.024733397242478257`
            ,
            0.0233528370315489`
            ,
            0.02104989809250691`
            ,
            0.019223030876311255`
            ,
            0.017747580078661774`
            ,
            0.01653421297084768`
          
          }
        
      
      }
    
  
  }





  
    Syntax
    
    ::
    
    sntxf
  
  
  
    :
    
      
    
  
  
  \"μ=.\" cannot be followed by \";\".
  
  





  
    μ
    =.
  
  ;





  
    thicknessOfChamberWall
    
    
      
    
    =.
  
  ;





  
    geometry
    
    
      
    
    =
    
      
    
    
    
      {
      
        
          rBot
          
          
            
          
          ->
          
            
          
          
          .005
        
        ,
        
          rTubesInner
          
          
            
          
          ->
          
            
          
          
          .001
        
        ,
        
          
        
        
        
          lStar
          
          
            
          
          ->
          
            
          
          
          .275
        
      
      }
    
  
  ;





  
    Solve
    
    
      [
      
        
          1000
          
          maxtstressformula
        
        ,
        thicknessOfChamberWall
      
      ]
    
  
  ;





  
    
      maxtstressformula
      /.
      
        {
        
          
            r1
            
            
              
            
            
            rInner
          
          ,
          
            p
            
            chamberPressure
          
          ,
          
            μ
            
            .3
          
          ,
          
            ρ
            
            density
          
          ,
          
            r
            
            
              rInner
              
              
                
              
              +
              
                
              
              
              linterference
            
          
          ,
          
            radialelongation
            
            
              
            
            
            linterference
          
          ,
          
            r2
            
            
              
            
            
            
              
            
            
            rOuter
          
          
          
            
          
          ,
          
            wallthickness
            
            
              
            
            ->
            
              
            
            
            thicknessOfChamberWall
          
          ,
          
            
          
          
          
            ω
            ->
            
              
            
            
            
              rotationalVelocityNominal
              /
              rInjector
            
          
        
        
        
          
        
        }
      
    
    /.
    
      Join
      
      
        [
        
          geometry
          ,
          fuel
          ,
          oxidizer
          ,
          velocity
          ,
          aluminum
        
        ]
      
    
  
  ;





  
    
      
        {
        
          {
          
            thicknessOfChamberWall
            
            
              
                -
                
                  (
                  
                    4
                    
                    
                      
                    
                    
                    
                      (
                      
                        
                          
                            -
                            combustionChamberHeight
                          
                          
                          
                            
                          
                          
                          p
                          
                          
                            
                          
                          
                          
                            r
                            2
                          
                          
                          
                            
                          
                          
                          
                            r1
                            5
                          
                        
                        -
                        
                          2
                          
                          
                            
                          
                          
                          combustionChamberHeight
                          
                          
                            
                          
                          
                          p
                          
                          
                            
                          
                          
                          
                            r
                            2
                          
                          
                          
                            
                          
                          
                          
                            r1
                            3
                          
                          
                          
                            
                          
                          
                          
                            r2
                            2
                          
                        
                        -
                        
                          combustionChamberHeight
                          
                          
                            
                          
                          
                          p
                          
                          
                            
                          
                          
                          
                            r
                            2
                          
                          
                          
                            
                          
                          
                          r1
                          
                          
                            
                          
                          
                          
                            r2
                            4
                          
                        
                        +
                        
                          combustionChamberHeight
                          
                          
                            
                          
                          
                          p
                          
                          
                            
                          
                          
                          
                            r
                            2
                          
                          
                          
                            
                          
                          
                          
                            r1
                            5
                          
                          
                          
                            
                          
                          
                          μ
                        
                        -
                        
                          combustionChamberHeight
                          
                          
                            
                          
                          
                          p
                          
                          
                            
                          
                          
                          
                            r
                            2
                          
                          
                          
                            
                          
                          
                          r1
                          
                          
                            
                          
                          
                          
                            r2
                            4
                          
                          
                          
                            
                          
                          
                          μ
                        
                      
                      )
                    
                  
                  )
                
              
              /
              
                (
                
                  
                    (
                    
                      
                        r1
                        2
                      
                      -
                      
                        r2
                        2
                      
                    
                    )
                  
                  
                  
                    
                  
                  
                  
                    (
                    
                      
                        
                          -
                          32000
                        
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        r1
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                      
                      -
                      
                        3
                        
                        
                          
                        
                        
                        
                          r
                          4
                        
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        3
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r1
                          4
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        3
                        
                        
                          
                        
                        
                        
                          r
                          4
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        6
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        3
                        
                        
                          
                        
                        
                        
                          r1
                          4
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        3
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          4
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        3
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          4
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        2
                        
                        
                          
                        
                        
                        
                          r
                          4
                        
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        μ
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        2
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r1
                          4
                        
                        
                        
                          
                        
                        
                        μ
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        2
                        
                        
                          
                        
                        
                        
                          r
                          4
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        μ
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        4
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        μ
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        2
                        
                        
                          
                        
                        
                        
                          r1