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
      
    
    
    
      
    
    ;
  
  
  
    &IndentingNewLine;
  
  
  
    (*
    
    
      
    
    
    
      rTop
      ,
      
        
      
      
      rCenter
      ,
      rBot
    
    
    *)
  





  
    fuelfeedvelocity
    
    
      
    
    =
    flowRateInnerLox
  
  
  
    
  
  ;





  
    
  
  
  
    
      qPerKey
      
      
        
      
      =
      
        
      
      
      
        Q
        /
        
          (
          nominalFuelFlowMass
          )
        
      
    
    
    
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  
    
  
  
  
    
      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
            
            )
          
        
      
      ]
    
  
  
  
    
  
  
  
    &IndentingNewLine;
  
  
  
    (*
    
    
      
    
    
    
      seems
      
      
        
      
      
      to
      
      
        
      
      
      be
      
      
        
      
      
      about
      
      
        
      
      
      5.000
      
      
        
      
      
      or
      
      
        
      
      
      about
      
      
        
      
      
      2.500
      
      
        
      
      
      C
      
      
        
      
      
      for
      
      
        
      
      
      propane
      
      
        
      
      
      5.000
      
      
        
      
      
      C
      
      
        
      
      
      for
      
      
        
      
      
      oxygen
    
    
    *)
  




Null




  Q = 
  
  
  
  
    -
    1243.4339874544225`
  





  coldQ per kilogram of fuel = 
  
  
  
  
    -
    483.7522934733797`
  





  cf kcal 
  
  
  
  2.`
  
  
  
   
  
  
  
  8373.6`
  
  
  
   Watts





  fuelfeedvelocity  = 
  
  
  
  47.955059258751795`





  nominalFuelFlowMass = 
  
  
  
  2.5703939893007397`





  aprox degrees fuel temperature rise 
  
  
  
  
    -
    0.057771125140128464`
  





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





  analisys
  
  
    
  
  
  boundary
  
  
    
  
  
  by
  
  
    
  
  
  Cold
  
  
    
  
  
  convection
  
  
    
  
  
  Cooling
  
  
    
  
  
  dominated
  
  
    
  
  
  layer
  
  
    
  
  
  of
  
  
    
  
  
  side





  
    test
    
    
      
    
    
    firs
    
    
      
    
    
    for
    
    
      
    
    
    an
    
    
      
    
    
    aproximation
    
    
      
    
    
    
      I
      '
    
    
    ll
    
    
      
    
    
    use
    
    
      
    
    
    a
    
    
      
    
    
    formula
    
    
      
    
    
    for
    
    
      
    
    
    horizontal
    
    
      
    
    
    pipes
    
    
      
    
    
    which
    
    
      
    
    
    I
    
    
      
    
    
    have
    
    
      
    
    
    
      handy
      .
      
        
      
      
      I
    
    
    
      
    
    
    expect
    
    
      
    
    
    that
    
    
      
    
    
    both
    
    
      
    
    
    the
    
    
      
    
    
    horizontal
    
    
      
    
    
    and
    
    
      
    
    
    vertical
    
    
      
    
    
    components
    
    
      
    
    
    wull
    
    
      
    
    
    be
    
    
      
    
    
    very
    
    
      
    
    
    large
    
    
      
    
    
    with
    
    
      
    
    
    the
    
    
      
    
    
    vertical
    
    
      
    
    
    being
    
    
      
    
    
    larger
    
    
      
    
    
    because
    
    
      
    
    
    of
    
    
      
    
    
    the
    
    
      
    
    
    lenght
    
    
      
    
    
    of
    
    
      
    
    
    the
    
    
      
    
    
    tube
  
  ,
  
    
  
  
  
    but
    
    
      
    
    
    first
    
    
      
    
    
    
      we
      '
    
    
    ll
    
    
      
    
    
    see
    
    
      
    
    
    what
    
    
      
    
    
    this
    
    
      
    
    
    
      does
      .
      
        
      
      
      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
      .
    
  





  
    
      I
      '
    
    
    ll
    
    
      
    
    
    start
    
    
      
    
    
    with
    
    
      
    
    
    the
    
    
      
    
    
    WRONG
    
    
      
    
    
    simple
    
    
      
    
    
    formula
    
    
      
    
    
    for
    
    
      
    
    
    isothermal
    
    
      
    
    
    horizontal
    
    
      
    
    
    circular
    
    
      
    
    
    cylinders
    
    
      
    
    
    Nu
  
  
  
    
  
  =
  
    
  
  
  
    
      (
      
        0.60
        +
        
          
            0.38
            
            
              Ra
              
                1
                6
              
            
          
          
            
              (
              
                1
                +
                
                  
                    (
                    
                      0.559
                      Pr
                    
                    )
                  
                  
                    9
                    16
                  
                
              
              )
            
            
              8
              27
            
          
        
      
      )
    
    2
  





  
    

  
  
  
    

  
  
  
    
      
        ρlocal
        
        
          
        
        =.
      
      ;
    
    
    
      

    
    
    
      

    
    
    
      

    
    
    
      
        
          c
          p
        
        
        
          
        
        =.
      
      
      
        
      
      ;
    
    
    
      

    
    
    
      
        
          ρ
          am
        
        =.
      
      ;
    
    
    
      
    
    
    
      

    
    
    
      
        
          ρ
          
        
        =.
      
      ;
    
    
    
      

    
    
    
      
        
          μ
          am
        
        =.
      
      ;
    
    
    
      

    
    
    
      
        
          μ
          0
        
        =.
      
      ;
    
    
    
      

    
    
    
      
        μlocal
        =.
      
      ;
    
    
    
      

    
    
    
      

    
    
    
      

    
  





  
    Unset
    
    ::
    
    norep
  
  
  
    :
    
      
    
  
  
  Assignment on \!\(Subscript\) for \!\(c\_p\) not found.





  
    Unset
    
    ::
    
    norep
  
  
  
    :
    
      
    
  
  
  Assignment on \!\(Subscript\) for \!\(ρ\_am\) not found.





  
    Unset
    
    ::
    
    norep
  
  
  
    :
    
      
    
  
  
  Assignment on \!\(Derivative\) for \!\(\*SuperscriptBox[\"ρ\", \"′\", Rule[MultilineFunction, None]]\) not found.





  
    General
    
    ::
    
    stop
  
  
  
    :
    
      
    
  
  
  Further output of \!\(Unset :: \"norep\"\) will be suppressed during this calculation.





  Null
  7





  
    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
          
        
        }
      
    
    ;
  
  
  
    &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
        
      
      ;
    
    
    
      &IndentingNewLine;
    
  
  
  
    (*
    
    
      
        Nuhoriz
        
        
          
        
        =
        
          
        
        
        
          
            (
            
              0.60
              +
              
                
                  0.38
                  
                  
                    Ra
                    
                      1
                      6
                    
                  
                
                
                  
                    (
                    
                      1
                      +
                      
                        
                          (
                          
                            0.559
                            Pr
                          
                          )
                        
                        
                          9
                          16
                        
                      
                    
                    )
                  
                  
                    8
                    27
                  
                
              
            
            )
          
          2
        
      
      ;
      
        &IndentingNewLine;
      
      
      
        nussresult
        
        
          
        
        =
        
          
        
        
        
          
            
              
                
                  
                    
                      Nuhoriz
                      /.
                      
                        μ
                        
                        
                          
                        
                        
                        μlocal
                      
                    
                    /.
                    LOXcharisterics
                  
                  /.
                  
                    L
                    
                    
                      
                    
                    ->
                    
                      2
                      
                      
                        
                      
                      
                      rTubesInner
                    
                  
                
                
                
                  
                
                /.
                
                  geffective
                  
                  
                    
                  
                  
                  
                    
                  
                  
                  
                    10
                    7
                  
                
              
              /.
              
                β
                
                
                  
                
                
                1
              
            
            
            
              
            
            /.
            
              
            
            
            
              TFluid
              
              
                
              
              
              
                
              
              
              100
            
          
          
          
            
          
          /.
          geometry
        
      
    
    
    *)
  
  
  
    
  
  
  
    (*
    
    
      
        oops
        
        
          
        
        
        wrong
        
        
          
        
        
        equation
      
      ,
      
        
      
      
      
        this
        
        
          
        
        
        is
        
        
          
        
        
        for
        
        
          
        
        
        wires
      
    
    
    *)
  





  
    raresult
    
    
      
    
    =
    
      
    
    
    
      
        
          
            
              
                
                  
                    Ra
                    
                    
                      
                    
                    /.
                    
                      μ
                      
                      
                        
                      
                      
                      μlocal
                    
                  
                  /.
                  
                    ρ
                    
                    
                      
                    
                    
                    ρlocal
                  
                
                /.
                LOXcharisterics
              
              /.
              
                L
                
                
                  
                
                ->
                
                  2
                  
                  
                    
                  
                  
                  rTubesInner
                
              
            
            
            
              
            
            /.
            
              geffective
              
              
                
              
              
              
                
              
              
              
                10
                7
              
            
          
          /.
          
            β
            
            
              
            
            
            1
          
        
        
        
          
        
        /.
        
          
        
        
        
          TFluid
          
          
            
          
          
          
            
          
          
          100
        
      
      
      
        
      
      /.
      geometry
    
  
  ;





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





  
    
  
  
  
    
      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
    
  





  
    &IndentingNewLine;
  
  
  
    
      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
            
          
          ]
        
      
    
  





  
    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
    
  
  ;





  
    
      ralocal
      
      
        
      
      =
      
        
          
            
              
                
                  
                    
                      Ra
                      
                      
                        
                      
                      /.
                      
                        μ
                        
                        
                          
                        
                        
                        μlocal
                      
                    
                    /.
                    
                      ρ
                      
                      
                        
                      
                      
                      ρlocal
                    
                  
                  /.
                  propanecharisterics
                
                /.
                
                  L
                  
                  
                    
                  
                  
                  lTube
                
              
              
              
                
              
              /.
              
                geffective
                
                
                  
                
                
                
                  
                
                
                
                  10
                  7
                
              
            
            /.
            
              β
              
              
                
              
              
              1
            
          
          
          
            
          
          /.
          
            
          
          
          
            TFluid
            
            
              
            
            
            
              
            
            
            100
          
        
        
        
          
        
        /.
        geometry
      
    
    ;
  
  
  
    &IndentingNewLine;
  





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





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





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





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





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





  
    Print
    
    
      [
      
        heat LOX =
        ,
        
          
        
        
        
          
            
              nuavllocalLOX
              *
              nTubesOuter
              
              
                
              
              *
              thermalConductivity
            
            /.
            LOXcharisterics
          
          /.
          geometry
        
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        heat propane =
        ,
        
          
        
        
        
          
            
              nuavllocalpropane
              *
              nTubesOuter
              
              
                
              
              *
              thermalConductivity
            
            /.
            propanecharisterics
          
          /.
          geometry
        
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        heat LOX.25 =
        ,
        
          
        
        
        
          
            
              nuavllocalLOX25
              *
              nTubesOuter
              
              
                
              
              *
              thermalConductivity
            
            /.
            LOXcharisterics
          
          /.
          geometry
        
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        heat propane.25 =
        ,
        
          
        
        
        
          
            
              nuavllocalpropane25
              *
              nTubesOuter
              
              
                
              
              *
              thermalConductivity
            
            /.
            propanecharisterics
          
          /.
          geometry
        
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        Ra = 
        ,
        ralocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        Gz = 
        ,
        gzlocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        Ren = 
        ,
        renlocal
      
      ]
    
  
  ;





  
    Print
    
    
      [
      
        Pr = 
        ,
        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
              
            
          
        
      
      ]
    
  





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





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





  heat LOX =
  
  
  
  50727.81066938628`





  heat propane =
  
  
  
  17853.334259333`





  heat LOX.25 =
  
  
  
  31957.93919030494`





  heat propane.25 =
  
  
  
  11248.316773655595`





  Ra = 
  
  
  
  8.280710963738316`*^14





  Gz = 
  
  
  
  17.475182282601978`





  Ren = 
  
  
  
  853.8752872733797`





  Pr = 
  
  
  
  0.07235728729166667`





  



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
      
      
      *)
    
  
  
  
    &IndentingNewLine;
  
  
  
    

  
  
  
    

  
  
  
    

  




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




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





  badness ratio = 
  
  
  
  182.41583839231004`





  


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
                
                }
              
            
          
          }
        
      
      }
    
  
  ;





  
    (*
    
    
      
        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
          
        
        }
      
    
    ;
  
  
  
    &IndentingNewLine;
  





  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
                          4
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        μ
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        2
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          4
                        
                        
                        
                          
                        
                        
                        μ
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        2
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          4
                        
                        
                        
                          
                        
                        
                        μ
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        
                          r
                          4
                        
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        
                          μ
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r1
                          4
                        
                        
                        
                          
                        
                        
                        
                          μ
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        
                          r
                          4
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        
                          μ
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        2
                        
                        
                          
                        
                        
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        
                          μ
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        
                          r1
                          4
                        
                        
                        
                          
                        
                        
                        
                          r2
                          2
                        
                        
                        
                          
                        
                        
                        
                          μ
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      -
                      
                        
                          r
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          4
                        
                        
                        
                          
                        
                        
                        
                          μ
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                      +
                      
                        
                          r1
                          2
                        
                        
                        
                          
                        
                        
                        
                          r2
                          4
                        
                        
                        
                          
                        
                        
                        
                          μ
                          2
                        
                        
                        
                          
                        
                        
                        ρ
                        
                        
                          
                        
                        
                        
                          ω
                          2
                        
                      
                    
                    )
                  
                
                )
              
            
          
          }
        
        }
      
      /.
      
        {
        
          
            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
  
  
    {
    
      0.025648834079727574`
      ,
      0.02473339724247823`
      ,
      0.023352837031548883`
      ,
      0.021049898092506885`
    
    }
  





  rBot
  
  
    
  
  
  
    {
    
      .001
      ,
      .0025
      ,
      .005
      ,
      .01
    
    }
  





  combustionChamberHeight
  
  
    {
    
      0.025648834079727574`
      ,
      0.02473339724247823`
      ,
      0.023352837031548883`
      ,
      0.021049898092506885`
    
    }
  





  rBot
  
  
    {
    
      0.001`
      ,
      0.0025`
      ,
      0.005`
      ,
      0.01`
    
    }
  





  combustionChamberHeight
  
  
    {
    
      0.025648834079727574`
      ,
      0.02473339724247823`
      ,
      0.023352837031548883`
      ,
      0.021049898092506885`
    
    }
  





  combustionChamberHeight
  
  
    {
    
      0.025648834079727574`
      ,
      0.02473339724247823`
      ,
      0.023352837031548883`
      ,
      0.021049898092506885`
    
    }
  




|




  
    Syntax
    
    ::
    
    sntxi
  
  
  
    :
    
      
    
  
  
  Incomplete expression; more input is needed.\!\(\"\"\)




System`Convert`MathMLDump`ToSymbolicMathML[ErrorBox["|"]]


Converted by Mathematica      May 25, 2002