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

Geometry

[Graphics:Images/index_gr_28.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
    = (1+)
     = (1-)
    Stresses for the rotational component are
    σ=ρ(- - )
    σ=ρ()

    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.)

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

[Graphics:Images/index_gr_48.gif]

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 ....

Chemistry

Pressure

Thermal

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 =
equations (8-20) & (8-23) from Sutton 7th ed. My intuition fails me here without a good reference.

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 =
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.

Combined Hot & cold thermal balance and temperatures distribution

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

[Graphics:Images/index_gr_161.gif]

`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`

`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`

`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`

`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`		260.67452314614565`	0.38362015126401744`	0.04602083984793304`		`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`

`rBot`	`Wall`	`stress lbf`	`sp thrust`	`weight`	`dia`	`r max stress`	`min # noz`	`max # noz`
0.0025`	0.001`		3273.952061017332`	0.3054412469586574`	0.05646679448495651`		`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`		2547.7445930861268`	0.39250402207259033`	0.058705674063097804`		`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`		1534.486416625366`	0.6516838397300347`	0.06409979618501382`		`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`		963.5640341262127`	1.0378137462413992`	0.07044606175262251`		`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`

`rBot`	`Wall`	`stress lbf`	`sp thrust`	`weight`	`dia`	`r max stress`	`min # noz`	`max # noz`
0.0025`	0.001`		4333.554870198931`	2.3075743355110583`	0.1170812639592089`		`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`		3774.5097922538043`	2.6493506575403214`	0.11902867496457668`		`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`		2866.725523401293`	3.4883004732644487`	0.1234323786454386`		`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`		2196.9721349878114`	4.551719086803748`	0.1284433825685633`		`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`

`rBot`	`Wall`	`stress lbf`	`sp thrust`	`weight`	`dia`	`r max stress`	`min # noz`	`max # noz`
0.0025`	0.001`		4856.236815975474`	10.296038248282276`	0.1974952024011159`		`3`	`13`
0.0025`	0.005`		2975.346855971591`	16.804763417632753`	0.2054952024011159`		`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`		4446.369341676335`	11.24512971321213`	0.19932929524494244`		`5`	`13`
0.005`	0.005`		2797.6893609868675`	17.871891246125635`	0.20732929524494245`		`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`		3732.1330144195595`	13.397164518740043`	0.20331407466593046`		`5`	`17`
0.01`	0.005`		2464.99341116506`	20.284029877535424`	0.21131407466593047`		`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`		3145.2351295950316`	15.897062680473685`	0.20769542669610866`		`5`	`19`
0.015`	0.005`		2166.7817249827262`	23.075697668808147`	0.21569542669610867`		`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`

`rBot`	`Wall`	`stress lbf`	`sp thrust`	`weight`	`dia`	`r max stress`	`min # noz`	`max # noz`
0.0025`	0.001`		5026.560122709375`	19.89432087924552`	0.24784899936255095`		`5`	`11`
0.0025`	0.005`		3330.125954675533`	30.028894210322264`	0.25584899936255096`		`5`	`11`
0.0025`	0.0075`		2718.642689303403`	36.78306104493011`	0.26084899936255096`		`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`		4677.246955945027`	21.38009836596178`	0.2496493037286791`		`5`	`11`
0.005`	0.005`		3158.6482716400988`	31.659112189808937`	0.2576493037286791`		`5`	`11`
0.005`	0.0075`		2596.964205150805`	38.50649916608805`	0.2626493037286791`		`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`		4053.1877419928333`	24.671938820882986`	0.25350565087896476`		`5`	`13`
0.01`	0.005`		2835.7699448774197`	35.263791472450585`	0.26150565087896477`		`5`	`13`
0.01`	0.0075`		2363.3392739626674`	42.3130107055377`	0.2665056508789648`		`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`		3523.86606578568`	28.377923034854074`	0.25768672058002184`		`5`	`13`
0.015`	0.005`		2543.6065812819593`	39.3142558821344`	0.26568672058002185`		`5`	`13`
0.015`	0.0075`		2146.5854064768296`	46.58561438937997`	0.27068672058002186`		`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`

`rBot`	`Wall`	`stress lbf`	`sp thrust`	`weight`	`dia`	`r max stress`	`min # noz`	`max # noz`
0.0025`	0.001`		5319.413101774797`	93.99533189726844`	0.42116194020677555`		`0`	`0`
0.0025`	0.005`		4074.244955787645`	122.72212530808392`	0.42916194020677556`		`0`	`0`
0.0025`	0.0075`		3536.5699911331044`	141.3799249706923`	0.43416194020677557`		`0`	`0`
0.0025`	0.01`		3113.55562091914`	160.58810597139652`	0.43916194020677557`		`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`		5089.1002664583275`	98.24919412483227`	0.42290746170104015`		`0`	`0`
0.005`	0.005`		3930.464689955211`	127.21142140719691`	0.43090746170104016`		`0`	`0`
0.005`	0.0075`		3424.206700786919`	146.01922246256177`	0.43590746170104017`		`0`	`0`
0.005`	0.01`		3023.347477125991`	165.37960118143693`	0.44090746170104017`		`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`		4660.852128513697`	107.2765207334406`	0.42655225493353544`		`7`	`7`
0.01`	0.005`		3656.7496486044147`	136.73345130171094`	0.43455225493353544`		`7`	`7`
0.01`	0.0075`		3208.081205780216`	155.85640385259472`	0.43955225493353545`		`7`	`7`
0.01`	0.01`		2848.4101171564353`	175.53652017608678`	0.44455225493353545`		`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`		4273.311985988555`	117.00526468449134`	0.4303964194776103`		`7`	`7`
0.015`	0.005`		3401.626694800693`	146.9884984040837`	0.4383964194776103`		`7`	`7`
0.015`	0.0075`		3003.965020790616`	166.44667848642416`	0.4433964194776103`		`7`	`7`
0.015`	0.01`		2681.441634426067`	186.46685931205047`	0.44839641947761033`		`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`

Converted by Mathematica May 25, 2002