AIAA 97-3340 - Private Data · AIAA 97-3340 3-D Grain Design and ... although new Macros can be ......

AIAA 97-33403-D Grain Design and Ballistic AnalysisUsing the SPP97 CodeS.S. Dunn and D.E. CoatsSoftware and Engineering Associates, Inc.Carson City, NV

American Institute of Aeronautics and Astonautics1

3-D GRAIN DESIGN AND BALLISTIC ANALYSISUSING THE SPP97 CODE

S.S. Dunn† and D.E. Coats‡

Software and Engineering Associates, Inc.Carson City, NV

Copyright © 1997 by D.E. Coats. Published by the American Instituteof Aeronautics and Astronautics, Inc. with permission.† Stuart S. Dunn, Vice President, Member AIAA‡ Douglas E. Coats, President, Associate Fellow AIAA

Abstract

The Solid Performance Program (SPP) has become thestandard reference computer program throughout theUnited States for predicting the delivered performanceof solid propellant rocket motors. The code embodiesa methodology for calculating the deliveredperformance of solid propellant rocket motorsprescribed by JANNAF. The nozzle performancemethodology starts with the ideal performance andaddresses each of the following performance lossmechanisms: finite rate chemical kinetics, nozzle throaterosion, nozzle submergence, nozzle flow divergence,two phase flow, combustion efficiency, and the nozzlewall boundary layer. The Grain Design and Ballistics(GDB) module calculates the ideal pressure-thrusthistory, and subsequently modifies these values basedon the nozzle performance efficiencies. The GDBmodule combines existing 3-D grain design andballistics methods with modern graphics and ease ofuse to provide a tool which allows even novice users toobtain successful results.

Introduction

The ability to accurately predict the performance of asolid rocket motor (SRM) has critical importance in theoverall design of a missile system. It allows for moreaccurate prediction for mission, range and payloadcapability while minimizing overdesign of the totalimpulse margin and thus reduce missile weight, size,and payload. The analytical tools necessary for anaccurate performance prediction also give the designerand test engineer an insight into the potential problemsof a new missile system. In addition, these tools allowthe analyst the ability to reconstruct a motor based onknown or observed performance.

The Solid Performance Program (SPP) was originallyreleased in 19751 and has been substantially upgradedever since2,3,4,5. The SPP analysis can be separated intothree categories: 1) Nozzle Performance, 2) GrainDesign and Ballistics, and 3) Instability Analysis. TheNozzle Performance Module has received aconsiderable amount of attention in the past6,7,8,9, andwill not be addressed. The Instability Analysis Moduleis currently being re-formulated, and also will not beaddressed. The remainder of this discussion pertains tothe Grain Design and Ballistics module.

The Grain Design analysis can be separated into threedistinct motor categories: 1) Two-Dimensional, 2)Axisymmetric, and 3) fully Three-Dimensional. TheSPP97 code allows the user to analyze all three of theabove motor classifications. Both the axisymmetricand two-dimensional grain design analysis are straightforward and will not be further addressed. The fullythree-dimensional grain design analysis can beextremely complex, and can be a challenge for even themost experienced analyst. With increased speed,reduced cost, and abundance of graphical software,modern computers allow the software developer thetools to aid the analyst in ways never thought possible.The SPP97 computer code has taken the first step tointegrate these tools into the Grain Design Module,resulting in a greatly improved design tool.

Discussion

The Three-Dimensional Grain Design Module (GDM)is based on the analysis of J. G. Barron10, et.al. Thegeometry calculations performed by the GDM arebased on the computation of volumes and changes involumes. The method used simulates drafting

American Institute of Aeronautics and Astronautics2

techniques. The motor case is assumed full ofpropellant initially. Simulation is accomplished usingfive input figures in various combinations to describethe initial geometry. These figures include the frustumof a right circular cone, a right circular cylinder, a righttriangular prism, a sphere, and a torus. These figuresmay overlap and/or protrude outside the case, and canbe input as a outburning void in the propellant, grain-filled inburning figures, or nonburning solid figures. Inaddition, these figures may have rounded corners andedges. Each figure may be placed in any orientation inspace, inside or outside of the grain. Ordinarily, a solidpropellant grain is symmetric about the motor axis, sothat only one sector of symmetry is analyzed.

Burning is assumed to be normal to the surface and thevolume of propellant is calculated by integrating thepropellant area along the grain axis. The propellantburning surface is obtained from the derivative of thevolume with respect to the burn distance. Thecalculations are general in that any grain can beevaluated if the initial grain geometry is describedusing any combination of the five basic input figures.Since the analysis is formulated in an orthogonalcoordinate system, auxiliary quantities, such as centerof gravity and moment of inertia, are easily calculated.

Two types of figures may be input: 1) "Primitive"figures, which are the cone, cylinder, prism, sphere,and torus, and 2) "Macro" figures, which can be usedto represent several different standard grain designtypes. Each Macro is composed of a set of Primitivefigures. Macro figure input allows a standard graindesign to be input from a drawing of the grain crosssection shown in a typical set of blueprints. Currently,Macros are available for four of the most commongeometry configurations, although new Macros can beadded when needed. The four Macros currentlyavailable are: 1) Finocyl design, 2) Tapered Stardesign, 3) Simple Tapered Star design, and 4) ForwardStar design. The methods used for combining primitivefigures to obtain each of the Macro operations aredescribed below.

Finocyl Grain Design

The finocyl (acronym for "fin on cylinder") is acommonly used three dimensional grain configu-ration. An example of a grain design using a finocylat the forward end of the motor is shown below:

The valley of the fin is usually defined on a blueprintby a table that gives valley depth (as measured fromthe motor centerline) versus axial location. A methodhas been provided in the computer program thatutilizes this information in order to generate a set ofsolid figures that will model a finocyl. The figurename used for this purpose is FIN, which is short forfinocyl. The method involves the generation of a setof prisms that have one common edge, and arestacked face-to-face. The faces opposite the commonedge define the grain valley shape. The commonedge can be placed normal to the XY plane at aspecified point. The fin can be tapered by a slightrotation of the common edge. Corner rounding canbe accomplished by placing sets of cylinders alongthe valley contour. Tapering and cornerrounding aredone automatically using input data. An example XYplane view of a prism set is shown below:


Tapered Star Design

The generalized cross section of a star grain is shownin the symmetry sector figure given below.

A tapered star can be defined by input of a star designat cross section A-A, and a star design at crosssection B-B. If these inputs are different, then thestar design will be tapered. Nomenclature for the lefthand and right hand defining cross sections (A-A andB-B, respectively) are shown below. The input willgenerate a set of four solid figures, which aresufficient to model the generalized tapered star grainconfiguration.

Note that r1, r2, and η are the same at A-A and B-Bbut ξA and ξB may or may not be the same. Theradius of the outer propellant boundary is defined bythe input table of radius vs. axial position.

Simple Tapered Star Design

A simplified star with taper is shown in the figurebelow. The design is determined from input ofgeometric information at cross sections A-A and B-B.A simple star design differs from a generalized star inthat the tip of the propellant grain is sharp (r2 = 0).

Forward Star Design

Usually, a star grain design is cast using a taperedmandrel. The forward end of the mandrel is machinedso that a forward star design will be cast into thepropellant. At the interface between the forward starand the tapered star, the YZ cross section will appearas shown below on the right. This is the A-A crosssection of the adjacent tapered star. The forwarddome XY cross section is shown below on the left.


Note that provision has been made for a tapered port,and note that the forward star valley (arc defined byRd) is not necessarily tangent to the tapered starvalley (line perpendicular to RA

v ). The macro that is

used to design the forward dome will round the edgesof the mandrel to match the radius, r1. In this way itwill simulate the process by which the forward end ofthe mandrel is machined. The macro contains avariable number of figures.

Alternate Star MACRO input

An alternate specification for a STAR grain has beenimplemented, where the conventional inputs havebeen modified, as described below. The followingfigure defines the new input (although only section A-A has been shown, the nomenclature also applies tosection B-B). This new design allows for a center-perf cone, which is corner rounded into the star lateralside. It should be noted that for all MACROS thevariable RTA is replaced by RCCA and BETAA, andsimilarly the variable RTB is replaced by RCCB andBETAB.

Symmetry Sector at A-A

New inputs at A-A: RACC (RCCA)

βA (BETAB)

New inputs at B-B: RBCC (RCCB)

βB (BETAB)

Ballistics Module

The Ballistic Module is automatically supplied withburning surface area, cross sectional area, and

perimeter from the Grain Design Module. In addition,equili-brium gas properties (such as molecular weight,isentropic exponent, C*, etc.) are automatically trans-ferred from the One Dimensional EquilibriumChemistry (ODE) Module. The Ballistic Module solvesthe one dimensional flow problem with energy andmass addition. The analysis employs a pseudo-transient treatment of the startup problem, and a quasi-steady state solution thereafter. Included in the analysisare the effects of time dependent nozzle erosion,erosive burning, the "hump" factor, and the pressureloss across a slot.

The energy, momentum, and continuity equations areintegrated along the bore to calculate both static andtotal pressure. Closure is achieved by matching thecalculated total pressure at the throat with the valueobtained from C*. An iteration procedure is employedwhich results in rapid convergence. The resultingballistic parameters (such as pressure, burn rate,perimeter, port area, gas properties, etc.) are written toa linkage file, which automatically supplies data to theAxial Mode Standard Stability Program (SSP) Module.The ideal thrust is calculated from the equilibrium Isp

from ODE as a function of area ratio. These values aresubsequently modified by the efficiencies calculated bythe nozzle performance modules.

Application

a) Extended Delta Motor

The Extended Delta Motor11 is representative ofmodern finocyl grain designed whose complexitywarrants the use of a three dimensional grain designprogram. A sketch of this motor is shown in Figure 1.Input to the Grain Design Module that defines theinitial grain geometry is shown in Figure 2.

Figure 1. The Extended Delta Motor


SYMFAC=16, $ENDSSTAR $IN XA=17.92, RTA=1.77233, RVA=7.2, XB=45.72, RTB=1.77233, RVB=7.2, ETA=27.1, R1=.25, MIRROR=T, $ENDCYLINDER CENTRAL PORT $IN C1=0,0,0, C2=46,0,0, R=1.88, $ENDCYLINDER FOR SUBMERGED NOZZLE $IN C1=34.22,0,0, C2=46,0,0, R=4.55, CR=.75, $ENDCONE FOR SUBMERGED NOZZLE $IN C1=45.72,0,0, C2=39.4,0,0, R1=7.3, R2=4.55,$ENDCYLINDER AFT VOLUME $IN C1=45.7,0,0, C2=46,0,0, R=11.562, $ENDFSTAR $IN XA=17.92, RTA=1.77233, RVA=7.2, ETA=27.1, R1=.25, R2=0., RDOME=7.2, MIRROR=T, $ENDEND FIGURES

Figure 2. Computer Input for the Extended DeltaGrain

In this example problem the input of SYMFAC=16specifies that a pie section containing 1/16th of themotor will be analyzed. This section is sufficient torepresent the entire motor since the smallest symmetricsection of an 8-point star is one-half of an arm of thestar. Although the Extended Delta is a relativelysimple grain design, plotted output is required to allowthe analyst to determine if he has modeled the graingeometry properly.

Figure 3 shows a grain cross-section plot with webburn-back and Figure 4 shows a longitudinal trace ofthe star tip with web burn-back.

Figure 3. Extended Delta Cross-Section

Figure 4. Extended Delta Longitudinal Plots

Although the above figures are very informative, theydo not show a complete or accurate representation ofthe entire burning surface. The burning surface can beviewed with the aid of a GUI driven PostProcessor,GnuGen, and FreeWare software from Dartmouth,GnuPlot12 (both are supplied with SPP97). Theresulting plots represent the actual program solution,not a parallel solution. Figures 5 through 7 show theburning propellant surface at web burns of 0, 5, and 10inches. These figures show how the three dimensionaleffects dominate the solution. The significance of thethree dimensional graphical capability becomes moreapparent as the complexity of the motor increases.

Figure 5. Extended Delta (Web = 0)

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The resulting surface area as a function of web burn isshown in Figure 8. The results of the Ballistic solution,head-end pressure and vacuum thrust, are shown inFigures 9 and 10, respectively.

Figure 8. Extended Delta Surface Area vs. Web

Figure 9. Extended Delta Pressure vs. Time

Figure 10. Extended Delta Thrust vs. Time

The above Figures represent a limited selection of thequantities available for display. The accuracy andsmoothness of the above quantities are dependent onthe fineness of the X-Y grid, which is common for boththe Grain Design and the Ballistic solutions.

b) Space Shuttle ASRM

The Space Shuttle Advanced Solid Rocket Motor(ASRM) was designed and analyzed by GenCorpAerojet Space Boosters and the NASA MSFC,respectively. The Grain Design and Ballistic Moduleof the SPP code was used during the design phase toevaluate the effect of grain modifications on surfacearea, ballistic performance, mass properties, etc. Sincethis motor was never built, the analysis consisted solelyof blue prints and drawings. The ASRM consists ofthree segments. The forward segment contains elevenfins at the head end which transition to an axiallysymmetric center perforated shape. The middle and aftsegments are both axially summetric. The forward faceof these two segments are fully inhibited, while the aftfaces of segments 1 and 2 are allowed to burn.


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SPP97 input defining the grain is given in Figure 11.The prime sector of the grain is modeled by specifyinga symmetry factor of 22. The grain design inputconsists of twenty-three figures, including 19 Primitivefigures (eleven cones, seven cylinders, and one prism)and four Macro figures (two finocyls and two stars).These figures are required to model such minute detailsas "stress relief" notches. For example, a detailed lookat the head end fin shows that it is defined using the

table star Macro "FIN", which contains an input tablegiving the shape of the fin valley. The coordinates(XTAB, RVTAB) in this table were taken directly fromthe ASRM blueprint. The fin is automatically placed inthe grain by the "FIN" Macro which uses a set ofstacked prisms with a common edge centered at(42.216, 8.0) inches. Each figure carves out a differentsection, with some sections requiring several figures.

SYMFAC = 22, $ENDCONE $IN NB=1, C1=0,0,0, C2=5.333,0,0, R1=12.,R2=10.858, $ENDCYLINDER $IN C1=5.332,0,0, C2=7.616,0,0, R=10.858, $ENDCYLINDER $IN C1=7.615,0,0, C2=190.,0,0, R=17, CR=3., $ENDFIN R1=1.62 $IN VALDEP = 17., 60., VALWID = 1.8, 1.75, R1 = 1.62, XTAB = 7.616,7.716,8.266,9.286,10.766,12.696,15.066,17.846, 21.016,24.566,28.446,33.326,35.866,38.556,42.216, RVTAB = 12.906,16.4,21.69,26.91,32.02,36.97,41.73,46.26,50.53, 54.49,58.13,61.72,62.92,63.75,64.26, NTAB = 15, XA=42.216, XCENT = 42.216, RCENT=8., MIRROR=T, $ENDSSTAR $IN XA=42.215, RVA=64.26, XB=81.066, RVB=66., R1=1.62, VALWID=1.8,1.75,1.8,1.75, VALDEP=17.,60., 17.,60., MIRROR=T, XMIN = 41.0, $ENDSSTAR $IN XA=81.065, RVA=66., XB=183.561, RVB=66.2, R1=1.62, VALWID=1.8,1.75,1.8,1.75, VALDEP=17.,60.,17.,60., MIRROR=T, $ENDFIN $IN VALDEP = 17., 60., VALWID = 1.8, 1.75, R1 = 1.62, XTAB = 183.560,185.276,186.326,187.226,203.001,203.001, RVTAB = 66.2,65.82,65.1,63.81,28.,8., NTAB = 6, XA=183.560, XCENT = 183.560, RCENT=8., MIRROR=T, $ENDPRISM 14 (PRISM PROGRAM GENERATED) REMOVE GRAIN FOR THE FIN AFT RELIEF CUT $IN P1= 0.19699701E+03, 0.42934673E+02, 0.47291088E+01, P2= 0.19750662E+03, 0.41673340E+02, -0.11255110E+02, P3= 0.17577530E+03, 0.33918076E+02, -0.91228843E-01, CR= 0.20000000E+01, H= 0.47350E+02, $ENDCONE $IN C1=183.551,0,0, C2=199.056,0,0, R1=17.00, R2=28.00, $ENDCONE $IN C1=199.055,0,0, C2=471.315,0,0, R1=28.00, R2=30.200, XMAX=471.4, $ENDCYLINDER *****SEGMENT 1-2 DISK..NON-BURNING VOID $IN NB = 1,C1=471.314,0,0, C2=473.625,0,0, R=75.0, $ENDCYLINDER *****SEGMENT 1-2 DISK..BURN SURFACE AFT FACEING $IN C1=471.315,0,0, C2=471.4,0,0, R=55.0, XMAX = 471.5, $ENDCONE $IN C1=473.624,0,0, C2=511.783,0,0, R1=30.2, R2=28.8, $ENDCYLINDER $IN C1=511.782,0,0, C2=572.835,0,0, R=28.8, $ENDCONE $IN C1=572.835,0,0, C2=909.995,0,0, R1=28.8, R2=31.3, XMAX=910., $ENDCYLINDER *****SEGMENT 2-3 DISK..NON-BURNING VOID $IN NB = 1, C1=909.994,0,0, C2=912.235,0,0, R=75.0, $ENDCYLINDER *****SEGMENT 2-3 DISK..BURN SURFACE AFT FACING $IN C1=909.995,0,0, C2=910.,0,0, R=55.0, XMAX = 910.1, $ENDCONE $IN C1=912.234,0,0, C2=941.535,0,0, R1=31.000, R2=30.00, $ENDCONE $IN C1=941.534,0,0, C2=1129.535,0,0, R1=30.20, R2=31.000, $ENDCONE $IN C1=1129.534,0,0, C2=1323.535,0,0, R1=31.000, R2=42.000, $ENDCONE $IN C1=1323.534,0,0, C2=1339.535,0,0, R1=42.000, R2=51.300, $ENDCONE $IN C1=1339.534,0,0, C2=1353.535,0,0, R1=51.30, R2=51.65, $ENDCONE $IN C1=1353.535,0,0, C2=1375.002,0,0, R1=51.65, R2=52.695, $ENDEND FIGURES

Figure 11: Computer Input for the ASRM Grain


Figure 12 shows a grain cross-section plot with webburn-back and Figure 13 shows a longitudinal trace ofthe star tip with web burn-back. Figures 14 through 17show the burning propellant surface for the entiremotor at web burns of 0, 5, 10, and 15 inches. Due tothe immense size of this motor, it is difficult to evaluatesome of the modeling details from the above plots.Therefore, a ZOOM function was incorporated into theGnuGen code, which allows the user to view anyselected section of the motor. Figures 18 through 21show the burning propellant surface for the head endfin for the same web burns.

Figure 12. SRM ASRM Cross Plots

Figure 13. SRM ASRM Longitudinal Plots

Figure 14. SRM ASRM (Web=0)



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The above figures show the importance of the ZOOMoption for large motors.

The resulting surface area as a function of web burn isshown in Figure 22. The head-end pressure andvacuum thrust are shown in Figures 23 and 24,respectively. It should be noted that the arraydimensions of the GDB module has been designed toaccommodate a very large motor, such as the ASRM,since the quality of the solution is directly dependenton the fineness of the X-Y mesh.

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Figure 22. SRM ASRM Surface Area vs. Web

Figure 23. SRM ASRM Pressure vs. Time

Figure 24. SRM ASRM Thrust vs. Time

Results

The SPP is in use at all of the major solid propellantrocket motor manufacturers in the United States, andseveral foreign countries. It has been used to predictand/or analyze the performance of hundreds ofdifferent rocket motors13. Unfortunately most of thisdata is generally unavailable. However, as part of thedevelopment effort of the SPP, twelve different nozzleconfigurations have been thoroughly analyzed using theSPP. These motor tests cases were approached in an a'priori manner to establish the range of accuracy of thecode. The characteristics of the unclassified motorconfigurations are shown in Table 1. Computationalresults for each of these motors are presented in Table2.

The average absolute difference between predicted andmeasured performance loss was 0.45%, with a standarddeviation of 0.52%. The confidence level in themeasures data is estimated to be no better than ± 0.5%loss in Isp. Analysis of the trends shown in Table 2indicates that the calculations tend to under predict themeasured values of Isp. Effects which are not modeledin the SPP could account for an additional 0.5% loss inIsp. Hence it is remarkable that the analysis is able topredict Isp within the range shown in Table 2 withoutpost priori modifications of the input data.

The availability of solid rocket motor pressure andthrust histories are even sparser than performancedata. A limited amount of data was available for fourdifferent motors, and is presented below. Figures 25and 26 show the Head End Pressure and Thrustverses Time for the Titan 34D Stage 0, respectively.Figures 27 and 28 show the Head End Pressure andThrust verses Time for the Trident C4 Stage 2,respectively. Figures 29 and 30 show the Head EndPressure and Thrust verses Time for the SidewinderMK-35, respectively. Figures 31 and 32 show theabove quantities for the RSRM. The agreementbetween prediction and data is quite remarkable,considering the simplified model. It should be notedthat the SPP analysis for the RSRM was provided byCharles Martin of NASA/MSFC, who was involvedin the design, development, and analysis of theRSRM.

11American Institute of Aeronautics and Astronautics

Figure 25. Titan 34D Stage 0Head End Pressure vs. Time

Figure 26. Titan 34D Stage 0Thrust vs. Time

Table 1. Motor CharacteristicsCase Motor PC

PSID43

MICRONSRTIN

AL % AreaRatio

1 AIM 730. 4.47 1.015 16.40 103.22 IUS Large Motor 549. 6.37 3.411 18.00 35.73 Reduced Smoke Maverick 1520/368 0.00 1.189 0.26 2.14 Minute Man II, Stage 2 445. 7.05 4.817 15.00 24.85 Titan IIIC 546. 10.52 18.850 14.11 8.06 IUS - SRM 2 609. 6.37 2.150 18.00 48.07 IUS - SRM 2 W EEC 658. 6.37 2.142 18.00 174.38 TITAN 34D STG 0 606. 12.00 18.846 16.12 8.09 SEP (CSD) 506. 4.55 1.080 20.00 149.4

Table 2: Motor Performance Predictions

Case Motor TSType

VERS ETATD2P

ETAKIN

ETACohb. Eff.

ETAThrt.EROS

ETASUB

DELTABou.Lay.

IspTheory

IspDel.

IspMeasured

1 AIM ATA 4 0.9243 0.9921 0.9985 0.9971 0.9933 2.12 324.600 292.230 292.3802 AIM FCT 4 0.9219 0.9921 0.9985 0.9971 0.9933 2.20 324.600 291.430 292.3803 IUS Large Motor ATA 4 0.9359 0.9942 0.9968 0.9944 0.9930 1.45 313.660 285.810 287.1604 IUS Large Motor FCT 4 0.9359 0.9942 0.9968 0.9944 0.9930 1.54 313.660 285.880 287.1605 Red SM Maverick ATA 4 0.9936 0.9990 0.9999 0.9904 0.0000 1.71 226.904 221.327 223.3206 Red SM Maverick FCT 4 0.9932 0.9990 0.9999 0.9904 0.0000 1.71 226.904 221.242 223.3207 MM II, Stage 2 ATA 4 0.9505 0.9940 0.9978 0.9993 0.9952 1.43 306.690 286.110 287.4008 MM II, Stage 2 FCT 4 0.9427 0.9940 0.9978 0.9993 0.9952 1.54 306.690 283.660 287.4009 TITAN IIIC ATA 4 0.9639 0.9994 0.9995 0.9976 1.0000 0.64 278.600 267.014 265.880

10 TITAN IIIC FCT 4 0.9621 0.9994 0.9995 0.9977 1.0000 0.75 278.600 266.400 265.88011 IUS - SRM 2 ATA 5 0.9315 0.9948 0.9962 0.9934 0.9949 1.76 318.605 288.959 289.80012 IUS - SRM 2 FCT 5 0.9339 0.9948 0.9962 0.9934 0.9949 1.76 318.605 289.557 289.80013 IUS - SRM 2 W EEC ATA 5 0.9329 0.9917 0.9963 0.9960 0.9949 2.71 335.439 303.659 303.10014 IUS - SRM 2 W EEC FCT 5 0.9329 0.9917 0.9963 0.9960 0.9949 2.84 335.439 305.218 303.10015 TITAN 34D STG 0 ATA 5 0.9628 0.9995 0.9996 0.9968 1.0000 0.75 278.692 266.443 265.60016 TITAN 34D STG 0 FCT 5 0.9649 0.9995 0.9996 0.9968 1.0000 0.81 278.692 266.998 265.60017 SEP ATA 5 0.9191 0.9888 0.9975 0.9938 0.9938 2.95 339.908 301.366 300.40018 SEP FCT 5 0.9174 0.9888 0.9975 0.9938 0.9938 3.08 339.908 300.652 300.400


Figure 27. Trident C4 Stage 2Head End Pressure vs. Time

Figure 28. Trident C4 Stage 2Thrust vs. Time

Figure 29. Sidewinder MK-35Stagnation Pressure vs. Time

Figure 30. Sidewinder MK-35Thrust vs. Time


Summary and Conclusions

The basic goal of the Solid Performance Program(SPP) has been to supply an accurate tool for predictingthe performance of solid rocket motors over a widerange of motor designs. Recently, modifications havebeen incorporated into the Grain Design Module whichallows the user to easily model complex threedimensional grains. With the aid of several Macrofigures, the GnuGen post processor, and the GnuPlot 3-D graphics package, the user can easily visualize themodeling effort, and compare with design parameters.Analysis of the data presented in this paper and thewide spread acceptance of the code in government andindustry would indicate that these basic goals havebeen met. However, the trend for ever more energeticpropellants and higher area ratio nozzles has alreadyunderscored the need for improvements to the existingcode.

Figure 31. RSRM Stagnation Pressure vs. Time

Figure 32. RSRM Thrust vs. Time

References

1 Coats, D.E., Levine, J.N., Nickerson, G.R., Tyson,T.J., Cohen, N.S., Harry, D.P., and Price, C.H., "AComputer Program for the Prediction of SolidPropellant Rocket Motor Performance", Vol. I, II, andIII, AFRPL-TR-75-36, Ultrasystems, Inc. July 1975.

2 Nickerson, G.R., Coats, D.E., Hermsen, R.W., "AComputer Program for the Prediction of SolidPropellant Rocket Motor Performance", InterimTechnical Report, Vol. I, II, and III, AFRPL-TR-80-34,Software and Engineering Associates, Inc., April 1981.

3 Nickerson, G.R., Coats, D.E., Hermsen, R.W., and

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