Range Optimization Using Trajectory Shaping Analysis

8/7/2019 Range Optimization Using Trajectory Shaping Analysis

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Proceedings National Conference on EngIneering and Technology (NA


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ProceedingsNational Conference on Engineering and Technology (NACET),26-27 May2004, Universiti Malaya

Proceedings N a t ~ n f e r e n c e on EngineeCing and Technology(NACET),26-2_2004 , _ t i Malaya

DEFINITIONSThe followings are the major parameters that initially drive rocket design and its flight performance,These arethe aerodynamicconfigurationsizingparametersemphasized in this paper.

gives readers an insight into the interaction between the many important parameters in the rocket design,Due to l imit ed length for the paper , the author s have to eliminate nearly all equations and thestep-by-step mathematical procedureto be able to keep the paper within the allowed number ofpages.

Flightconditionparametersthat are most imponant in the design of tactical rockets areangle ofanack(a), Mach number (M), and altitude (h), For the aerodynamicconfiguration, the rocket diameterandlength havea first order effect on characteristics such as rocket drag, subsystem packaging availablevolume, launch platform integration, seeker and warhead effectiveness, and body bending. Anotherconfiguration driver is nose fineness, an imponant contributorto rocket drag for supersonic rockets,Also, nose fineness affects seeker performance, available propellant length, and rocket observables.Anotherexampleis rocket propellant/fuel type and weight, which drive flight perfonnance range andvelocity. The aerodynamic configuration wing geometry and size are often set by maneuverabilityrequirements andaerodynamic efficiency. Stabilizer geometry andsize areoften established bystaticmargin requirements. In the flight control area, the geometry and size of the flight control surfacesdetermine the maximum achievable angle of anack and the resulting maneuverability, Finally, thethrust profiledetermines the rocket velocity time history.

Table 1- Tvnical Values for PrecisionStrike RocketTotal Rocket Wei!!ht of2,ooolb

Subsonic I.; 'd F I ! HydrocarbonParameter Turbojet .qu. ue f Fuel Solid RocketRocket Ramjet Rocket ScramjetRocketL/ D, Lift/ Drag 10 5 3 5Specific Impulse (lsr) 3,000sec 1300 sec 11,000 sec 250secAverage Velocity(VAve) 1,000 ft / sec 3500 ft I sec 6,000 ft / sec 3,000 ft / sec

._._.

I"'Cruise Propellant or FuelWeigh t / Launch Weigh t 0.3 0.2 0.4(Wp/WLlCruise Range (R) 1,800nm 830 nm 310nm 250nm

propulsion types are held to a rocket launch weight of 2,000 pounds, a representative weight limit forcarriage ona small fighter aircraft such as the F- J8e

As it can be seen from thetable, ramjetand scramjet rockets booster propellant for Machs 2.5 to 4 takeoverspeed not included in Wr forcmise, Rockets require thrust magnitudecontrol (e.g., pintle, pulse, orgel motor) for effective cmise. 11,emaximum range for a rocket is usually anained by semi-ballisticflight profile, instead of cmise flight. It can be also noticed from the table that the subsonic cruiseturbojet propulsion is thepreferred approach for long-range strikeagainst targets thatare nottime-criticaLSubsonic cruise turbojet propulsion has 120 percent greater range than the next best altemative, asupersoniccruise liquid fuel ramjet ( 1,800 n autical m iles v ersus 8 30 n autical m iles). '

Flight conditions (a, M, h)Nose finenessDiameterPropellant/fuel rypeand weightWing geometry/size

Stabilizer geometry/sizeFlight control geometry/sizeLengthThrust profile

CRUISE RANGE EQUATIONThe cruise range is driven by LID, I,,,, velocity and propellant or fuel weigh t f ract ion. As a goodestimation fora conceptualdesign, i t i s calculated from the Breguel RangeEquation.

Table I compares four propulsion alternatives for a long range precision strike rocket The propulsionalternatives are subsonic cruise turbojet, supersonic cruise liquid hydrocarbon fuel ramjet, hypersoniccruise liquid hydrocarbon fuel scramjet, and supersonic cruise solid propellant rocket. All four

Based on an examination of the Breguet range equation,new technology development has payoff in theareas of higher cruisevelocity, aerodynamic efficiency (lift/drag), specific impulse, lightweight structure,lightweightllow volume subsystems,and higher density fuel/propellant.

An examination of the Breguet range equation explains the difference in performance. 11,e subsoniccruise turbojet rocket is superior to ti,e supersonic cruiseramjet rocket in themaximum lift-lo-dragratio(LID = 10 versus 5),specific impulse (lsp =3,000 seconds versus 1,300 seconds),and availablefuel forarocket launch weight limited to 2,000 pounds (600 pounds of fuel versus400 pounds of fuel).Theramjet rocket has lessavailableweighl for fuel because il requires a rocket to boost therocket up toabout Mach 25 for transition to ramjet propulsion, However, a ramjet rocket has an advantage of ashoner response time against time critical targets, It may also have an advantage in survivability due tothe higher flight altitude and higher speed. If time critical targets are of utmost imponance, scramjetpropulsion may be preferred. As shown in the figure the scramjet rocket example is 70 percent tasterthan theramjet (6,000 feet persecond versus 3,500 feet per second).However, the maximum rangeof a scramjet rocket Ihat is limned to 2,000 pounds launch weight isonly37 percent that of a liquid fuel ramjet (310 nautical miles versus 830 nautical miles). Again, i t isinsmlctive to examine the Breguel range equation. The liquid fuel ramjet rocket is superior to thescramjet in the aerodynamicefficiency (UD =5 versus 3), specific impulse (lsp = 1300 seconds versus1,000 seconds), and available fuel fora rocketlimiled to 2,000 pounds launch weight (400 pounds of fuelversus 200 pounds of fuel).11,e scramjet rocket has less available weighl for fuel because it requires a larger rocket booster for ahigher takeover Machnumber (Mach 4 versus 2.5), requires a longer combustor forefficientcombustion,and requires moreinsulation, Finally, the supersonic cmise rocket has a maximum flight range of 250nautical miles, The most efficient cruise condition for the long range rocket was found to be Mach 3cmise at high altinlde. The solid propellant rocketexample uses tlUllSt magnitude control from a pintlemotor, for more efficient acceleration and cntise, Although it is not shown, a semi-ballistic flight

(Eq,I)

R =cruiserangeLID = lift-to-drag ratioIs,' = specific impulse

R = (LID)' I". ,V , In[W,/(W" - Wp)]WI, = launch weightWI' = propellantweight

where,

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Proceedings NatIOnal Conference on Engineeringand Technology{NACEn,26-27 May2004. Universui Malaya

Proceedings N a ( ~ n f e r e n c e on Engineering and Technology(NACET),26 - _2004 , Witi Malaya

trajectory (e.g.. launch. pitch-up. ballistic climb. glide) would have provided a more efficient flighttrajectoryfor therocke!. sensitiveto theramjet specific impulse, fuel weight. zero-liftdrag coefficient.and theramjet thrus!. Theflight range is relatively insensitive to inen weightand lift curve slope.especially for lowaltin,de flighl(high dynamic pressure).

Glide

L i n e - O r - S i ~ h t T r a j e c t o r ~

Figure3. Flighl trajectory shaping provides extendedrangeRoAX

. . . . . - - - - - - - - . , ; ; : : : . . . . - - - - - - - ~ RoAX

ALTITUDE

Figure 3 illustrates the extended range advantage of rockets that use flight trajectory shaping. Fligllltrajectory shaping is particularly beneficial for high performance supersonic rockets, which have largepropellantor fuel weight ITaction. To takeadvantageof fligJll trajectoryshaping., the rocketmust rapidlypitch upand climb to an efficientcruise altitude. Duringthe climb.the rocketangle-


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ProceedingsNational Conferenceon Engineering and Technology (NACET).26-27 May2004. Universlti Malaya Proceedings N a ( ~ ~ e r e n c e on Engineering and Technology (NACET).26 -1 .2004 . .llMalaya .

[J-l@STAO 19.2 46.1Nose Forebody

Body Fineness Ratio 5 < 1/ d < 25Nose FinenessRatio IN i d ' " 2 ifM > IE ff ic ientCmiseDynamicPressure q < 700 psfRocket Homing Velocity VM/ V, > 1.5SubsystemsPackaging; Maximize available volume forfuel/propellantTrim Control Power a /0 > IRocket Maneuverability nM / nl > 3

Figure 5. Rocket baseline configuration similar to theSparrow rocket(dimensions in inches)(Source: l3ithell. R.A. andStoner,R.c., "RapidApproach forRocketSynthesis,Vol. I, Rocket

SynthesisHandbook." AFWAL-TR-81-3022, Vol. I. March 1982).

three radial slots and aft end longitudinal slots . 11,e nozzle has a 1.81 square inch d,roat area. andprovides an expansion rario of 6.2atetram the Figure5 thatthe diameterd = 8 inches, total wingspan b" 40.2 inches, and length I =143.9 inches. Shown arethe length of the rocket motorand the section length:;lbulkhead locations. Therocket is divided intothe nose. forebody. payload bay. midbody, aftbody. and the taileone sections of therocket. The wing geomerry in the figure includes rhe wingspan. sweep angle. location of the meanaerodynamic chord, length of the root chord and irs location, and the length of the tip chord. 11,e railgeometry shown in the figure includes rhe tail span. sweep angle, location of the mean aerodynamicchord. lenb'lh of theroot chord andthe locationof the rootchord.

MA,XIMUM FLIGHT RANGE OF BASELINE ROCKET

fon"ard Range ..-Max --------/-Min

'" Beam 00' BOl"cslght F I ~ ' ( l u l"" Rangl:

-Min

A boost-eoast rocket has less velocity andavailable maneuverability in a highaltitude intercept than in alow alritudeintercept. Otherconstraintson the maximumrange include the fire control system maximumrangeand rocketrime of flight limits(e.g., batteryduration). Theminimum rangemay beestablishedbythe maneuverabili ty required to correct an inirial headingerror. For a beam flight (to the side of rhelaunch platfonn). the rocket mustoperate at high angleof attackto rapidly rum thevelocity vector ro 90degreesoffboresight. The rime to ann thewarhead,based on establishinga safestandofftram thelaunchplatfonn may also set rhe minimum range. Finally, theseekergimblelimit may set theminimum rangein off boresght maneuvers. The maximum/minimum range for a beam imercep t may bed r iven byacombination of parameters such as theseeker gimbal limit. maneuverability. stability, and thedrag duetolift. For flight to rhe rear of thelaunch platfonn, therocket must make a headingchangeof 180 degrees.Thedrivers fora rear intercept maybe a combination of parameters such as zero-lift drag and thedragdueto lift (see Figure 4).

supersonic rocketat 1g flight and at low altitudeflies near zero angle of attack. Themaximum range fora supersonicrocket in snaight-ahead flight is often drivenby the zero-liftdrag coefficient. Themaximumrange may be established by the speed and maneuverability required for an intercept. It was shownpreviously thathigherrocket speed and higher maneuverability are requiredagainsta maneuveringtarget.Thisaffects the maximum effectiverange for low miss distance. 11,emaximum effectiverange against amaneuvering target i s l ess t han t he maximum range against a non-maneuvering target. Also. themaximum effective range is a ftUlction of theintercept altitude.

Figure4. Flightperfonnance envelope

ROCKET BASELINE CONFIGURAnO NA confib'llfation drawing of the rocket baseline configuration. which is similarto the Sparrow rocket. isshown in Figure5 tram Bithell & Stoner(1982). Therocket baseline is a radar-guided rocket. It has adesign flight rangeofabout 7 nautical mileswhen launched at an altitude of 20.000 feet. Therocket usescnlcifonn wingsas control surfaces. Fixed crucifonn tailsurfaces provide static stability. Rocket launchweight is 500 POlUlds, including 133 pounds of propellant. The rocket motor has a boost-sustain thrustprofile with 29,8000 Ib-sec total impulse. The motor grain configuration is an internal bumer type wirh

Therocket baselineconfigurationflight range isshown in thefigure asa fuuction of time. The launchconditions are Mach 0.8. 20K feet alt irude. Note that the flight range a1 " t ime of flight tf = 24.4seconds exceeds the requirement by 15 percent (7.7 natll ical miles versus 6.7 nautical miles). Therocket baseline achieves rhe required flight range of 6 .7 nau ti ca l miles a t a t ime tha t i s 14 percentshaner than the required time-of-flight (21 seconds versus 24.4 seconds).

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ProceedingsNational Conference on Engineering and Technology (NACET).26-27 May2004. Universiti Malaya

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Proceedings i ' ~ n f e r e n c e on Engineenng and Technology ( ACET).26 - .2004 . _iti Malaya

(Eq.4)where.

8',; 6a::

4u::: t'" 2

Boosto ;o 5

Coast

SUstainNote:Ml =0.8hl = 2GKleet

10 15t. TIme, sec

20 25

6Rc"", = incremental range during coastVl3C = begin-of-coast velocityWH


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Proceedings NatlonaJ Conferenceon Englneenng and Technology (NACET),26-27 May2004. Universiti Malaya

REFERENCES

:.[1] Lesieutre, D., et ai, "Recent Applica tions and Improvements to the Engineering-LevelAerodynamic Prediction Software MISL3," AIAA-2002-o274[2] Fleeman, E.L., "Tac/icalrocke/ Desifin." AIAA, Reston, VA, 2001[3] Moore, F.G .. et ai, "Application of the 1998 Version of the Aeroprediction Code," Journal ofSpacecraft and Rockets. Vol. 36, No.5, September-October 1999[4] Giragosian, P.A., "Rapid Synthesis for Evaluating rocket Maneuverability Parameters," 10thAIAA Applied Aerodynamics Conference, June 1992[5] Briggs, M.M., Systematic Tactical rocket Design, Tactical rocket Aerodynamics: General Topics,"AIAA Vol. 141 Progress in Astronautics and Aeronautics," American Institute of Aeronautics,Reston, VA, 1992[6] Bruns, K.D., Moore, ME , Stoy, S. L Vukelich, S.R., and Blake, W.B., "rocket Datcom,"AFWAL-TR-9J-3039, April 1991[7] Eichblan, EJ .. Test and Evaluation of theTactical rocket, American Institute of Aeronautics andAstronautics, Reston, VA, 1989[8] BitheIl, R.A., and Stoner, R.c., "Rapid Approach for rocket Synthesis," AFWAL TR 81-3022,Vol. I, March J982[9] Fleeman, E.L. and DonateIli, G.A.. "Conceptual Design Procedure Applied to a Typical AirLaunched rocket," AIAA 81-1688, August 1981[1O]Hindes, J.W.,"Advanced Design of Aerodynamic rockets (ADAM ),';October 1993

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Range Optimization Using Trajectory Shaping Analysis

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