J. Aerosp. Technol. Manag. vol.4 número2

LIST OF SYMBOLS A_e: Exit area A_t: Throat area

A_w: Wall area (surface area) c: Effective exhaust velocity CF 7KUXVWFRHI¿FLHQW D: Rocket diameter İ ([SDQVLRQUDWLR F: Thrust

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m_i ,QLWLDOPDVV m_inert ,QHUWPDVV m_insul ,QVXODWLRQPDVV m_pay: Payload mass m_prop 3URSHOODQWPDVV m_pv: Pressure vessel mass m_sk: Skirt mass

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P_c &KDPEHUSUHVVXUH P_e: Exit Pressure t_b %XUQLQJWLPH T/W 7KUXVWWRZHLJKWUDWLR v: Velocity

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Design Optimization of Micro Air Launch Vehicle Using

Differential Evolution

Mohammed Abdulmalek Aldheeb1,*_{, Raed Kafafy}1_{, Moumen Idres}1_{, Hanafy M. Omar}2_{, Mohammad A.} Abido3

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3.LQJ)DKG8QLYHUVLW\RI3HWUROHXPDQG0LQHUDOV'KDUKDQ±6DXGL$UDELD

Abstract: In this paper, we have used the differential evolution to optimize the design of a Micro Air Launch Vehicle and its launch trajectory. Since trajectory design of a launch vehicle requires prior knowledge of the masses and propulsion performance parameters of the Micro Air Launch Vehicle, whereas the vehicle design requires prior knowledge of the required velocity ¨V to insert the required payload into the target orbit, a twostep optimization cycle was adopted. A Micro Air Launch Vehicle was designed to launch a 20kg payload into a 00km circular polar orbit. The preliminary design of the Micro Air Launch Vehicle was conducted given the required ¨V, which was obtained from trajectory optimization, and then applied in mission analysis to obtain the initial masses. These initial masses were used in the vehicle design to get the performance and geometry parameters. The objective function of the Micro Air Launch Vehicle design optimization is to minimize the initial mass under speci¿ed constraints on the insertion orbit. The objective of trajectory optimization is to maximize the payload mass under constraints on orbit speci¿cations and design variables. For the 20kg payload mass, the optimal initial mass is 1267.8 kg and optimal payload is 20.6 kg, which slightly exceeds the mission requirements.

Keywords: Micro Air Launch, Vehicle design, Optimization, Differential evolution.

Received: 15/01/12 Accepted: 16/03/12 DXWKRUIRUFRUUHVSRQGHQFHDOGKHHE#\DKRRFRP 32%R[.XDOD/XPSXU0DOD\VLD

INTRODUCTION

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DESIGN PROCESS

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Mission requirement:

¾ǻV total = ('Vorbit+ 'Vloss) ¾Payload mass

Initial mission analysis output:

¾Initial mass ¾Propellant mass

Preliminary design decision ¾Nozzle cone angle ¾Propellant grain type. ¾Material selection.

Mission analysis and design process

START

NO

Preliminary component design ¾Motor case ¾Thrust skirts ¾Igniter ¾Insulator ¾nozzle

Total masses of the designed components Calculation of NEW inert

mass fraction

NEW finert - Old finert=Error

YES

New finert

Thermo chemistry calculation of Nozzle

?

NEW Isp- Old Isp= Error

New I_sp

YES END

?

Initial Mass

PSO

?

Yes NO

END L/D, T/W , f 1,2,3 , Pc , NDF

Design Variables

Vehicle Design Optimization

Guess Values

¾finert ¾Isp

Error=0.0005

Output Objective function Converged

F, Mi, Mprop, Tb, Isp, finert, expansion ratio, Dimensions

Vehicle Trajectory Optimization

Design Variables ¾D’s , coasting time

PSO

Output

Payload mass 'V loss

DE

DE

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Design requirements

Mission requirements

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Orbit and altitude

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Payload mass

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Decisions

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total ¨VLVDOVRUHTXLUHGWRVWDUWWKHGHVLJQSURFHVV

Design of micro air launch vehicle subcomponents

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prop

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pay I inert

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c

m

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h

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b

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t r

= c + m ₍₉₎

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of small payloads. Thus,

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m m m

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( )

sin cos cos

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L F mg

r

mV2

d a c c

= + + - + (23)

The total ¨VZKLFKLVUHTXLUHGIURPWKHODXQFKYHKLFOHLV

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ǻV_total = V_orbit V_aircraft+ǻV_loss (24)

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ǻV_loss=ǻV_drag+ǻV_gravity+ǻV_steering+ǻV_performance (25)

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Micro air launch vehicle design optimization results

Optimal design variables

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Generation No.

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Į3 5.525553

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Į₆ 31.6511

Į 66.8022

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SUMMARY AND CONCLUSIONS

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0 100 200 300 400 500

278 280 282 284 286 )LJXUH'HVLJQYDULDEOHWKLUGVWDJHFRDVWLQJWLPH Generation No. P a y lo a d ma s s (k g )

0 100 200 300 400 500

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0 100 200 300 400 500

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X X X X X X X X X X X X + + + + + + + + ++ + + + + + + + + + + Generation No. D e s ig n V a ri a b le s (d e g ) D e s ig n v a ri a b le 5 (A lp h a 5 )

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ACKNOWLEDGMENTS

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REFERENCES

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