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MAE 4262: ROCKETS AND MISSION ANALYSIS

MAE 4262: ROCKETS AND MISSION ANALYSIS. Single and Multi-Stage Rockets September 6, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk. SINGLE-STAGE SOUNDING ROCKET SUMMARY.

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MAE 4262: ROCKETS AND MISSION ANALYSIS

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  1. MAE 4262: ROCKETS AND MISSION ANALYSIS Single and Multi-Stage Rockets September 6, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

  2. SINGLE-STAGE SOUNDING ROCKET SUMMARY • Want to reduce burn time as much as possible while accelerating against a gravity field • Short burn time reduces energy consumed in lifting propellants • Very short burn time implies very high accelerations • Structural limitations • High mass flows, lots of weight for nozzles, turbo-machinery, cooling, etc. • Drag goes as V2 • Is there an optimum acceleration for a given rocket configuration? • In limit of no drag and no gravity, burn time has no influence on velocity increment Velocity during Powered flight Height at burnout Maximum altitude

  3. PRELIMINARY DEFINITIONS • Total mass of rocket, Mo, may be written as sum of 3 primary components: • Payload mass, ML • Propellant mass, MP • Structural mass, MS • Includes everything but payload and propellant • Engines, tanks, controls, etc. • If rocket consumes all its propellant during firing, burnout mass consists of structure and payload: • NOTE: Other texts and references will breakdown rocket components in various ways and into many more parts (i.e., Sutton, Kerrebrock, Turner, Humble)

  4. DEFINITIONS

  5. PRELIMINARY DEFINITIONS • Using previous definitions, we can write mass ratio as: • Also note that propellant ratio and structural coefficient are related by:

  6. PICTURES OF DEFINITIONS Payload Propellant Structure Rocket Initial Propellant is Full Mo = + +

  7. PICTURES OF DEFINITIONS Payload Propellant Structure Rocket Final Propellant is Empty Mass at Burnout Mb = +

  8. MASS RATIO DEFINITION Payload Propellant Structure Rocket Initial Rocket Final + + R= +

  9. PAYLOAD RATIO DEFINITION Payload Propellant Structure l= +

  10. STRUCTURAL COEFFICIENT DEFINITION Payload Propellant Structure e = +

  11. PROPELLANT FRACTION DEFINITION Payload Propellant Structure z = +

  12. SUMMARY: SINGLE-STAGE ROCKETS Payload + + R = + l = Propellant + e = + Structure z = +

  13. MULTISTAGE ROCKETS • Main idea is to discard empty tanks and extra structure as rocket travels, so that this mass is not subjected to gravity losses • Large engines used for initial high thrust phase, may produce excessive accelerations when propellant is nearly consumed • Multistage rocket is a series of individual vehicles or stages, each with its own structure, tanks and engines • Each stage accelerates payload before being detached Two points: • Stages are ordered in number of firing • Analysis of multistage rockets is similar to that for single stage • Payload for an particular stage is the mass of all subsequent stages

  14. MULTISTAGE ROCKET EXAMPLE ML 3 Total Mass 3: Mo3=MP3+MS3+ML 2 Total Mass 2: Mo2=MP2+MS2+Mo3 Total Mass 1: Mo1=MP1+MS1+Mo2 1 Total Mass i: Moi=MPi+MSi+Mo(i+1)

  15. MULTISTAGE ROCKET EXAMPLE ML 3 Total Mass 3: Mo3=MP3+MS3+ML Payload for Stage 3: ML3=ML 2 Total Mass 2: Mo2=MP2+MS2+Mo3 Payload for Stage 2: ML2=Mo3 Total Mass 1: Mo1=MP1+MS1+Mo2 Payload for Stage 1: ML1=Mo2 1 Total Mass i: Moi=MPi+MSi+Mo(i+1) Payload for Stage i: MLi=Mo(i+1)

  16. PAYLOAD RATIO: MULTISTAGE ROCKETS ML The payload ratio for stage 1 is: 1 1

  17. PAYLOAD RATIO: MULTISTAGE ROCKETS ML 2 The payload ratio for stage 2 is: 2

  18. PAYLOAD RATIO: MULTISTAGE ROCKETS ML 3 The payload ratio for stage 3 is: 3

  19. STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS ML The structural coefficient for stage 1 is: 1 1

  20. STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS ML 2 The structural coefficient for stage 2 is: 2

  21. STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS ML 3 The structural coefficient for stage 3 is: 3

  22. SUMMARY: MULTISTAGE ROCKETS

  23. SOME EXAMPLES: SATURN V

  24. PROTON (SOVIET) • First Launch: July 1965 • Flight Rate: 13 per year • Capability: 44,100 lb to LEO; 12,100 lb to GTO; 4,850 lb to GEO • Originally intended as a ballistic missile but converted to a space launch vehicle during development • Two, three, and four-stage versions were developed • Used to launch satellites into GEO, interplanetary spacecraft, and manned space stations such as Salyut and Mir • Three or four-stage liquid-fueled vehicle • Stage 1 has six strap-on boosters with RD-253 engines burning N2O4 fed from the core stage 1 tank with UDMH fuel carried in the strap-on tanks, generating a total of 1,986,000 lb of thrust • Stage 2 has four RD-0210 sustainer engines burning N2O4/UDMH fed from stage 2 tank, generating a total of 540,000 lb of thrust • Stage 3 has one RD-473 engine with four verniers burning N2O4/UDMH, generating a total thrust of 142,000 lb • Stage 4 has one RD-58 burning LO2/kerosene, generating a total thrust of 19,100 lb • Length: 197 ft • Launch Weight: 1,550,000 lb • Diameter 22.6 ft • Liftoff Thrust: 1,986,000 lb • Payload Fairing: 24.6 ft x 12 ft

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