MAE 4262: ROCKETS AND MISSION ANALYSIS Single and Multi-Stage Rockets September 9, 2014 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk 1

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 V 2 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 2

PRELIMINARY DEFINITIONS Total mass of rocket, M o, may be written as sum of 3 primary components: –Payload mass, M L –Propellant mass, M P –Structural mass, M S 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) 3

DEFINITIONS 4

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

PICTURES OF DEFINITIONS Payload Propellant Structure Rocket Initial Propellant is Full M o =++ 6

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

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

PAYLOAD RATIO DEFINITION Payload Propellant Structure = + 9

STRUCTURAL COEFFICIENT DEFINITION Payload Propellant Structure  = + 10

PROPELLANT FRACTION DEFINITION Payload Propellant Structure  = + 11

SUMMARY: SINGLE-STAGE ROCKETS Payload Propellant Structure  = +  = + == + R =

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: 1.Stages are ordered in number of firing 2.Analysis of multistage rockets is similar to that for single stage –Payload for an particular stage is the mass of all subsequent stages 13

MULTISTAGE ROCKET EXAMPLE 1 MLML 3 2 Total Mass 1: M o1 =M P1 +M S1 +M o2 Total Mass 2: M o2 =M P2 +M S2 +M o3 Total Mass 3: M o3 =M P3 +M S3 +M L Total Mass i: M oi =M Pi +M Si +M o(i+1) 14

MULTISTAGE ROCKET EXAMPLE 1 MLML 3 2 Total Mass 1: M o1 =M P1 +M S1 +M o2 Payload for Stage 1: M L1 =M o2 Total Mass 2: M o2 =M P2 +M S2 +M o3 Payload for Stage 2: M L2 =M o3 Total Mass 3: M o3 =M P3 +M S3 +M L Payload for Stage 3: M L3 =M L Total Mass i: M oi =M Pi +M Si +M o(i+1) Payload for Stage i: M Li =M o(i+1) 15

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

PAYLOAD RATIO: MULTISTAGE ROCKETS MLML The payload ratio for stage 2 is:

PAYLOAD RATIO: MULTISTAGE ROCKETS MLML The payload ratio for stage 3 is:

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

STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS MLML The structural coefficient for stage 2 is:

STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS MLML The structural coefficient for stage 3 is:

SUMMARY: MULTISTAGE ROCKETS 22

SOME EXAMPLES: SATURN V 23

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 N 2 O 4 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 N 2 O 4 /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 N 2 O 4 /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 24