MAE 4262: ROCKETS AND MISSION ANALYSIS

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MAE 4262 ROCKETS AND MISSION ANALYSIS

• Single and Multi-Stage Rockets
• January 24, 2008
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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SINGLE-STAGE SOUNDING ROCKET SUMMARY
Velocity during Powered flight Height at burno
ut
Maximum altitude

• 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

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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)

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DEFINITIONS
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PRELIMINARY DEFINITIONS

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

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PICTURES OF DEFINITIONS
Payload
Propellant
Structure
Rocket Initial Propellant is Full
Mo


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PICTURES OF DEFINITIONS
Payload
Propellant
Structure
Rocket Final Propellant is Empty Mass at Burnout
Mb

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MASS RATIO DEFINITION
Payload
Propellant
Structure
Rocket Initial
Rocket Final


R

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PAYLOAD RATIO DEFINITION
Payload
Propellant
Structure
l

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STRUCTURAL COEFFICIENT DEFINITION
Payload
Propellant
Structure
e

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PROPELLANT FRACTION DEFINITION
Payload
Propellant
Structure
z

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SUMMARY SINGLE-STAGE ROCKETS
Payload


R

l
Propellant

e

Structure
z

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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
  

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MULTISTAGE ROCKET EXAMPLE
ML
3
Total Mass 3 Mo3MP3MS3ML
2
Total Mass 2 Mo2MP2MS2Mo3
Total Mass 1 Mo1MP1MS1Mo2
1
Total Mass i MoiMPiMSiMo(i1)
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MULTISTAGE ROCKET EXAMPLE
ML
3
Total Mass 3 Mo3MP3MS3ML Payload for Stage 3
ML3ML

2
Total Mass 2 Mo2MP2MS2Mo3 Payload for Stage 2
ML2Mo3

Total Mass 1 Mo1MP1MS1Mo2 Payload for Stage 1
ML1Mo2

1
Total Mass i MoiMPiMSiMo(i1)
Payload for Stage i MLiMo(i1)

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PAYLOAD RATIO MULTISTAGE ROCKETS
ML
The payload ratio for stage 1 is
1
1
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PAYLOAD RATIO MULTISTAGE ROCKETS
ML
2
The payload ratio for stage 2 is
2
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PAYLOAD RATIO MULTISTAGE ROCKETS
ML
3
The payload ratio for stage 3 is
3
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STRUCTURAL COEFFICIENT MULTISTAGE ROCKETS
ML
The structural coefficient for stage 1 is
1
1
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STRUCTURAL COEFFICIENT MULTISTAGE ROCKETS
ML
2
The structural coefficient for stage 2 is
2
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STRUCTURAL COEFFICIENT MULTISTAGE ROCKETS
ML
3
The structural coefficient for stage 3 is
3
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SUMMARY MULTISTAGE ROCKETS
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SOME EXAMPLES SATURN V
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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