MAE 4262: ROCKETS AND MISSION ANALYSIS Single and Multi-Stage Rockets Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk 1
MAE 4262: ROCKETS AND MISSION ANALYSIS
Feb 25, 2016
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. - PowerPoint PPT Presentation
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MAE 4262: ROCKETS AND MISSION ANALYSIS
Single and Multi-Stage Rockets
Mechanical and Aerospace Engineering DepartmentFlorida 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 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
1ln12
ln
21
1ln
111ln
22
max
2
RRRtu
gRuh
gtRRtutuh
gttt
RutV
bee
bbebeb
be Velocity during
Powered flight
Height at burnout
Maximum altitude
2
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)
SPLo MMMM
SLb MMM
3
DEFINITIONS
Symbol Ratio Description
R SL
o
b
o
MMM
MM
R
Mass Ratio: initial mass / mass at the end of the thrust period. Want this ratio large.
SP
L
Lo
L
MMM
MMM
Payload Ratio: ratio of payload to everything but payload. Want this large, but larger the payload, the lower maximum attainable velocity.
Lo
Lb
SP
S
MMMM
MMM
Structural Coefficient: ratio of the structural weight to everything but the payload. Want this small.
Lo
P
SP
P
MMM
MMM
Propellant Ratio: Ratio of propellant
to everything but the payload.
4
PRELIMINARY DEFINITIONS• Using previous definitions, we can write mass ratio as:
• Also note that propellant ratio and structural coefficient are related by:
1R
1
5
PICTURES OF DEFINITIONS
Payload
Propellant
Structure
Rocket InitialPropellant is Full
SPLo MMMM
Mo = + +
6
PICTURES OF DEFINITIONS
Payload
Propellant
Structure
Rocket FinalPropellant is EmptyMass at Burnout
SLb MMM
Mb = +
7
MASS RATIO DEFINITION
Payload
Propellant
Structure
SL
o
b
o
MMM
MM
R
R=+ +
+
Roc
ket I
nitia
l Rocket Final
8
PAYLOAD RATIO DEFINITION
Payload
Propellant
Structure
=
+
SP
L
Lo
L
MMM
MMM
9
STRUCTURAL COEFFICIENT DEFINITION
Payload
Propellant
Structure
=
+
Lo
Lb
SP
S
MMMM
MMM
10
PROPELLANT FRACTION DEFINITION
Payload
Propellant
Structure
=
+
Lo
P
SP
P
MMM
MMM
11
SUMMARY: SINGLE-STAGE ROCKETS
Payload
Propellant
Structure
Lo
P
SP
P
MMM
MMM
=
+
Lo
Lb
SP
S
MMMM
MMM
=+
SP
L
Lo
L
MMM
MMM
=
+
SL
o
b
o
MMM
MMR
R =
+ +
+
1R 1 12
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 firing2. 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
ML
3
2
Total Mass 1: Mo1=MP1+MS1+Mo2
Total Mass 2: Mo2=MP2+MS2+Mo3
Total Mass 3: Mo3=MP3+MS3+ML
Total Mass i: Moi=MPi+MSi+Mo(i+1)
14
MULTISTAGE ROCKET EXAMPLE
1
ML
3
2
Total Mass 1: Mo1=MP1+MS1+Mo2
Payload for Stage 1: ML1=Mo2
Total Mass 2: Mo2=MP2+MS2+Mo3
Payload for Stage 2: ML2=Mo3
Total Mass 3: Mo3=MP3+MS3+ML
Payload for Stage 3: ML3=ML
Total Mass i: Moi=MPi+MSi+Mo(i+1)
Payload for Stage i: MLi=Mo(i+1) 15
PAYLOAD RATIO: MULTISTAGE ROCKETS
1
ML
21
2
)1(
)1(
oo
o
iooi
io
Lo
Li MM
MMM
MMM
M
The payload ratio for stage 1 is:
1
16
PAYLOAD RATIO: MULTISTAGE ROCKETS
ML
32
3
)1(
)1(
oo
o
iooi
io
Lo
Li MM
MMM
MMM
M
The payload ratio for stage 2 is:
2
2
17
PAYLOAD RATIO: MULTISTAGE ROCKETS
ML
Lo
L
iooi
io
Lo
Li MM
MMM
MMM
M
3)1(
)1(
The payload ratio for stage 3 is:
3
3
18
STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS
1
ML
The structural coefficient for stage 1 is:
1
21
1
)1( oo
S
iooi
Si
SP
Si MM
MMMM
MMM
19
STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS
ML
The structural coefficient for stage 2 is:
2
32
2
)1( oo
S
iooi
Si
SP
Si MM
MMMM
MMM
2
20
STRUCTURAL COEFFICIENT: MULTISTAGE ROCKETS
ML
The structural coefficient for stage 3 is:
3
Lo
S
iooi
Si
SP
Si MM
MMMM
MMM
3
3
)1(
3
21
SUMMARY: MULTISTAGE ROCKETS
)1(
)1(
iooi
ioi MM
M
)1(
iooi
sii MM
M
)1(
)1(
iooi
iobii MM
MM
bi
oii MM
R ii
iiR
1
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 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 24
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