Principles of Propulsion and its
Application in Space Launchers
Prof. Dr.-Ing. Uwe Apel
Hochschule Bremen
13.07.2012
REVA Seminar
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Overview
•
•
•
•
•
•
•
•
•
How Rockets are Propelled
Thrust Generation in a Rocket Engine
Rocket Engine Performance Parameters
Classification of Space Vehicles
Application of Rocket Engines
Classification of Rocket Propulsion Systems
Physical Limits of Chemical Space Propulsion
The Rocket Equation
Staging of a Rocket
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How Rockets are Propelled
•
The Change of the state of motion of a rocket follows the principle of
repulsion
•
Newton‘s law applies:
ACTIO = REACTIO
Any force acting on a mass creates an force of the same size in the
opposite direction!
•
By ejection of a mass at a high velocity (usually a hot gas flow ) from the
rocket engine a force is produced changing the momentum of the rocket.
Important: According to Newton‘ law of momentum conservation
d
d
( m1 × v1 ) + ( m2 × v2 ) = 0
dt
dt
the sum of the momentum changes of working fluid and vehicle equals 0 !
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Functional Principle of a Rocket
Thrust
is generated
pi
pi
m
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F = m× we
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exits nozzle with velocity
we
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Thrust Generation in a Rocket Engine
m × we =
òp
( x,r )
dx - Ae × pe + Ae × pa = F - Ae × pe + Ae × pa
CS
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Rocket Engine Performance Parameters
Thrust :
Characteristic velocity :
F = m × we + Ae × ( pe - pa ) = C × m
Thrust :
Mass - specific Im pulse :
tc
A × ( pe - pa )
C = we + e
= Is =
m
òF
(t )
× dt
t0
Weight - specific impulse :
F
I sp =
m × g0
Thrust coefficient :
mTr
=
F
m
Fc* pc × At
C =
=
m
m
F = Fc* × CF = m × C * × CF
*
= pc × At × CF = m × C
F
F
C
CF =
=
= *
*
m×C
pc × At C
Rocket engine
ther mod ynamic efficiency : hC =
Cexp.
Ctheor.
Thrust chamber efficiency :
*
Cexp.
hC* = *
Ctheor.
Nozzle efficiency :
hC =
F
= hC* × hCF
CF,exp.
CF,theor.
Thrust chamber performance
Fc* = pc × At = m × C *
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The Rocket Equation
• Describes Movement of • Differential form:
a rocket in force-free
space
• Calculates velocity
change achievable with
• Integral form:
a rocket geaturing a
certain mass ratio and
average specific Impulse
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Classification of Space Vehicles
Space Vehicles
Earthbound
Systems
Launch Vehicles
Space Ferries
Planetary Launch
and Landing
Vehicles
Sounding
Rockets
Expendable
Launch Vehicles
Interorbital
Ferries
Atmosphere
reentry Bodies
Rocket Planes
Reusable
Launch Vehicles
Space Tugs
Manned
Support Vehicles
Unmanned
Ballistic Missiles
Ballistic
Winged
Landers
Launchers
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Classification of Rocket
Propulsion Systems
• Origin of propulsion energy
– Chemical
– Nuclear
– Solar
• Propellants and their aggregate state
–
–
–
–
Solid propellants
Liquid propellants
Hybrid engines
Cold gases
• Thrust level
– High thrust (> engine weight)
– Low thrust (< engine weight)
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Application of Rocket Engines
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Typical Performances of Rocket Engines
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Rocket Engine Performance Map
specific impulse [m/s]
thrust to mass [N/kg]
acceleration [m/s]
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∆V Requirement
• The ∆V requirement of a space mission is
dependent on:
– Size and orbit of launch planet
– Size and orbit of destination planet
– Propulsion concept (thrust level, propulsion
time)
– Chosen trajectory and resulting flight time
– Accuracy of orbit and attitude control system
– Vehicle aerodynamics
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∆V Calculation
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Typical ∆V Requirements
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Elements of a Space
Transportation System
Space Transportation System
Vehicle (Launcher, Upper Stage,
Transfer Vehicle, Lander)
Ground Infrastructure
Rocket Engine
AI&T Buildings
Tankage
Propellant Production
and Storage Facilities
Structure
Control Center
Avionics
Tracking and Data Relay
Facilities
Electrical and
Hydraulical systems
Launch Platform
Payload
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Elements of a Rocket
The take-off mass of a rocket consists of three major mass elements:
• Structure and Engine(s)
–
–
–
–
–
–
Body and tankage
Engines and related equipment
Non-usable propellant residuals
Usable propellant reserve
Recovery equipment (parachutes, wings, landing gear, etc.)
Instrumentation and avionics
• Propellants
– Expected propellant consumption during flight
– Propellants expended prior to lift-off
• Payload
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Design Parameters
•
•
•
•
According to the rocket equation a maximisation of the ratio between the initial
mass m0 and the cut-off mass mc is required for a high velocity capability
Thus 80% ÷ 90% of the initial mass of a rocket is propellant mass
This requires an ultra-light structural design and small, efficient engines with a
very high power density!
Key design parameters of a rocket are:
– The propellant mass fraction
– The propellant ratio
– The payload ratio
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Technological limits for a rocket
• The performance of a single-stage rocket is limited
by the technologically achievable values for the
mass ratio R and the exhaust velocity C and the
∆V requirements of the mission:
• Limits:
– useful minimum payload mass fraction of
– achievable propellant mass fraction of
– today’s engines performance of
m/s
–minimum velocity increment to reach orbit
l
µ
C0
Cvac
>=
=
=
=
∆V
=
1%
0.90
4300 m/s
4600
9100 m/s
• Thus, it is very difficult to design a one-stage
launch vehicle!
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Technological Limits: Single-stage
to Orbit (SSTO)
me =
mpropellant
mpayload
mpropellant + mstructure
mpropellant
mstructure
mpropellant ³ 87,9% × m0
mstructure ³ 9,8% × m0
mpayload £ 2,3% × m0
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High
Development Risk!
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Staging of a rocket
• The problem can be overcome by "staging" the rocket which means
distributing the total propellant mass over more than one tank for each
propellant component and not further accelerating empty tankage by
cutting it off
• In theory a rocket with an infinite number of stages would provide a
maximum payload ratio
• Practically the number of stages is limited by the propellant mass fraction
of each stage which increases with decreasing stage size because tanks
and engines cannot be downsized linear
• For transportation in orbits around Earth, 2-3 stages provide an optimum
performance depending on the selected propellant combination and other
design aspects
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Influence of staging on payload
mass (example)
One-stage
design
Two-stage
design
Assuming a launch vehicle
based on following design data:
Mission velocity requirement
(Earth to orbit):
Average specific Impulse
of engines:
Launch mass:
Propellant mass fraction:
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∆V=9200 m/s
C=4400 m/s
m0=100 Mg
µ=0.9
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Influence of staging on vehicle
mass and payload
One-stage design
Two-stage design
émù
U 0 ³ DV = 9200 ê ú
ësû
m propellant
émù
U0
= 4600 ê ú
ësû
2
m1 = m 2 = 0.90
ö
æ
÷
ç
1
÷ × m0 = 64847[kg]
ç
m propellant,1 = 1ç exp æ U1 ö ÷
ç ÷÷
ç
è C øø
è
æ1 ö
mstage,empty,1 = m propellant,1 × ç -1÷ = 7205[kg]
è m1 ø
m0,2 = m0 - m propellant,1 - mstage,empty,1 = 27948[kg]
U1 = U 2 =
æ
ö
ç
÷
1
ç
÷ × m0 = 87643[kg]
= 1æ
ö
U
ç exp 0 ÷
ç ÷÷
ç
è C øø
è
æ1 ö
mstage,empty = m propellant × ç -1÷ = 9738[kg]
èm ø
ö
æ
÷
ç
1
÷ × m0,2 = 18123[kg]
m propellant,2 = ç1ç exp æ U 2 ö ÷
ç ÷÷
ç
è C øø
è
m payload = m0,2 - m propellant,2 - mstage,empty,2 = 7811[kg]
m payload = m0 - m propellant - mstage,empty = 2619[kg]
l=
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m payload
= 0.0262 = 2.6%
m0
l=
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m payload
= 0.0781 = 7.8%
m0
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Optimum staging of a launch
vehicle
• Optimum distribution of total ∆V between the stages of a
rocket depends of specific impulses of stage engines
and stage propellant mass fractions
• For a two-stage vehicle, the payload mass fraction l of
the rocket with respect to a given mission ∆V can be
obtained from the following equation
æ
æ
ö ö æ
æ
ö ö
ç
ç
÷ ÷ ç
ç
÷ ÷
1
1
1
÷ ç1
÷
l = lstage1 × lstage2 = çç × çç
-1÷ +1÷ × ç × ç
-1÷ +1÷
æ U1 ö ÷
æ U2 ö ÷
m1
m2 ç
çç
ç exp ç ÷ ÷ ÷÷ çç
ç exp ç ÷ ÷ ÷÷
è C1 ø ø ø è
è C2 ø ø ø
è
è
è
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Optimum staging of a launch
vehicle
• For a rocket with the same average specific impulse
and propellant mass fraction in each stage, the l Function has its maximum at U1=U2=∆V/2
• This means, that the first stage of a two-stage rocket
should have a mass which is 3.6 times the mass of the
second stage if the same technology is used in both
stages
• For a launch vehicle going from Earth‘s surface to an
orbit the described theoretical optimum is additionally
influenced by the ascend trajectory due to:
– gravity and drag losses (changes theoretical ∆V
distribution)
– engine performance (C depends on ambient pressure)
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Optimum staging of a launch
vehicle (Example)
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