Andy Stamp
Department of Communication
& Electronic Engineering
UoP 2002
SATELLITE PROPULSION
Modern propulsion systems are based on the research of a great many physicists
including Newton, Keppler, Tsiolkovsky and Goddard. Newton’s laws are a good
place to start:
1. Every body continues in its state of rest, or in uniform motion in a straight line,
except in so far as it is compelled by impressed forces to change that state.
2. Change in motion (momentum) is proportional to the impressed force and
takes place in the direction of the straight line in which the force acts.
Force = Rate of change of momentum x some constant
Force = Mass x Acceleration
Force = Mass flow rate x Velocity
Force = Pressure x Area
3. Action and Reaction Force are equal and opposite
Rocket Propulsion
Photo: Sirius Web site
Without rockets there would be no artificial satellite systems in use, they remain the
only means for placing communications systems into space (the space shuttle, or
Space Transportation System (STS) uses strap-on rockets too!). Ariane and other
expendable launch platforms are classic users of staged liquid propellant rocket
technology. Launch vehicles typically use liquid propellant rockets supported by
strap-on solid propellant boosters to provide additional thrust.
None of the systems mentioned above have the ability to place satellites directly into
geosynchronous orbit, but may be used to place a satellite into a Geosynchronous
Transfer Orbit (GTO). Currently, conventional staged expendable rockets place the
satellite into GTO, or the STS may place the satellite into a low Earth orbit and then
use a rocket at perigee to convert to GTO. None of the systems mentioned above
have the ability to place satellites directly into geosynchronous orbit. In practice a
solid propellant rocket motor, actuated at the point in the GTO furthest from Earth
(apogee), is invariably used to ‘kick’ the satellite into a geosynchronous orbit. This
unit is known as the Apogee Boost Motor (ABM), it is a once-only device!
A rocket motor burns propellant in a controlled way at a given rate. The rate at which
the propellant mass is used up (known as the mass flow rate, M p ) is fundamentally
related to the force the rocket motor can develop. In theses situations, the result of
controlled combustion within a pressure vessel (chamber) is a very high relative
pressure (with respect to the ambient pressure outside the chamber).
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The chamber is fitted with an exit aperture designed to accelerate any flow through it
(i.e. a nozzle), and because the pressure builds-up very quickly, the difference in
relative pressure causes the gaseous products of combustion to leave the chamber
as a high velocity exhaust gas (known as Efflux).
Nozzles
Rocket systems use a device which is first convergent and then divergent,
consequently this type of nozzle is sometimes known as a Con-Di nozzle, propulsion
engineers know this type of nozzle as a DeLaval Nozzle.
When propellant is burnt in a combustion chamber fitted with a DeLaval Nozzle, the
Efflux leaves the chamber as a sub-sonic flow and accelerates as it journeys through
the convergent (constricting) nozzle becoming transonic at the throat (the narrowest
part of the nozzle). The convergent nozzle accelerates sub-sonic flows up to Mach
1(340m/S). The divergent nozzle will accelerate any flow at Mach 1 or above. As the
velocity of the Efflux increases accelerates its pressure falls, from a very high
chamber pressure to a pressure around ambient at the output. Simultaneously, the
Efflux velocity goes from zero in the chamber to a high supersonic value at the exit
of the DeLaval Nozzle. The resulting force causes the rocket motor to accelerate in a
direction opposite to the exhaust. This will cause an untethered to move very
quickly!
Maximum propulsive force is generated when nozzle exit pressure P E is equal to the
ambient pressure PA . So for most rocket applications, rocket motor designers try to
ensure that PE = PA , in which case the nozzle is said to be fully expanded. However,
in space the ambient pressure is zero, so a fully expanded is not possible.
The reactive force due to the motor Efflux is proportional to the chamber pressure
multiplied by the area of the throat.
F  PC.A T
Photographs courtesy of: The Communications Satellite by M Williams
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Rocket Performance Factors
Specific Impulse ISP
A frequently quoted, and most important, measure of rocket performance is its
Specific Impulse. This is given by the ratio:
ISP 
Thrust Provided F

Mass Flow Rate M
P
Newtons
 kg 
 
S
 

 kg.m 

2 
 sec 
 kg 


 Sec 

m
S
Clearly, specific impulse has units of velocity, but sometimes, specific impulse is
expressed in units of seconds. This occurs when specific impulse is defined in terms
of thrust per propellant weight flow rate. At sea level, the acceleration due to gravity
is 9.81 m/s2 (i.e. about 10m/s2, and can be used to convert mass into weight.
Hence, these values represent the same impulse:
2500
Newton .Sec
m
= 2500
kg
S
= 250 Seconds
Typical values of specific impulse are as follows:
Solid propellant rocket:
Liquid propellant rocket
290 Seconds
200 to 290 Seconds
Specific Impulse is based on two factors which are combustion efficiency (mainly the
ratio of chamber temperature and mean molecular weight of propellant); and the
nozzle efficiency (mainly the thrust developed). As will be shown shortly,
F
ISP
 CF .C *

MP
Combustion Efficiency (C*) is proportional to the product of Chamber Pressure
and the size of the nozzle throat; but inversely proportional to the mean molecular
weight of the propellant.
Combustion Temperatur e
C* 
Mean Molecular Weight of Propellant
C* 
PC AT
MP
Thrust Coefficient (CF)
Is an indicator of nozzle performance and is proportional to thrust and inversely
proportional to chamber pressure and nozzle aperture size. Thrust Coefficient is a
measure of the amount of expansion and lies in the range 1.2 to 1.6 and is roughly a
P
measure of the ratio E
PC
Note that the nozzle:
F
is fully expanded when
PE = PA
CF 
PC .A T
is under expanded when PE > PA
is under expanded when
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PE < PA
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Background to Solid Propellant
Solid propellant is safe, manageable and easy to handle, even when not installed in
a casing. It offers high specific impulse and is used extensively especially for
Apogee Boost Motors (ABM’s) and often used for strap-on boosters.
There are two commonly used types of solid propellant; homogenous and
heterogeneous.
1. Homogenous Solid Propellant
Is often called double-base because the fuel and oxidant are contained in the same
molecule, and is in the form of solidified slurry. Favourite double bases are, Nitrocellulose (50%) and Nitro-glycerine (35%) C3H5(ONO2)3, and the desired shape is
produced either by casting or extrusion. The remaining ingredients are additives
used as performance enhancers:
Platonizer
Plasticiser
Smoke Suppressant
Stabiliser
Flash suppressant
Lubricant
Lead Salts
Diethyl-Phthalate
Potassium
Carbamite
Potassium Sulphate
Candle wax
2 to 3%
3%
1%
2%
X%
0.08%
2. Heterogeneous Solid Propellant
Heterogeneous Solid Propellant is a very popular choice for commercial satellite
rocket motors. A mix of oxidising crystals and organic fuel is usual. The oxidant is
most often Ammonium Perchlorate (NH4CLO4), in which case 70% of the propellant
is Ammonium Perchlorate and 12% to 15% organic fuel such as Hydroxyl
Terminated Poly Butadiene (HTPB), or Carboxyl Terminated Poly Butadiene
(CTPB), which is similar to polyurethane. The Apogee motor for Ariane, the Mage
(Moteur Apogee Geosynchronous), uses CTPB 12.
CTPB12
72% (NH4CLO4), 12% CTPB and 16% Fine ground Al (10µm)
Some propellant is elastomer modified which is used to reduce the tendency of
double base propellant to crack or split. This would be catastrophic, so nondestructive testing is used to make sure motors are satisfactory.
Photograph courtesy of: esa
Solid propellant is usually initiated with a (pyro-electric) igniter and propellant burns
at exposed surfaces. Greater thrust (shorter burn times) results from burning more
exposed propellant. Once initiated the motors can be extinguished but cannot be reused. Control during use is by means of thrust vector control.
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Background to Liquid Propellant Motors
Liquid propellant systems can be controlled much more easily and offer full thrust
control on demand by varying the flow of propellant. In terms of satellite systems,
liquid propellant is either cryogenic or packaged.
As was indicated earlier, propellant with low ‘mean molecular weight’ provides a high
specific impulse. Investigation into suitable mixtures of oxidant and fuel with low
mean molecular weight will show that many suitable propellant mixes are very
harmful to people. What’s more many are hypergolic and will spontaneously
combust on contact. One sensible way of dealing with difficult to handle and manage
material such as this is to package them. Other options such as oxygen and
hydrogen are highly attractive but must be kept very cold to remain in gaseous form
(resulting in the use of many cryogenic liquid options).
Cryogenic systems
Every school boy is familiar with the ‘steaming’ stacks of NASA STS launcher and
Arianespace rockets containing liquid oxygen (LOX) and liquid hydrogen (if you’re
older it will be images of Saturn 5 rockets that spring to mind). The propellant is
deeply cooled and needs constant topping-up whilst on the ‘pad’ to replace losses
due to evaporation the nozzle.
Packaged systems
Most packaged propellants, which are extremely toxic and hypergolic, use a
pressurised bi-propellant system. Oxidant and fuel are packaged separately in
sealed tanks and operated at ambient temperature. Complete separation and
isolation must be maintained until combustion is required at which time the two
components must be made to meet in a combustion chamber where ignition is
instantaneous.
The usual methods of delivering the oxidant and fuel to the burner are:
1. Use of an inert gas to pressurise propellant tanks and cause
2. Use of centrifugal force (Pelton wheel drives, or spin stabilised systems)
3. Gravity feed (terrestrial systems).
Liquid propellant systems are complex and need high levels of redundancy to
prevent failure. Exhaust Efflux is often toxic, but the propellant itself is horribly toxic
(examples: Inhibited Red Fuming Nitric Acid (IRFNA), Mono-methyl Hydrazine
(MMH), and Unsymmetrical Mono-Methyl-Hydrazine UDMH).
However, they do offer thrust on demand and high levels of specific impulse (a
typical propellant density ρ =1300 kg/m3). The exhaust plume is generally free from
radio reflectants and low in particulate output.
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Getting the Satellite into orbit
The Earth spins on it’s axis at a considerable speed, so launching a spacecraft from
Earth is made a good deal easier if the velocity of the Earth can be utilised. This is
highest at the equator and ‘zero’ at the poles. The equatorial velocity of Earth is
greater than 465 m/S (1674 km/Hr), which is a sizeable portion of the 11200 m/S
escape velocity needed by any spacecraft. For this reason, Launch sites tend to be
near to the equator.
Kourou (French Guiana)
Latitude 5.23o
436 m/S
Cape Canaveral (Kennedy USAFB)
Latitude 28.5o
409 m/S
A conventional launcher like Ariane uses 2 of its 3 stages to get the satellite into a
low earth orbit. Stage 1 separates at a height of 43km, stage 2 separates at a height
between 150km to 300km. The remaining structure orbits in a GTO with apogee at
38,850km and perigee 200km. After several orbits and various re-orientations to
adjust attitude, the Apogee Boost Motor is fired to give a final geosynchronous
satellite orbital height of 35,786km. Carrying all the propellant and related containers
into space is made much more efficient by disposing of the rocket motors that do
much of the work as soon as possible. This also allows them to be collected and reused (some of the NASA stages are re-used almost 20 times).
Illustration from: Satellite Communications by D Roddy
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Tsiolkovsky’s equations are used to calculate stage performance.
VB  ISP.logn
M0
MB
M0 is the total Mass at launch
MB is the total Mass at stage burn-out
The velocity of a two stage rocket (assuming the same specific impulse for each
stage), when the first stage is ejected and falls-away is given by:
VB1  ISP.logn
M0
MB1
At the end of second stage burning, the velocity is:
VB2  ISP.logn
VB2  ISP.logn
M0
 VB1
MB2
M0
M
 ISP logn 0
MB2
MB1
The effective mass ratio for ‘n’ stages is the product of the individual mass ratios.
Staging improves the overall performance because the percentage of propellant
mass becomes increasingly smaller (with respect to total mass) for the later stages.
Prove this for yourself by comparing the
performance a single stage system, with that of
a two stage system (in the example, both have a
total % propellant mass of 88% and a total %
structural mass of 12%).
Single Stage
88% Propellant
12% Structure
Stage 1:
72% Propellant
8% Structure
Stage 2:
16% Propellant
4% Structure
Two Stage:
The two stage system has a mass ratio 1.36
better than the single stage, and since range is
proportional to the square of the mass ratio; the
possible range is nearly doubled.
Illustration courtesy of 'Sirius'
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The Space Shuttle (STS) dumps its solid propellant boosters (which descend on
parachutes and are re-used many times) 2 minutes after launch (43km); at 115km
the main engines stop firing and the strap-on external tank separates from the
shuttle.
Photographs courtesy of: NASA
The payload bay is opened and the payload ejected at it pre-planned position, as the
shuttle orbits at 200km. Once the shuttle is away, the satellite initiates its perigee
kick motor, to place it in an elliptic transfer orbit. At an appropriate time the apogee
boost motor is fired to place the satellite into geosynchronous orbit.
Photographs courtesy of: NASA
Illustration from: Satellite Communications by D Roddy
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Station keeping
Although early satellites were spin stabilised, and some use a gravity gradient
device, most satellites are three-axis stabilised. This requires a full inertial platform
on the satellite to sense any movement of the satellite off its chosen station. The
satellite doesn’t stay where it’s placed because Earth is elliptical, and has two
gravitational foci instead of one at Earth’s centre (which would arise for a spherical
Earth in a circular rotation). Satellites tend to drift towards these foci at 105 oE and
75oW (the minor axes points). If the satellite ends up at these locations they will tend
to stay there, other semi-stable locations are 165oE and 15oW. There are many
other reasons why satellites might drift, whatever the reason; the system engineer
needs the means to make corrections.
As the three dimensional position of the satellite is constantly monitored, any drift
from the chosen location is soon discovered. Similarly, the movement which would
re-place the satellite would be easily found. The system engineers use the Tracking
Telemetry & Control (TT&C) sub-system to communicate changes if required.
Sun seeking sensors and RF beacons also support station sensing. A three axis
stabilised satellite is kept on station by firing appropriately selected liquid propellant
rocket motors, in short bursts, these very small (1Newton to 100 Newtons thrust) are
positioned all over the spacecraft and form the Reaction Control System (RCS) of
the satellite.
Photograph courtesy of esa
Illustration: Satellite Communications by D Roddy
Photograph: The Communications Satellite by M Williams
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mms://media.imedia.net/intelsat/906launch9-6-02highlites.asf
http://www.esa.int/export/esaLA/ASEVLU0TCNC_index_0.html
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