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Satellite EngineeringUniversidad de Concepción
November 2009
Gaëtan Kerschen
Space Structures & Systems LabUniversity of Liège
Day 3: Satellite Propulsion
Satellite EngineeringUniversidad de Concepción
November 2009
3
Launch Vehicles
The rest ? Mostly intercontinental ballistic missiles (ICBM)
4
Launch Vehicle: Order of Magnitudes
90%: propellant
9%: structure
1%: payload
5
Ascent Propulsion
Ascent propulsion is probably the factor over which a spacecraft designer has the least control.
Rarely is a mission so important that a specific engine or launch vehicle will be designed to fit its needs.
Yet it sets severe limits on payload, mass, volume and configuration !
6
Satellite Propulsion. Why ?
570 kilograms of propellant on board; the propellant mass is almost half of the overall spacecraft weight !
Venus Express (ESA)
7
Why ?
Venus Express (ESA)
Major spacecraft manoeuvres, like the injection into orbit around Venus, are performed by firing the main enginewhile minor manoeuvres are made using four pairs of thrusters located at the bottom corners of the spacecraft.
8
Propulsion for Orbit Transfer
Apogee motor for orbit circularization (Eutelsat)
9
Propulsion for Orbit Control
A nominal orbit is defined for the satellite. This is the orbit the satellite should maintain.
The orbit is controlled by applying forces to the satellite. Forces are applied by ΔV actuators.
Launch vehicle ~ 106 N, 10 minutes, ΔV~10 km/s
Apogee/perigee motors
~ 104 N, 1 minute, ΔV~2 km/s
Station keeping ~ [10-3 101] N, intermittent, ΔV~0.35 km/s (7 years)
10
Propulsion for Orbit Control
6 thrusters for orbit control (Meteosat)
11
Propulsion for Attitude Control
A nominal attitude is defined for the satellite. This is the attitude that the satellite should ideally maintain.
The satellite attitude is controlled by applying torques to the satellite. Torques are applied by attitude actuators.
12
Attitude Control vs. Orbit Control
How many DOFs does a (rigid) satellite possess ?
Trajectory dynamics ⎯Orbit control
Linear momentum
Motion of the center of mass
Attitude dynamics ⎯Attitude control
Angular momentum
Motion relative to the center of mass
Next lectureFocus in this lecture
13
Orbit and Attitude Are Interdependent
Examples:
1. In LEO, the attitude will affect the atmospheric drag which will affect the orbit
2. The orbit determines the spacecraft position which determines both the atmospheric density and the magnetic field strength, which will, in turn, affect the attitude
But this dynamic coupling is often ignored, and the time history of the spacecraft position is assumed to be known and to be an input for ADCS
14
Outline
1. Basics of space propulsion
2. The different engines
3. Orbit transfer
4. Orbit control
5. When propulsion does not suffice
15
1. Thrust: Theoretical Definition
The objective of a rocket engine is to produce thrust T:
Thrust is the result of all internal and external forces due to pressure and viscous effects developed by the fluid on all components of the engine.
, ,ax viscous int viscous extT pn dS F FΣ
= − −∫Not a helpful definition for a practical measure of thrust !
++
+
+ +
+ +
+
+-
T
Pressure imbalance at the nozzle exit
16
1. Thrust: Useful Equation
( )ej e a eT mv p p A= + −
Nozzle exit pressureAmbient pressure
(use of momentum balance)
Thrust is greater in a vacuum than at sea level
17
1. Thrust: Equivalent Exhaust Velocity
( )ej e a e eqT mv p p A mv= + − =
18
1. Performance Index: Specific Impulse
0
0
( )[ / ]
t
sp eqt
T t dt TI v m smmdt
= ≈ =∫∫
Total impulse of the mission (change in momentum)
Conventional method of comparing propellants: the higher the specific impulse, the less propellant is needed to gain a given amount of momentum.
19
1. Performance Index: Specific Impulse
0
0 00 0
( )[ ]
t
eqsp t
T t dt vTI sg m gg mdt
= ≈ =∫∫
Advantage of the definition: specific impulse is measured in seconds in any consistent system of units
20
1. Performance Index: Specific Impulse
Theoretical specific impulse of some propellantsEnergetic oxidizer but very difficult to contain; no practical use so farStorable: liquids at room temperature
LH2+LOX: cryogenics but best performing practical propellants (Ariane V, SSME)
No oxidizer !
21
1. ΔV Requirement ⎯ ΔV Budget
Thrust is not an essential quantity per se.
One of the main products of the mission design is a statement of the ΔV required for the mission (orbit transfer and orbit control):
ΔV (GTO ⇒ GEO) ≈ 1.5 km/s
In some cases, it is as important as power and mass budgets. For instance, it can be a principal design driver and impose complex trajectories for deep space probes !
22
1. Tsiolkovsky’s Rocket Equation (1903)
dVT mdt
=
eqT mv= −
( )ln lnf i eq f iv v v m m− = − −
eqdmdV vm
= −
0ln lni ieq sp
f f
m mv v I gm m
⎛ ⎞ ⎛ ⎞Δ = =⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
Propellant needs
Mission requirement Clear impact
of Isp !
Useful to convert ΔV in terms of propellant needs !
23
1. But… Coquilhat (1811-1890, Belgian)
Established the rocket equation in 1873 !
Trajectoires des fusées volantesdans le vide, Mémoires de la SociétéRoyale des Sciences de Liège.
Recent “discovery”.
24
100 101 102 103 10410-4
10-3
10-2
10-1
100
Δ v (m/s)
Δ m
/m
Isp=300s
(1000,0.288)
1. Delta-V: Order of Magnitudes
25
1. Digression: Single-Stage Rocket
[ ]
100ln ln 5 1.61100 80
5 7 km/s
ej ej ejv v v v⎛ ⎞Δ = = =⎜ ⎟−⎝ ⎠∈ −
80%: fuel
10%: dry mass
10%: payload
Vej = [3-4] km/s
What to conclude ?
26
Outline
1. Basics of space propulsion
2. The different engines
3. Orbit transfer
4. Orbit control
5. When propulsion does not suffice
28
2. Rocket Engines
29
2.1 Chemical Engines
Generate thrust by accelerating a high-pressure gas to supersonic velocities in a converging-diverging nozzle.
The high-pressure gas is generated by high-temperature combustion/decomposition of propellants.
Solid, monopropellant and bipropellant systems.
30
2.1 Chemical Engines: Monopropellant
Hot gases are obtained by decomposition of a single propellant and are expelled through a nozzle generating thrust.
Hydrazine is often used and is injected into a catalyst bed:Exothermic reaction: N2H4 ⇒ H2, N2 and NH3 (ammonia)
31
2.1 Chemical Engines: Monopropellant
Stored easily (freezing point at 2ºC).
Simplicity (no oxidizer).
Medium performance.
32
2.1 Chemical Engines: Monopropellant
Astrium CHT 400 N:
Hydrazine
Burn life: 30m
Length: 32cm
Ariane V attitude control system
Astrium CHT 1 N:
Hydrazine
Burn life: 50h
Length: 17cm
Attitude and orbit control of small satellites and deep space probes.
Herschel, Globalstar
33
2.1 Chemical Engines: Bipropellant
An injector introduces the oxidizer and the fuel into the combustion chamber.
Continuous and rapid combustion then occurs.
34
2.1 Chemical Engines: Bipropellant
Cryogenics (fluorine, oxygen and hydrogen) have never been used in satellites (storage reasons).
Nitrogen tetroxide (N2O4) and monomethylhydrazine(MMH) is the dominant combination.
35
2.1 Chemical Engines: Bipropellant
Complexity and cost.
High-performance system.
Wide range of thrust capability.
Versatility (pulsing, restart, variable thrust).
36
2.1 Chemical Engines: Bipropellant
Astrium S 400 N:
MMH (Fuel), N2O4-MON1-MON3 (Oxidizers)
For apogee orbit injection of GEO satellites and for planetary orbit maneuvers of of deep space probes
Venus Express, Artemis
Astrium S 10 N:
MMH (Fuel) N2O4-MON1-MON3 (Oxidizers)
Attitude and orbit control of large satellites and deep space probes
Venus Express, Arabsat
37
2.1 Chemical Engines: Solid
The oxidizer and fuel are stored in the combustion chamber as a mechanical mixture in solid form.
When the propellants are ignited, they burn in place.
38
2.1 Chemical Engines: Solid
Simplicity.
Reasonable performance.
No restart (single burn) ! Useful for orbit insertion or apogee kick motor.
39
2.1 Chemical Engines: Solid
ATK Star 27 (TE-M-616) 27 kN:
Burn time: 34s
Length: 1.3m
Gross mass: 361 kg
Apogee motor (GOES,GPS)
40
2.1 Comparison of Chemical Engines
41
2.2 Electric Engines
Low-thrust propulsion.
42
2.2 Electric Engines: Ion Engines
A cathode extracts electrons from the propellant which is ionized.
The ions are accelerated by a static electric field.
Propellant: Ar, Xe
44
2.2 Ion Engine: EADS Astrium
Astrium RITA 150 mN:
Xenon
Beam voltage: 1200V
Burn time: >20000h
Gross mass: 154 kg
Stationkeeping, orbit transfer, deep space trajectories
RITA-10 (Artemis)
45
2.2 Chemical vs. Electric Engines
Astrium CHT 1N: 210sAstrium CHT 400N: 220s
Astrium S 10N: 291sAstrium S 400N: 318s.
ATK STAR 27: 288s
Astrium RITA-150: 3000-5000s
[Cold gas: ~50s Liquid oxygen/liquid hydrogen 455s ]
Monopropellant
Bipropellant
Solid
Electric
46RITA, Astrium – The Ion Propulsion System for the Future
2.2 Chemical vs. Electric Engines
47
Outline
1. Basics of space propulsion
2. The different engines
3. Orbit transfer
4. Orbit control
5. When propulsion does not suffice
48
3. First Motivation
Without maneuvers, satellites could not go beyond the close vicinity of Earth.
For instance, a GEO spacecraft is usually placed on a transfer orbit (LEO or GTO).
49
3. From GTO to GEO: One-Impulse
Ariane V is able to place heavy GEO satellites in GTO: perigee: 200-650 km and apogee: ~35786 km.
GTO
GEO
50
For an orbit with a perigee at 320 km and an apogee at 35786 km, what is the velocity increment required to reach the geostationary orbit ?
24430 km2
a pr ra
+= =
10.13km/spv =
1.61km/sav =
GTO GEO
39800035786 6378
3.07km/s
circv =+
=
Answer: 1.46 km/s (apogee motor)
3. From GTO to GEO: One-Impulse
51
3. Delta-V Budget: GEO
52
The transfer between two coplanar circular orbits requires at least two impulses Δv1 and Δv2.
In 1925, Walter Hohmann conjectured that
The minimum-fuel impulsive transfer orbit is the elliptic orbit that is tangent to both orbits at its apse line.
The rigorous demonstration came some 40 years later !
3. Two-Impulse Transfer: Hohmann
53
1vΔ
2vΔ
1r2r
( )2
11 1 2 1
2v rr r r r
μ μΔ = −
+
( )1
22 1 2 2
2v rr r r r
μ μΔ = − +
+
circvrμ
=2 1
ellipvr a
μ ⎛ ⎞= −⎜ ⎟⎝ ⎠
3. Two-Impulse Transfer: Hohmann
54
3. Tangential Burns or Not ?
The major drawback to the Hohmann transfer is the long flight time.
Time of flight can be reduced at the expense of an acceptable increase in Δv.
A possible solution is a one-tangent burn. It comprises one tangential burn and one nontangential burn.
55
3. Tangential Burns or Not ?
Vallado, Fundamental of Astrodynamics and Applications, Kluwer, 2001.
56
Hohmann for interplanetary transfer
Dep.
Dep.
Dep.
Arr.
Arr.
Arr.
“ΔV1”
“ΔV2”
57
3. Second Motivation: Plane Change
A launch site location restricts the initial orbit inclination for a satellite.
Which one is correct ? For a direct launch
1. launch site latitude ≤ desired inclination.
2. launch site latitude ≥ desired inclination.
58
3. Hint
I
K
J
1 1ˆ( ).cos coszhi
h− − ⎛ ⎞×⎛ ⎞= = ⎜ ⎟⎜ ⎟ ⎜ ⎟×⎝ ⎠ ⎝ ⎠
r v Kr v
59
3. Launch Azimuth
0 50 100 150 200 250 300 3500
50
100
150
200
Launch azimuth, degrees
Incl
inat
ion,
deg
rees
Lat 0 degLat 20 degLat 40 degLat 60 deg
60
3. HST and Cape Canaveral
Hubble orbit inclination is 28.5º
What is the latitude of Kennedy Space Center (Cape Canaveral) ?
61
3. Inclination Change
Cranking maneuver: with a single Δv maneuver, one wants to change only the inclination of the orbit plane.
Where should we apply this maneuver ?
62
3. Inclination Change
The two orbit planes intersect in the equatorial plane. We can therefore change the inclination at an equator crossing, by a simple rotation of the velocity vector.
⊥vrv
⊥v
δ
View down the line of intersection of the two orbital planes
63
3. Delta-V Computation
( )2 1 2 1 2 2 1 1ˆ ˆ ˆr r rv v v v⊥ ⊥ ⊥ ⊥Δ = − = − + −v v v u u u
( )22 2 22 1 1 2 1 12 cosr rv v v v v v v δ⊥ ⊥ ⊥ ⊥Δ = − + + −
1 2 1 2,r rv v v v⊥ ⊥= =
2 sin2
v v δΔ =
64
3. Inclination Changes Are Expensive
0 10 20 30 40 50 60 70 80 900
0.5
1
1.5
δ, degrees
δ v
(% o
f v)
(24º , 41.6%)
(60º , 100%)
65
3. Remark: Hubble Servicing
Too costly ! Instead, NASA has chosen to have another shuttle ready to lift off to retrieve the astronauts if needed.
66
Outline
1. Basics of space propulsion
2. The different engines
3. Orbit transfer
4. Orbit control
5. When propulsion does not suffice
67
4. First Motivation: Orbit Raising
ISS reboost due to atmospheric drag (ISS, Shuttle, Progress, ATV).
68
4. Second Motivation: Stationkeeping
A GEO satellite orbit changes over time due to perturbations:
1. Inclination modified by the lunisolar attraction: N/S.
2. The longitude is modified by the tesseral terms of the geopotential: E/W.
69
4. GEO Satellites: Longitude Drift
C2,2 corresponds to the equatorial ellipticity.
70
4. GEO Satellites: Stationkeeping Box
A stationkeeping box is defined by a longitude and a maximum authorized distance for satellite excursions in longitude and latitude.
For instance, TC2: -8º ± 0.07º E/W ± 0.05º N/S
71
4. GEO Satellites: Delta-V Budget
72
Outline
1. Basics of space propulsion
2. The different engines
3. Orbit transfer
4. Orbit control
5. When propulsion does not suffice
73
5. How to Go to Saturn ?
VVEJGA
74
5. Gravity Assist
Also known as planetary flyby trajectory, slingshot maneuver and swingby trajectory.
Useful in interplanetary missions to obtain a velocity change without expending propellant.
This free velocity change is provided by the gravitational field of the flyby planet and can be used to lower the delta-v cost of a mission.
75
5. Basic Principle
SOI
Planet’s sun relative velocity
Resultant Vin
Resultant Vout
, ,out in∞ ∞= −Δv v v
76
5. Basic Principle
Inertial frame
Frame attached to the train
Inertial frame
Frame attached to the train
A gravity assists looks like an elastic collision, although there is no physical contact with the planet.
77
V VE
JS
5. Cassini: Swingby Effects
78
Satellite EngineeringUniversidad de Concepción
November 2009
Day 3: Satellite Propulsion
