PH508: Propulsion Systems.
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Transcript of PH508: Propulsion Systems.
PH508: Propulsion Systems.
Spring 2011: [F&S, Chapter 6]
Derivation of escape velocity: I
Q; What velocity, v, do I need to just escape the gravitational pull of the planet? (the escape velocity).
A: Think about the energies involved!
Initial state:
Kinetic energy = 0 (planet) +
Gravitational potential energy =
Derivation of escape velocity: II
2
21 mv
rGMm
Final state:
Kinetic energy = 0 (planet) + 0 (spacecraft)
Gravitational potential energy =
Initial state energy must equal final state energy
Derivation of escape velocity: III
0
GMm
Therefore:
Derivation of escape velocity: IV00
21 2
rGMmmv
rGMv
rGMv
rGMv
rGMmmv
2
22121
2
2
2
LEARN THIS DERIVATIONAND THE FINAL EQUATION!
Conceptually The various phases of a space mission from
‘concept’ through to ‘end-of-life’ phase. An appreciation of some of the details of each of
these phases and how financial, engineering and science constraints etc. affect mission design.
How a spacecraft’s environment changes from ground level, near earth orbit and deep space.
How these environments (radiation, thermal, dust etc.) feedback into the final mission design.
What you should now know at this point!
Mathematically
Understand how to use the drag equation to work out the force on a body as it travels through the atmosphere
Calculate the solar constant for Earth and (other bodies) making justifiable assumptions.
Derive the escape velocity of a body.
What you should now know at this point!
PH508: Propulsion Systems.
Spring 2011: [F&S, Chapter 6]
Propulsion systems: I
4 major tasks:
1. Launch
2. Station/trajectory acquisition
3. Station/trajectory keeping (staying where it should be, or going in the correct direction).
4. Attitude control (pointing in the correct direction)
Propulsion systems: II
Launch Need lift-off acceleration, a, to be greater
than gravitational acceleration, g. (“a>g”) for an extended period.
This implies a very high thrust for a long duration. E.g., the shuttle main engine: 2 x 106 N for 8 minutes.
Typical Δv ≥ 9.5 km s-1 (including drag and gravity losses).
Propulsion systems: III
Launch phase (continued) Still difficult to achieve with current
technology Only achievable with chemical rockets Massive launch vehicles required for
relatively small payloads Major constraint for spacecraft and mission
design is the mass cost: £1000s - £10,000s per kilogram.
Propulsion systems: IV
Station/trajectory acquisition Apogee motors (apogee = ‘furthest point’)
◦ Orbit circularisation ◦ Inclination removal◦ Requires a force of ~75 kN for 60 seconds. Δv = 2 km
s-1. Perigee motors (perigee=‘nearest point’)
◦ Orbit raising◦ Payload Assist modules (‘PAM’)◦ Interial Upper Stages (‘IUS’)◦ Δv ~4.2 km s-1 (30° inclination parking orbit ->
equatorial geostationary).
Propulsion systems: V
Earth Escape Δv ~ 7.6 km s-1 (Mars flyby) Δv ~ 16 km s-1 (Solar system escape
velocity)◦ Without using gravity assist manoeuvres.
Station/trajectory keeping Low thrust levels required (mN – 10s N)
pulsed for short durations. Δv ~ 10s – 100s m s-1 over duration of
mission.
Propulsion systems: VI
Attitude control (‘pointing’)
Very low thrust levels for short duration Small chemical rockets Reaction wheels (diagram).
Principle of operation of all propulsion systems is Newton’s third law
“...for every action, there is an equal and opposite reaction...”
Propulsion systems: VII
Rocket equation: I
Derivation: Need to balance exhaust (subscript ‘e’) momentum with rocket momentum.
∑momenta = 0 (Conservation of linear momentum)(Recall: momentum = mass x velocity)
∴ m dV = -dm Ve dV = -Ve dm/m
So, now some maths...
Rocket equation: II
mmVVV
mmVVVmmVVV
mVV
mdmVdV
oeo
oeo
oeo
mme
VV
V
V
m
me
oo
o o
ln
lnln]ln[ln
ln
Tsiolkovsky’s Equation (the rocket equation).
•dm is the mass ejected
•dV is the increase in speed dueto the ejected mass (dm)
•Ve is the exhaust velocity (ie. thevelocity of the ejected mass relative to the rocket)
•m is the rocket mass (subscript‘o’ denotes initial values)
In practice, drag reduces Vmax by~0.3 – 0.5 km s-1.
Recall (in zero g):
Now add gravity: (diagram)
Rocket equation: III (with gravity)
dtdmV
dtdVm e
Bfo
o
s tmm
me
V
e
e
e
gdtdmm
VdV
gdtdmm
VdV
gdtdm
mV
dtdV
mgdtdmV
dtdVm
00
1
1
1
Bfo
oes
Bfooes
Bmm
mes
tmm
me
V
gtmm
mVV
gtmmmVV
gtmVV
gdtdmm
VdV
fo
o
Bfo
o
s
ln
lnln
ln
1
00
Rocket equation: IV (with gravity)Integrating previous equation:
Define R as:
Rocket equation: V (with gravity)
fo
o
mmmR
e
Bs
es
e
Bses
e
Bsees
Bses
VtgRR
RVV
VtgRVV
VtgVRVV
tgRVV
exp
ln
expln
ln
ln
R’ is the “effective mass ratio
•Vs =spacecraft velocity•Ve= exhaust velocity•gs = accl. of gravity acting on spacecraft•tB = rocket burn time•mf= mass of fuel
Therefore, want a short burn time as possible to minimise gravitational losses.
Gravitational losses reduce V by ~1 km s-1
This conflicts with the requirements to reduce drag effects at low atmosphere (low speed at low altitude)
Resolve conflict by using non-vertical ascent.
Rocket equation: VI (with gravity)
Rocket equation: VII (with gravity)
Retarding gravitational force = ge cos θ
ge = net downward accl. = gravity - centrifugal
Typical launch sequence:◦ Lift-off (straight up!)
◦ Clear tower
◦ Roll to correct heading
◦ Pitch to desired trajectory
◦ Recall space shuttle launch sequence. Rolls and pitches almost immediately after clearing tower. Reason to minimise loss dues to drag and gravity!
Rocket equation: VIII (with gravity)
Assume a single stage, liquid propellant chemical rocket.◦ Fuel – kerosene◦ Oxidiser – liquid oxygen◦ Typical of fuel used for Atlas, Thor, Titan and
Saturn rockets.
Ve ~2.5 km s-1, assume mass: 20% structure, 80% fuel
Recall,
Rocket equation: an example
5
fo
o
mmmR (In this case)
Rocket equation: an example (cont.)
4lnmax RVV e km s-1
•Compare with Earth’s escape velocity ~ 11 km s-1!
•Velocity required for 300 km altitude Earth orbit ~7.8 km s-1.
•Taking into account drag and gravity losses implies arequired Vmax ≥ 9.3 km s-1
•Best performance from a fully cryogenic fuel system get Vmax ~9.5 km s-1.
SOLUTION: Multi-Staging!
Parallel staging◦ Partially simultaneous operation (e.g. Space
Shuttle) Series staging
◦ Sequential operation (e.g. Ariane, Saturn V etc.)
Principle: jettison inert mass to reduce load for subsequent rocket stages.
Stage velocity, Vs = Vmax – Vo = Ve ln R = -Ve ln (1-R)
Multi-stage rockets: I
Stage velocity, Vs = Vmax – Vo = Ve ln R = -Ve ln (1-R)
Jettisoning structure from stage ‘n’ increases R (the mass ratio) and thus Vs for the subsequent stages, n+1, n+2 etc.
However, since Vs ∝ ln R, improvement is slow with R
Multi-stage rockets: II
Assume a simple rocket where: mf = mass of propellant ms = mass of structure mp = mass of payload mo = mf + ms + mp Define mass ratio, R: Payload ratio, P: Structure ratio, S:
Multi-stage rockets: III – an example
RSSRP
mm
mmm
S
mmP
mmm
mmmR
s
f
s
sf
p
o
fo
o
sp
o
1
1
Assume a liquid propellant chemical rocket.◦ Fuel – kerosene◦ Oxidiser – liquid oxygen◦ Typical of fuel used for Atlas, Thor, Titan and
Saturn rockets.
Ve ~2.5 km s-1, assume: 1t structure, 8t fuel, 1t payload
Recall definition of payload ratio, R
Mutli-staging: an example
5210
8)811(811
fo
o
mmmR
(In this case)
RSSRP
mm
mmm
S
mmP
mmmR
mmmm
s
f
s
sf
p
o
sp
o
spf
1
1
0
Mutli-staging: an exampleNow calculate the payload ratio, P and the structure ratio, S.Recall: mo = 1 + 8 +1= 10, mf = 8, ms = 1 tons.
511
10
91811
10110
sp
o
s
f
p
o
mmmR
mm
S
mmP
For our kerosene rocket:Ve ~ 2.5 km s-1 , R =5
Recall, Vs = Ve ln R = 2.5 x ln 5 ~ 4 km s-1
∴ Vs = 4 km s-1 – suborbital!
Now consider this 10 ton rocket to be a payload (i.e. a stage) of a larger rocket…
Multi-stage rockets: IV – an example
Therefore, assume that the mass/fuel ratio is the same for the second stage, and thus we can use the same ratios (ie, this stage is just a scaled up version of the original stage):
∴ mp= 10t and thus,
mo= P x mp = 10 x 10t = 100t
Now our 1 ton original payload can reach: 4 + 4 = 8 km s-1 – orbital, just…
using a 100t rocket!
Multi-staging: example continued
Now consider this 100 ton rocket to be a payload (i.e. a stage) of an even larger rocket…
Therefore, assume that the mass/fuel ratio is the same for the previous stage, and thus we can use the same ratios:
∴ mp= 100t and thus,
mo= P x mp = 10 x 100t = 1000t
Multi-staging: example continued
Now our 1 ton original payload can reach: 4 + 4 + 4= 12 km s-1 – escape velocity
using a 1000t rocket!
Therefore a 3-stage kerosene rocket can put a payload into orbit, and reach Earth escape velocity, whereas a single stage could not!
Multi-stage rockets: V – an example
In general:
◦Vmax = ∑Vs
Maximum rocket velocity is the total of the stage velocities.
Using conventional definitions (i.e. 1st stage is the first to burn etc.), the payload ratio of the ith stage is, Pi:
Multi-stage rockets: VI
1
oi
oii m
mP
(ie. The payload ratio of stage 1 = mass of stage 1/ mass of stage 2)
Thus the total payload ratio, P is:
The structural payload, S is:
And the mass ratio, R is:
Multi-stage rockets: VII
np
o PPPPmmP 321
1
si
sifii m
mmS
fioi
oii mm
mR
Therefore,
And if all stages have the same Ve
(Generally, however, this is not the case)
Multi-stage rockets: VIII ieis RVVV lnmax
n
e
ne
ie
RRRRRRVV
RRRVV
RVV
321
max
21max
max
lnlnlnln
ln
Stage
Propellant Ve (km s-
1)
mf (tons)
ms (tons)
thrust(tons wgt)
burn time(secs)
1st Kerosene + O2 2.32 2160 140 3400 1502nd H2(l) + O2(l) 4.10 420 35 450 3903rd H2(l) + O2(l) 4.25 100 10 90 480
1st Stage
2nd Stage
3rd Stage
Fuel consumption (tons/sec) 14.40 1.08 0.21For a payload, mp, of 100 tonsmoi 2965 665 210Ri 3.69 2.72 1.91Pi 4.46 3.16 2.10Vsi (km s-1) 3.03 4.10 2.75
Multi-stage rockets: IX – the Saturn V
Note high thrust of 1st stage High efficiency of stages 2 and 3 P for a 3 stage kerosene rocket ~90 P for the Saturn V ~ 30 (more efficient).
Such a rocket could lift:◦ 100 tons into a low earth orbit◦ 40 tons into earth escape (i.e. to the moon)◦ 1 ton payload to Mars!◦ For Apollo, the Saturn V lifted the Command module to
LEO.◦ The command module went to the moon and back.
Multi-stage rockets: X – the Saturn V
Optimisation of number of stages:Q: What is the optimum number of stages?Theoretically...recall:
Multi-stage rockets: XI
22
2
11
121
321
321
11
1
1
RSS
RSSRRP
RSSRP
RRRRRPPPPP
RSSRP
ii
iii
n
n
P=payload ratio
R=mass ratio
S=structure ratio
Now, R=R1R2...Rn and if R1=R2=...=Rn
Then:
And if S1=S2=...=Sn, then:
Multi-stage rockets: XII
ni RR
1
n
nRS
SRP
1
1
(Effectively all this says is that the mass ratios of each stage are thesame, just scaled versions of each other).
Optimisation of number of stages involves minimising P
∴ want to minimise:
∴want to maximise 1/n, i.e., n→∞.
Q: Why don’t we see systems with very large numbers of small stages?
Multi-stage rockets: XIII
nRS
S1
1
Each stage requires:◦ Engine and nozzles◦ Ignition mechanism◦ Separation mechanism◦ Fuel pumps (for liquid propellants)◦ Small stages have worse P, R and S.
Therefore greater cost and complexity Thus a ‘trade-off’. ‘n=3’ is usually the maximum number of
stages (some ‘n=4’, but rare).
Multi-stage rockets: XIV
Because the Earth revolves on its axis from West to East once every 24 hours (86400 secs) a point on the Earth’s equator has a velocity of 463.83 ms-1.
Reason: radius of the Earth, RE = 6.3782 x 106 metres.
Earth’s circumference = 2πRE = 4.007 x 107 mEquatorial velocity = 4.007 x 107 / 86400 =
463.83 ms-1
Geographical velocity boost: I
Therefore, a spacecraft launched eastwards from the Earth’s equator would gain a free increment of velocity of 463.83 ms-1.
Away from the equator the Earth has a smaller circumference which is determined by multiplying the equatorial circumference by the cosine of the latitude in degrees.
For example, the Russian Baikonur Cosmodrome is at 45° 55’ north. The Earth’s rotational velocity at that point is: 322.69 m s-1.
Geographical velocity boost: II
System classification:◦ Various possible schemes (see F&S, Fig. 6.1)◦ Other ‘exotic’ systems possible
Function:◦ “Primary propulsion” – launch◦ “Secondary propulsion”
Station/trajectory acquisition and keeping Attitude control
Recall: vastly different requirements for different purposes:◦ ΔV of m s-1 – km s-1
◦ Thrust of mN – MN◦ Accelerations of μg - >10g
Different technologies applicable to different functions/regimes.
Propulsion systems: overview
Principle:◦ Combustion of propellants at high pressure in a small
confined volume produces high temperature gas.◦ Expansion through nozzles convert random thermal
energy to directed kinetic energy: “thrust”. Propellants:
◦ And fuel and oxidiser undergoing exothermic reaction producing gaseous products.
Considerations: ◦ Specific energy content, rate of heat release,
storage, handling, etc.
Chemical rockets: I
Chemical rocket types:◦ Solid propellant◦ Liquid propellant◦ Hybrid (usually solid fuel and a liquid oxidiser)
Solid propellant rockets:◦ Oldest rocket technology – Chinese 12th Century.◦ Very simple – no moving parts (nozzles?)◦ Only needs an igniter and a douser◦ Fuel stored in combustion chamber◦ Relatively cheap
Chemical rockets: II
Solid propellant rockets (continued) Advantages:
◦ Simple and cheap◦ Reliable◦ High thrust◦ High energy density propellant thus small volume
Disadvantages:◦ Only limited throttling◦ Generally only single burn (a firework effectively).
Chemical rockets: III
Solid propellant rockets (continued) Propellant is a fuel and oxidiser matrix with
aluminium powder regulator. Cast directly into casing of rocket Thrust is proportional to burn rate “Cigarette mode” – long duration, low thrust
because of small combustion area. Axial ignition used to increase burn area
and increase thrust.
Chemical rockets: IV
Solid propellant rockets (continued) Burn area and thrust defined by ‘grain’, produced
by the mandrel during casting of the fuel. This gives a limited amount of “pre-programmed”
throttling of the propellant. Ignition is via a pyrotechnic device which ignites
the propellant in the igniter. Axial burn. Applications:
◦ Early launch vehicles (missiles)◦ Launch vehicle strap-on boosters (e.g. Titan, Ariane,
Shuttle)◦ Secondary propulsion
Chemical rockets: V
Liquid propellant rockets First flight 16th March 1926.
◦ Robert Goddard using liquid oxygen and gasoline Max altitude = 12.5 metres Flight time = 2.5 seconds Engine thrust ~ 40 N Vmax ~ 96 km/hour Landed 56 metres from launch site
Advantages◦ Long burn time◦ Controllability
Throttling On-off-on operation Emergency shutdown Redundant systems
Chemical rockets: VI
Liquid propellants (continued) Disadvantages
◦ Complexity and reliability◦ Cost◦ Mass
Requirements◦ Separate storage of fuel and oxidiser remote from
combustion chamber ◦ Thus need propellant pump and feed system◦ Chamber injector and mixer◦ Igniter, combustion chamber and exit nozzle
Chemical rockets: VII
Liquid propellants◦ (Kerosene/ethanol) + liquid oxygen + N2O4◦ Monomethyl hydrazine (‘MMH’)◦ Unsymmetrical dimethyl hydrazine (‘UDHM’)◦ Aerozine50 (50/50 mix of hydrazine and UDMH)◦ Liquid hydrogen and liquid oxygen (cryogenic propellants)
Some combinations require ignition, others (known as ‘hypergols’) are self-igniting as soon as the fuel + oxidiser mix (e.g. Aerozine50 and N2O4).
Applications◦ Most modern launch vehicles◦ Secondary propulsion systems
Chemical rockets: VIII
Manned spacecraft, mainly reusable (unlike Ariane)
Expensive “launch vehicle” Designed to be multi-purpose
◦ Laboratory (‘Spacelab’)◦ Recovery repair and return of satellites◦ Space station servicing◦ Launch of satellites◦ Just about to be retired!
Space shuttle transport system (STS) : I
Primary propulsion system, two elements:◦ External fuel tanks feeding SSME (‘Space Shuttle
Main Engines’, x3)◦ Two solid rocket strap-on boosters
Burn for 120 seconds, separate, parachute into ocean 300 km downrange for recovery and reuse.
◦ SSMEs use closed cycle combustion with a chamber pressure of 207 Bar (20.7 GPa) and a burn time of 480 seconds
◦ 100% thrust ~2.1 x 106 N.◦ External fuel tank jettisoned (and burns up) pre
orbital insertion.
Space shuttle transport system (STS) : II
The space shuttle combines liquid and solid propellants.
Solid propellants give a lower ‘specfic impulse’ (thrust per mass of propellant) but are compact, simple and stable.
Once ignited it burns continuously. Thrust can only be controlled by varying the burn area.
The liquid propellant in the STS combines hydrogen and oxygen and can be throttled to vary the thrust.
The STS uses 2 SRBM (‘Solid Rocket Booster Motors’) and the liquid propellant in the main external tank during launch.
Space shuttle transport system (STS) : III
Thrusters (secondary propulsion units). Once in space there is still a need for thrust. There are two main types:
◦ Sustained high thrust for orbital manoeuvring etc.◦ Low thrust for atitude control (rotate the spacecraft, or to
controls its spin rate etc.) Cold gas thrusters
◦ Take an inert gas (nitrogen or argon) stored at high pressure and connected to a series of valves.
◦ The thrusters are arranged off-axis to control spin/rotation. ◦ Specific impulse is low with low volumes of gas◦ Typical thrust ~10 mN in short bursts.
Space shuttle transport system (STS) : IV
Monopropellant The decomposition of hydrazine (N2H4)
generates heat. Expansion of the hot gas through nozzles
produces a specific impulse. Hydrazine is a liquid between 275 – 387 K
and is held under pressure in tanks. Can provide ~10 N for orbital control and
station keeping.
Space shuttle transport system (STS) : V
Bi-propellant E.g. MMH/nitrogen tetroxide Propellants burn on contact They are mixed in the thruster/apogee
motor and can provide sustained thrust. Can be used for orbital rising as well as
atitude control. Provides precise amounts of thrust on
demand.
Space shuttle transport system (STS) : VI
Solid propellant apogee motors To launch into GEO etc. usually launch to a LEO
and then boost with a final stage burn. To achieve a high, circular orbit at apogee, need
a high thrust, short duration burn Usually provided by a solid propellant apogee
motor. For a GEO satellite of 1000 kg need 900 kg of
propellant and a ΔV of ~2 km s-1. Burn for 40-60 seconds with an average thrust
of 50 – 75 kN
Space shuttle transport system (STS) : VII
Space shuttle transport system (STS) : VIII
Shuttle external tankand SRBs
The characteristic feature of the SRB’s thrust curve’s profile is the period of reduced thrust (to about 70% of max. 50 secs. into the flight) giving a ‘sway-backed’ appearance (below).
SRBs ‘sway-back’ thrust profile: I
Its purpose is to reduce the thrust while the shuttle is passing through the region of maximum dynamic pressure. This is when the product of velocity and air pressure is a maximum and when the possibility of damage by aerodynamic forces is greatest.
Therefore minimise risk by reducing thrust for a short period.
SRBs ‘sway-back’ thrust profile: II
Another term sometimes seen is the ‘thrust impulse’, Is.
It is simply defined as:
And has units of “seconds”. The larger IS the greater the effective thrust (recall Ve is the exhaust velocity).
Definition of thrust impulse
gVI e
S
Space shuttle transport system (STS) : IX
Amount of thrust generated is proportional to exposed (burning) surface area of propellant.
Space shuttle transport system (STS) : X
Space shuttle transport system (STS) : XI
Space shuttle transport system (STS) : XII
Space shuttle transport system (STS) : XIII
Cross-sections of various solid propellant castingsand associated thrust profiles.
Space shuttle transport system (STS) : XIV
Space shuttle transport system (STS) : XV