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Rocket Propulsion
Guided Weapons Systems
MSc Course
Missile Propulsion
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Rocket Thrust
Rockets are reaction engines.
Operating principle based on Newtons laws
of motion.
2nd law- rate of change of momentum isproportional to applied thrust (i.e. F = m x
a)
3rd law- every action has an equal and
opposite reaction.
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Conservation of Momentum
Example A spaceman of mass
80 kg throws a ball of
mass 0.4 kg forwardsat 20 m/s.
The spaceman willthen move
backwards at avelocity of (0.4 / 80) x20 = 0.1 m/s
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Rocket Thrust
Rocket ejects mass at a given momentumratefrom the nozzle and receives a thrustin
the opposite direction.
Momentum rate = x Ue= thrustWhere = propellant mass flow rate (kg/s)
Ue = exhaust velocity (m/s).
There may also be a thrust component due
to pressure field in nozzle (see later). Thrust may be increased by either increasing
propellant flow rate or exhaust velocity.
pmpm
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Rocket Principles
High pressure/temperature/velocityexhaust gases provided through
combustion and expansion through
nozzle of suitable fuel and oxidisermixture.
A rocket carries both the fueland
oxidiseronboard the vehicle whereasan air-breatherengine (e.g. turbojet or
turbofan) takes in its oxygen supply
from the atmosphere.
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History of Rockets
First reaction enginesoriginated in Greece,
around 400 BC, using
steam. Followed by the
aeolipile, designed by
Hero of Alexandria in
about 100 BC.
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Military History of Rockets
First military use ofproper rockets was byChinese in 1232 in Battle
of Kai-Keng v Mongols. Used gunpowder(saltpeter, sulphur,charcoal mixture) to fill
capped bamboo tubesattached to arrows -known as fire arrows.
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History of Rockets (Cont.)
Mongols then produced rockets of their ownand use spread across Europe via Arabs.
In England, Roger Baconimproved
gunpowder mixture to greatly increase
range.
In France, Jean Froissantimproved flight
accuracy by tube-launching (forerunner of
bazooka). In Italy, Joanes de Fontanadesigned surface-runningtorpedo to attack ships.
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History of Rockets (Cont.) By 16th century, rockets were only used forfireworks, though one breakthrough was
made by German Johann Schmidlap.
He was the first to use staging- a firework
with a large sky rocket (1st stage) jettisoned
after burn-out with a smaller 2nd stage
going to a higher altitude. Basis behind all of todays space rockets.
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History of Rockets (Cont.)
By late 17th century, Newtons laws werebeing applied to rockets.
German and Russian rocket experimentersbuilt powerful rockets with masses above45 kg.
Military use again by Indian army in 1792 &1799 against British.
Led to British use, designs by Col WilliamCongreveused by British ships v FortMcHenry in war of 1814 (rockets redglare in Star-Spangled Banner).
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History of Rockets (Cont.)
Rocket inaccuracy continued to be a bigbugbear but was significantly improved due
to Englands William Halesdiscovery of
spin stabilisation- using the exhaust gas tostrike small vanes and give the rocket spin.
Advances in breech-loaded cannon with
rifled barrels and exploding warheads (e.g.
by Prussians v Austrians) led to anotherdemise in military rocket use.
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Modern Rocketry
Probably began with Russias KonstantinTsiolkovsky(1857-1935) who proposed
idea of space exploration by rockets in
1903! Suggested use of liquid propellants for
increased range and stated that speed and
range were limited only by jet velocity of
escaping gas.
Also came up with mathematical range
equations (see later).
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Modern Rocketry (Cont.)
Next major pioneering work done by RobertGoddard(1882-1945) in USA, conducting
practical rocket experiments.
Began with solid propellantrockets in 1915 but then
produced worlds first liquid
propellant rocket in 1926
(liquid oxygen and gasoline).
Later improvements: gyroscope for flight
control, payload compartment and parachute
recovery.
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Modern Rocketry (Cont.)
Followed by Herman Oberth(1894-1989) inTransylvania.
Published an important book on the use of
rockets for space travel in 1923. His work led to further military development
of the rocket in the form of the infamous
German V-2 (known as A-4 in Germany),
used against London in WW2.
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V-2
Programme directed by Wernher Von Braun. Burnt mixture of liquid oxygen and alcohol at
rate of 130 kg/s for about a 70 s to develop
maximum thrust of about 725 kN - ballistic
coast to target.
Introduced too late to change outcome of war
but led to swift development of ICBMs.
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V-2 (Cont.)
Maximum speed - approx 1340 m/s.
Impact velocity - approx 1100 m/s (> Mach 3).
Typical range/altitude of 350/90 km
respectively. Carried 1 ton explosive warhead.
Launch mass about 13000 kg, impact mass
about 4040 kg. Length 14 m Diameter 1.65
m
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V-2 Propulsion System
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Ballistic Missiles
V-2 technology developedafter WW2 into ballistic
missile applications with
German rocket engineersworking on both US and
USSR programmes.
Eventually came ICBMs,
many also serving asspace launch vehicles
(e.g. Soviet R-7 and US
Atlas).
R-7 Sapwood ICBM
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Some US Ballistic Missiles
Missile Launch
Mass
(t)
Propellant Range
(km)
Deployed
Redstone
27 Liquid 400 1959Atlas 120 Liquid 14,000 1959
Titan 2 150 2 stage
liquid
15,000 1963
Minuteman
234 3 stage solid 12,500 1966
Polaris 14 2 stage solid 4,600 1964
Trident 59 3 stage solid 12,000 1990
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Criteria of Performance
Many have been described previously inPropulsion Parameterssection of course.
Covered in more detail here and specific torockets only.
Includes: thrust
specific impulse
total impulse effective exhaust velocity
thrust coefficient
characteristic velocity
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Thrust (F)
For a rocket engine:
Where:
= propellant mass flow rate
pe= exit pressure, pa= ambient pressure
ue= exit plane velocity, Ae= exit area
m
e e a eF mu p p A (1)
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Specific Impulse (I or Isp)
The ratio of thrust / propellant mass flow rate is used todefine a rocketsspecific impulse- best measure of overall
performance of rocket motor.
In SI terms, the units of I are m/s or Ns/kg.
In the US:
with units of seconds - multiply by g (i.e. 9.80665 m/s2)
in order to obtain SI units of m/s or Ns/kg.
Losses mean typical values are 92% to 98% of ideal values.
/spI F m
/spI F mg
(2)
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Total Impulse (Itot)
Defined as:
where tb= time of burning
If F is constant during burn:
0
bt
totalI Fdt (3a)
Thrusttime of burningtotal m b
I F t (3b)
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Total Impulse (Itot) (Cont.)
Thus the same total impulse may be obtained byeither:
high F, short tb (usually preferable), or
low F, long tb
Also, for constant propellant consumption rate:
(3c)
specific impulse total mass of propellant consumed
m
total b
F
I mtm
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Effective Exhaust Velocity (c)
Convenient to define an effective exhaust velocity (c),
where:
The terms effective exhaust velocityandspecific
impulseare therefore synonomous.
From equation (1) it can then be shown that:
F mc F
c Im
e a ee
p p Ac u
m
(4c)
(4b)(4a)
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Thrust Coefficient (CF)
Defined as:
where pc= combustion chamber pressure,
At= nozzle throat area
Depends primarily on (pc/pa) so a good
indicator of nozzleperformancedominated by
pressure ratio.
F
c t
FC
p A (5b)
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Characteristic Velocity (c*)
Defined as:
Calculated from standard test data.
It is independent of nozzle performance
and is therefore used as a measure ofcombustionefficiencydominated by Tc
(combustion chamber temperature).
* c tp Acm
(6)
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Thermodynamic Performance
of Rocket Engines Parameters mentioned above now covered in
greater depth, using following simplifyingassumptions:
combustion gases obey perfect gas laws. constant specific heat for combustion gases.
1-D flow.
no frictional losses.
no heat transfer to walls. combustion complete before gas enters nozzle.
process steady with respect to time.
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Thermodynamic Performance
- Thrust Parameters affecting thrust are primarily:
mass flow rate
exhaust velocity
exhaust pressure nozzle exit area
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Thermodynamic Performance
- ThrustMass flow rate
Most easily evaluated at throat, whereconditions will always be chokedand M = 1.
Substituting A = Atand M = 1 into GD eq (13):
i.e.
1
2 1
1
11
2
c
t c
m T
A p R
1
2 12
1t c
c
m A pRT
(7)
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Thermodynamic Performance
- ThrustExhaust velocity
Several relationships may be derived:
(8a)
1 2
2
211
2
ee o
e
Mu RT
M
1
2 11
o ee
o
RT pup
(8b)
1 1
2 1 2 1e ee p oo o
p pu c T Q
p p
1
21
1
c ee
o
T pRu
M p
(8c)
(8d)
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Thermodynamic Performance
- Thrust Equations (7) and (8) may thus be used to
obtain a useful overall equation for the rocketthrust:
(9)
1 1
2 1
22 11 1
c et c e a e
c o
RT pF A p p p ART p
1 211
2 12 211 1
et c e a e
o
pF A p p p Ap
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Thermodynamic Performance
- Specific Impulse For a fully-expanded condition:
If not perfectly-expanded then I also
dependent upon Aeand pa.
(10)
1
21
1
c e
o
T pRI
M p
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Thermodynamic Performance
- Specific ImpulseInfluence of
Pressure Ratio
&
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Thermodynamic Performance
- Specific ImpulseVariable Parameters - Observations
Strong pressure ratio effect - but rapidly diminishing
returns after about 30:1.
High Tcvalue desirable for high I - but gives problemswith heat transfer into case walls and dissociation of
combustion productspractical limit between about
2750 and 3500 K, depending on propellant.
Low value of molecular weight desirablefavouringuse of hydrogen-based fuels.
Low values of desirable.
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Thermodynamic Performance
- Thrust Coefficient May be theoretically represented as:
Thus independent of combustion temperature
and propellant composition.
mainly a function of pressure ratio and closelycontrolled by nozzle conditions therefore auseful measure of nozzle performance.
1 211
2 12 21
1 1
e e a eF
o c c t
p p p AC
p p p A
(11)
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Thrust Coefficient (CF)
Maximum thrust when exhausting into a vacuum
(e.g. in space), when: max
11 22 2 12 2
1 1FC
(11a)
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Thrust Coefficient (CF)
- Observations
More desirable to run a rocket under-expanded (to
left of optimum line) rather than over-expanded.
Uses shorter nozzle with reduced weight and
size.
Increasing pressure ratio improves performance
but improvements diminish above about 30/1.
Large nozzle exit area required at high pressure
ratiosimplications for space applications.
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Thermodynamic Performance
- Characteristic Velocity May be shown to be theoretically represented
by:
Thus, in contrast to thrust coefficient, isindependent of pressure ratio but isdependent on chamber temperature.
Therefore used as indicator of combustionefficiency.
(12)
1 1
2 1 2 1* 1 1
2 2
c oRT ac
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Actual Rocket Performance
Performance may be affected by any of thefollowing deviations to simplifyingassumptions:
Properties of products of combustion vary with
static temperature and thus position in nozzle. Specific heats of combustion products vary with
temperature.
Non-isentropic flow in nozzle.
Heat loss to case and nozzle walls. Pressure drop in combustion chamber due to heatrelease.
Power required for pumping liquid propellants.
Suspended particles present in exhaust gas.
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Internal Ballistics
Liquid propellant enginesstore fuel andoxidiser separately - then introduced into
combustion chamber.
Solid propellant motorsuse propellant
mixture containing all material required forcombustion.
Majority of modern GW use solid propellant
rocket motors, mainly due to simplicity and
storage advantages. Internal ballisticsis study of combustion
process of solid propellant.
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Solid Propellant Combustion
Combustion chamber is highpressure tank containingpropellant charge at whosesurface burning occurs.
No arrangement made for itscontrolcharge ignited and left toitself so must self-regulateto
avoid explosion. Certain measure of control
provided by charge and
combustion chamber design and
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Solid Propellant Combustion
Fundamental property of combustion processis burn rate.
Burning recedes linearly in direction
perpendicular to surface by parallel layers,
sometimes known as rate of regression
(usually measured in mm/s)constant for
given charge under set conditions.
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Propellant Burn Rate
Propellant burn rate (r) is determined empirically fromburning of small slabs under standard conditions:
Propellant temperature = 294 K
Chamber pressure = 68.95 bar Mass flow rate from combustion given by:
Where: Ab= burning area and p= propellant density
b pm A r (13)
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Propellant Burn Rate
Burn rate (r) of the solid propellant is a function of:
Propellant composition
Combustion chamber conditions
combustion pressure on propellant (pc)
propellant initial temperature (Tp)
velocity of gaseous combustion products
combustion gas temperature
time since start of burn
motor motion
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Burning Rate versus
Combustion Pressure
These graphs can be approximated by:
n
cr ap (14)
where:
r = burning rate
pc = combustion pressure
a = empirical constant(influenced by Tp)
n = burn rate exponent
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Burning Rate versus
Combustion Pressure
Typical Double
Base
Propellant Burn
RateCharacteristics
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Self-Regulation of Combustion
Intersection of burn rate and propellant exit mass flow rate
curves gives equilibrium combustion pressure.
With n < 1, the combustion processself regulates, the lower
the value of n the more stable is the process.
With n > 1, the system will explode!
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Effect of Nozzle Throat Area (At)
on Combustion Stability
pc
r
n
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Propellant Area
(Restriction) Ratio (K)
Know that:
And for stability:
Restriction ratiodefined as:
So that (since r = a pcn):
K thus exerts very strong influence on equilibrium pc.
For n = 0.75 (say),pcK4, so very sensitive - hence
preferable to have low values of n for reduced sensitivity.
1
* 1 nc pp c a K
*
b c
t p
A pK
A c r
o b p bm m r A
*c t
o
p Am
c
(15)
(16)
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Effect of Burn Area (Ab)
on Burn Rate (r)
Since r = a pcn
and pc= (c* a pK)1/(1n)
Increase in K or Abfor
a fixed Atvalue modifies
the burn rate curve as
shown to shift the
operating point upwardsand increase thrust.
m
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Ballistic Additives Some substances (e.g. lead salicylate, lead stearate, etc.)
may be added to a solid propellant to reduce n and thus reduce
sensitivity and improve combustion stability - known as
platonisation.
Gives relatively flat curve of r versus pcover pcrange.
Propellant Initial
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Propellant Initial
Temperature Effect Affects burn rate coefficient (a) and thus burn rate (r).
Variations of up to 35% possible for pcand tb.
Total impulsehardly affected but thrustis and can give
problems.
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Temperature Sensitivity
Sensitivity expressed in form of temperaturecoefficients:
Burn rate:
Typically 0.2% per oC
Pressure:
Typically 0.15 to 0.35% per oC
ln 1
c c
p
p pp p
d r dr
dT r dT
ln 1c c
K
p c pK K
d p dp
dT p dT
(17b)
(17a)
T
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Temperature
Sensitivity (Cont.) Effect of temperature of burn rate and pressure
obtained from:
It may also be shown that:
(18b)
(18a)o pr r T
o Kp p T
1
1K p
n
B R t
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Burn Rate
Gas Velocity Effect Most solid
rocket motors
are in form of
perforated,cylindrical stick.
Gas produced by burning charge flows past
burning surface and out through nozzle.
Very high velocities producedaffects heat
transfer rate and increases burn rateerosive
burning.
B R t
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Burn Rate
Combustion Instabilities
Burning not necessarily smooth and regularprocess.
May produce sudden unpredictable pressure
peaks and result in burst cases, propellantlosses, reduced range and loss of accuracy.
Known as resonant burning.
Oppositelow pressure troughscan cause
intermittent stopping of burningchuffing. Particularly a problem with low initial
temperatures and over-sized nozzle throats.
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Rocket Propellants
Require a suitable mix of fueland oxidiser.
Four main possibilities:
Petroleum + oxidiser
Cryogenic
Hypergolic
Solid
Solid propellants generally favoured formilitary applications.
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Rocket Propellants
Petroleum Uses refined kerosene known as
RP-1(rocket propellant 1), burnt
with liquid oxygen (LOX) or, on
older rockets, with nitric acid asoxidiser.
Used, for example, on first stage
boosters of Delta, Atlas-Centaurand Saturn rockets with typical
Ispof 2600 m/s. Atlas-Centaur
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Rocket PropellantsCryogenic
Generally uses liquid hydrogen(LH2) as fuel
with liquid oxygen(LOX) as oxidiser.
Requires temperatures of -183oC for LOX and
-253oC for LH2, giving formidable engineeringproblems.
In liquid state, density is vastly increased so
that much smaller tanks are needed. Major storage problems so mostly unsuitable
for military rockets.
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Rocket Propellants
Cryogenic (Continued) Used on J-2 engines
on Saturn V 2nd/3rd
stages with Isp
of
about 4250 m/s and
also on Space Shuttle
(Isp= 4550 m/s).
LH2and LOX burnclean so by-product is
water vapour.
Saturn V
J-2 engine
Rocket Propellants
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Rocket Propellants
Hypergolic
Fuels and oxidisers which ignite on contact giving
easy start/restart capabilities often needed for
spacecraft systems.
Much easier to store than cryogenics.
Fuel usually monomethyl hydrazine(MMH) with
oxidiser nitrogen tetroxide(N2O4) - both highly
toxic. Isptypically 3100 m/s.
Used on second stage of Delta, Titan and also on
Space Shuttle for orbital manoeuvres.
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Solid Propellant Selection
Desirable properties May be divided into those concerned with:
performance
satisfactory operation storage & handling
supply
Many are mutually conflictive in nature.
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Propellant Selection -
Performance Considerations By considering specific impulse (eq. 10), require:
Molecular weight of combustion products as low as
possible.
Temperature of combustion as high as possible.
Average propellant density as high as possible.
Specific heat ratio of combustion products as low aspossible.
Calorific value per unit mass as high as possible.
P ll t S l ti
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Propellant Selection -
Operation Considerations Combustion temperature not too high otherwise mechanical
difficulties.
Chemically inert - oxidisers affect pumps, valves, seals, etc.
Similar expansion coefficient for propellant and case.
Good mechanical properties to prevent distortion from high
acceleration loads.
High thermal conductivity to minimise temperaturegradients.
High specific heat if used for cooling.
P ll t S l ti
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Propellant Selection -
Storage/Supply ConsiderationsStorage
Low vapour pressure for liquid propellants.
Non-toxic propellants & products of combustion.
Low explosion & fire hazards - no detonation risk.
Supply
Readily available in peace and war time.
Low cost, though only small part of total R & D costs.
Solid Propellant
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Solid Propellant
Classifications
Double Base Propellants Homogeneous mixture of two explosives - usually
nitroglycerine (NG) dissolved in nitrocellulose (NC),
sometimes with additives.
Advantagesare:
Smokeless; low cost; low n value (about 0.3) and can beeasily platonised for good burning stability.
Disadvantagesare: Lower density than composites so low specific impulse;hazardous to manufacture; grain requires structural support.
Solid Propellant
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Solid Propellant
Classifications
Composite Modified Double Base
(CMDB) Propellants
Double-base propellants which include
addition of compounds, such as:
Ammonium perchlorate (AP)
Aluminium fuelSolid explosive nitramine compounds
(HMX, RDX).
Typical CMDB Ingredients
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Typical CMDB Ingredients
Solid Propellant
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Solid Propellant
Classifications
Composite Propellants
Heterogeneous mixture of powdered metal, crystalline
oxidiser and polymer binder.
Most common type used.Advantagesare:
Higher density & specific impulse than DB; easier tohandle, store & manufacture; more reliable combustion.
Disadvantagesare:
Smoky (depending on aluminium content); toxic exhaustgases.
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Solid Propellant Properties
n
Solid Propellant
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Solid Propellant
Applications Predominant in GW applications, mainly due to
ease of utilisation, straightforward handling, lack of
servicing equipment and simple firing.
Thrusts vary from 5 N to 10 MN.
No moving parts, unless TVC included.
Rarely able to turn thrust on/off and modify thrust
on demandthoughsolid propellant pulse rocket
motor may change this in the future.
Solid Propellant
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Solid Propellant
Applications - Profiles
Different profiles include:
Boost thrustfor anti-tank, ramjet boost, etc.
Boost-sustainanti-missile, anti-aircraft, etc.
Boost-coastair-to-air.
UK Missile Solid
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UK Missile Solid
Propellant Applications
Include:
Sea Cat (boost & sustain)
Sea Dart (boost)
Sea Wolf (boost)
VL Sea Wolf (TVC launch &
boost)
Starstreak (eject & boost)
Sea Wolf
Sea Dart
UK Missile Solid
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UK Missile Solid
Propellant Applications (Cont.)
Include:
Swingfire (dual boost & TVC
sustain)
Sea Skua (boost & sustain)
Rapier (dual boost & sustain)
Javelin (eject & boost)
Skyflash (boost)
Sea Skua
Javelin
Rocket Motor
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Rocket Motor
Applications (Cont.)
Solid Propellant Rocket
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Solid Propellant Rocket
Motor Design
Cylindrical body good shape for pressure vessel - also easy
to manufacture, store & transport and good aerodynamically.
In this example, charge bonded to insulation layer which is
bonded to case.
Grain Design Charge
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Grain Design - Charge
Geometries
(a) cigarette (axial/end) burner - long burn time, big CGchange;
(b) slotted-tube radial burner; (c) star centre radial burner.
Different shapes
used to vary burn
rate/time and thus
thrust.
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Grain Design - Thrust
ProfilesThe grain design can be used to give thrust variation. Progressive
Burn during which thrust, pressure and burning area
increases.
Neutral
Burn during which thrust, pressure and burning area
remain constant (15%). Regressive
Burn during which thrust, pressure and burning area
decreases.
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Grain Burn
Characteristics
Grain Design (Cont )
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Grain Design (Cont.)
More possible grain geometries
Propellant Grain
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Propellant Grain
Definitions
Web thickness (b)
Minimum thickness from burning surface to case
wallfor an end-burner, equal to length of
grain.
Web fraction (bf)
ratio of web thickness (b) to grain radius
Volumetric loading
ratio of propellant volume (Vb) to chamber
volume (Vc)
C P ll t
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Common Propellant
Grain Configurations
C D i
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Case Design
Metal Cases Typical metals used are high strength steels and
titanium alloys.
Many advantages: Toughness - preventing damage during handling.
High melting temperature - allowing less insulation.
Good aging properties with time and resistance to
weather exposure.
Thin walls possible so more propellant may be packed in.
Case Design
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Case DesignFibre Reinforced Plastic Cases
Glass or carbon fibre laid into patterns and bonded
with epoxy resin.
Advantages:
High strength/weight ratio (up to 10 x metals); lay-
up may be tailored to suit stress requirements.
Disadvantages:
Lower melting temperatures (approx 180oC);reinforcements needed in mounting areas; high
thermal expansion coefficient; low thermal
conductivity.
P ll t G i M ti
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Propellant Grain Mounting
Secure mounting needed due to high loadsexperienced during manoeuvres.
Case bondedmethod
used for large grains
(diameter > 0.5 m, mass
> 300 kg).
Free standingmethod
used for smaller grain
types and when grain
has good stiffness
properties (DB types).
Case Bonding
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Case Bonding Major problem due to different expansion
coefficients of case and propellant.
Particular problem
in air-to-air
systems with big
temperature
fluctuations.
S lid R k t N l
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Solid Rocket NozzlesNozzle must provide thrust along rocket axis and
maximise it for given pressure ratio.
Three major
configurations
used.
Solid Rocket Nozzle Design
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Solid Rocket Nozzle Design
Possibilities
S lid R k t N l D i
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Solid Rocket Nozzle Design
Bell shape gives
maximum
performance and
lowest losses butalso the biggest
so only tends to
be used for
space
applications.
Nozzle Heat Transfer
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Nozzle Heat Transfer
Rates
Very high heat
transfer rates in
nozzle due to
combination of highgas temperatures
and high velocities
peak at throat.
Metals unsuitable in
such areas.
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Typical Nozzle Materials
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Typical Nozzle Temperatures
& Ablative Losses
Rocket Nozzle Cooling
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Rocket Nozzle Cooling If ablation rates are excessive, cooling may be
achieved by burning lower temperature propellant
on side of chamber - but reduces specific impulse.
Th t V t C t l (TVC)
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Thrust Vector Control (TVC)
Sometimes a requirement to change flight directionwithout using aerodynamic control methods - TVC
then used.
TVC methods may be placed into four main
categories:
Mechanical deflection of nozzle.
Insertion of heat resistant bodies into the main
jet.
Injection of fluid into the side of the diverging
nozzle section.
Separate thrust producing devices.
Th t V t C t l (TVC)
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Thrust Vector Control (TVC)
Common Approaches to TVC
L = Liquid
S = Solid
Th t V t C t l (TVC)
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Thrust Vector Control (TVC)
More Common Approaches to TVC
L = Liquid
S = Solid
Li id P ll t R k t
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Liquid Propellant Rockets Fuel & oxidant are stored outside the
combustion chamber with two possible
supply methods:
pressurised storage tanks (pressure-feed
system). use of pumps (turbopumpsystem)
complex.
Turbopump system only needs tanks to
sustain ambient pressure values -mainly space applications.
Lance
Pressure-feed systems have upper size/weight
limitation - mainly GWapplications.
Typical Liquid Propellant
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yp ca qu d ope a t
Turbopump Rocket
S lid Li id R k t
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Solid v Liquid Rockets
Solid Rocket Advantages High propellant density (volume-limited designs).
Long-lasting chemical stability.
Readily available, tried and trusted, well proven in
service.
No field servicing equipment & straightforward
handling.
Cheap, reliable, easy firing and simple electricalcircuits.
S lid Li id R k t
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Solid v Liquid Rockets
Solid Rocket Disadvantages
Lower specific impulses.
Difficult to vary thrust on demand.
Smoky exhausts.
Performance affected by ambient
temperature.
Advantages less distinct compared with
modern packaged liquid propellant rocket
(e.g. Lance).
Packaged Liquid-
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g q
Propellant Rocket Engine Some tactical missiles require total impulse
of < 500 kNs - range favourable to
pressure feed liquid-propellant system.
If hypergolic propellants used then startingand ignition systems can be simplified.
Concept further simplified by pre-packing
and sealing propellants into respectivetanks well before use.
Packaged Liquid Propellant v
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Solid Propellant
Packaged liquid propellant system advantages
include:
control of thrust on command, typically over 5:1
range. wide operating temperature limits.
no limitation on temperature cyclingno grain to
crack.
low smoke and flash emission levels.
reduced radio interference fromexhaust.
long term storage.
modular design.
Packaged Liquid Propellant v
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Solid Propellant (Cont.)
Packaged liquid propellant system disadvantages
include:
relatively new technology.
reduced reliability due to greater number of parts.
fire hazard if both tanks are ruptured.
toxic fumes.
more fragile and liable to handling damage.
MGM-52C Lance Packaged
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Liquid Propellant System
Pre-packaged bi-propellant liquid-rocket system using
unsymmetrical dimethylhydrazine (UDMH) as fuel and
red fuming nitric acid (IRNFA) as oxidizer.
Rocket Design Example
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Rocket Design Example
A sea level rocket requires 10 kN of thrust for 20 sand is restricted in size to a maximum length of 1 m.
Size the nozzle throat, nozzle exit, propellant charge
and suggest a suitable charge shape given the burn
duration and required thrust.
Assume sea level pressure pa= 1 bar, propellant is
XLDB/AP where a (constant) = 3 x 10-6, = 1.25, R
= 0.325 kJ/kgK.
Rocket Design Example
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Rocket Design Example
Solution For XLDB/AP, using Table 1
p = 0.067 lb/in3= 1851 kg/m3, Isp= 269 s = 2639 m/s
To= 6060o
F = 3621 K, r = 0.35 in/s = 8.88 mm/s, n = 0.5
If fully-expanded,
Using the X-flow function for a choked throat and
M=1:
e spF mu mc mI
10000 / 2639 3.789 kg/sm
( 1) /2( 1)/( ) /(( 1) / 2) 0.658o c tm RT p A
Rocket Design Example
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Rocket Design Example
Solution (Cont.) Using r = a pc
n,
8.88 x 10-3= 3 x 10-6pc0.5and pc= 87.6 bar
From X-flow function, At = 3.789 (325 x 3621)/ (0.658 x 87.6 x 105)
= 7.131 x 10-4m2dt= 30.1 mm
pc/pa= 87.6 and, from charts, Ae/At= 10,
Ae= 7.131 x 10-3m2and de= 95.2 mm
/(0.658 )t o cA m RT p
Rocket Design Example
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Rocket Design Example
Solution (Cont.) For long range missile, assume use of end burner
propellant and = 3.789 x 20 = 75.78 kg
Also,
Ap= 3.789 / (1851 x 8.88 x 10-3) = 0.231 m2
dp= 0.54 m
and mp= Aplpp, lp= 75.78 / (0.231 x 1851) = 0.178m
Unrealistic grain dimensions so redo with another type.
p bm mt
p pm A r
Rocket Design Example
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Rocket Design Example
Solution (Cont.) Use slotted radial burner instead with inside and
outside diameters of dpiand dpo
Assume lp= 800 mm, leaving 200 mm for the nozzle.
Using mp= Aplpp, Ap= 75.78 / (0.8 x 1851) = 0.051
m2
0.051 = (/4)(dp22
dp12
) (dp22
dp12
) = 0.04 m
2
For dp1= 0.05 m, dp2= 206 mm(reasonable)
Though this will give a progressive thrust profile