Propulsion 2 notes

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Unit-1
AIRCRAFT GAS TURBINES
Impulse and reaction blading of gas turbines – Velocity triangles and power output – Elementary
theory – Vortex theory – Choice of blade profile, pitch and chord – Estimation of stage
performance – Limiting factors in gas turbine design- Overall turbine performance – Methods of
blade cooling – Matching of turbine and compressor – Numerical problems.

Axial and radial flow turbines
As with the compressor, there are two basic types of turbine—radial flow and axial flow. The
vast majority of gas turbines employ the axial flow turbine.
The radial turbine can handle low mass flows more efficiently than the axial flow machine and
has been widely used in the cryogenic industry as a turbo-expander, and in turbochargers for
reciprocating engines. Although for all but the lowest powers the axial flow turbine is normally
the more efficient, when mounted back-to-back with a centrifugal compressor the radial turbine
offers the benefit of a very short and rigid rotor. This configuration is eminently suitable for gas
turbines where compactness is more important than low fuel consumption. Auxiliary power units
for aircraft (APUs), generating sets of up to 3 MW, and mobile power plants are typical
applications.

Impulse and Reaction Turbine



Work can be extracted from a gas at a higher inlet pressure to the lower back pressure by
allowing it to flow through a turbine. In a turbine as the gas passes through, it expands. The work
done by the gas is equivalent to the change of its enthalpy.
It is a well known fact that the turbines operate on the momentum principle. Part of the energy of
the gas during expansion is converted into kinetic energy in the flow nozzles. The gas leaves
these stationary nozzles at a relatively higher velocity. Then it is made to impinge on the blades
over the turbine rotor or wheel. Momentum imparted to the blades turns the wheel. Thus, the two
primary parts of the turbine are,
(i) The stator nozzles, and
(ii) the turbine rotor blades.
Normally a turbine stage is classified as
(i) an impulsion stage, and
(ii) a reaction stage
An impulse stage is characterized by the expansion of the gas which occurs only in the stator
nozzles. The rotor blades act as directional vanes to deflect the direction of the flow. Further,
they convert the kinetic energy of the gas into work by changing the momentum of the gas more
or less at constant pressure.
A reaction stage is one in which expansion of the gas takes place both in the stator and in the
rotor.
The function of the stator is the same as that in the impulse stage, but the function in the
rotor is two fold.
(i) the rotor converts the kinetic energy of the gas into work, and
(ii) contributes a reaction force on the rotor blades.
The reaction force is due to the increase in the velocity of the gas relative to the blades. This
results from the expansion of the gas during its passage through the rotor.

A Single Impulse Stage
Impulse machines are those in which there is no change of static or pressure head of the fluid in
the rotor. The rotor blades cause only energy transfer and there is no energy transformation. The
energy transformation from pressure or static head to kinetic energy or vice versa takes place in
fixed blades only. As can be seen from the below figure that in the rotor blade passage of an
impulse turbine there is no acceleration of the fluid, i.e., there is no energy transformation.



Hence, the chances are greater for separation due to boundary layer growth on the blade surface.
Due to this, the rotor blade passages of the impulse machine suffer greater losses giving lower
stage efficiencies.
The paddle wheel, Pelton wheel and Curtis stem turbine are some examples of impulse
machines.



A Single Reaction Stage
The reaction stages are those, in which, changes in static or pressure head occur both in the rotor
and stator blade passages. Here, the energy transformation occurs both in fixed as well as
moving blades. The rotor experiences both energy transfer as well as energy transformation.
Therefore, reaction turbines are considered to be more efficient. This is mainly due to continuous
acceleration of flow with lower losses.

The degree of reaction of a turbomachine stage may be defined as the ratio of the static or
pressure head change occurring in the rotor to the total change across the stage.
Note: Axial-flow turbine with 50% reaction have symmetrical blades in their rotor and stators. It
may be noted that the velocity triangles at the entry and exit of a 50% reaction stage are also
symmetrical.



Velocity Triangles of a Single Stage Machine
The flow geometry at the entry and exit of a turbomachine stage is described by the velocity
triangles at these stations. The velocity triangles for a turbomachine contain the following three
components.
1. The peripheral / whirl / tangential velocity (u) of a rotor blades
2. The absolute velocity (c ) of the fluid and
3. The relative velocity (w or v) of the fluid
These velocities are related by the following well-known vector equation.

This simple relation is frequently used and is very useful in drawing the velocity triangles
for turbomachines.



The notation used here to draw velocity triangles correspond to the x-y coordinates; the
suffix (a or α) identifies components in the axial direction and suffix (t) refers to
tangential direction. Air angles in the absolute system are denoted by alpha (α), where as
those in the relative system are represented by beta (β).

Since the stage is axial, the change in the mean diameter between its entry and exit can be
neglected. Therefore, the peripheral or tangential velocity (u) remains constant in the velocity
triangles.
It can be proved from the geometry that
ct2 + ct3 = wt2 + wt3
It is often assumed that the axial velocity component remains constant through the stage. For
such condition,
ca = ca1 = ca2 = ca3



For constant axial velocity yields a useful relation,
tan α2 + tan α3 = tan β2 + tan β3

Expression for Work Output
Though force and torque are exerted on both stationary and moving blades alike, work can only
be done on the moving rotor blades. Thus the rotor blades transfer energy from the fluid to the
shaft. The stage work in an axial turbine (u3 = u2 = u) can be written as,
W = u2 ct2 – u3ct3
= u{ct2- (-ct3)}
= u(ct2-ct3)
{Note: Usually this equation will be written with a minus sign between ct2 and ct3. Whenever this
is written with a plus sign it is implied that ct3 is negative}
This equation can also be expressed in another form,

 ct 2 ct 3 
W = u 
+

u 
 u
2

c 
The first term  t 2  in the bracket depends on the nozzle or fixed angle (α2) and the ratio
 u 
u
c 
. The contribution of the second term  t 3  to the work is generally small. It is also
c2
 u 
observed that the kinetic energy of the fluid leaving the stage is greater for larger values of ct3.
The leaving loss from the stage is minimum when ct3 = 0, i.e., when the discharge from the stage
is axial (c3 = ca3). However, this condition gives lesser stage work as can be seen from the above
two equations.

σ =



Blade loading and Flow coefficients
Performance of turbomachines are characterized by various dimensionless parameters. For
example, loading coefficient (ψ) and the flow coefficient (Ф) have been defined as,

W
Ψ= 2
u
c
φ = a
u
Since the work, W in the above equation is frequently referred to as the blade or stage work, the
coefficient, ψ would also be known as the blade or stage loading coefficient.
For constant axial velocity (ca), it can be shown that
Ψ = Ф(tan α2 + tan α3) = Ф(tan β2 + tan β3)
The Ф – ψ plots are useful in comparing the performances of various stages of different sizes and
geometries.

Blade and Stage efficiencies
Even though the blade and stage work (outputs) are the same, the blade and the stage efficiencies
need not be equal. This is because the energy inputs to the rotor blades and the stage (fixed blade
ring plus the rotor) are different. The blade efficiency is also known as the utilization factor (ε)
which is an index of the energy utilizing capability of the rotor blades. Thus,
ε = ηb
= Rotor blade work / Energy supplied to the rotor blades
= W / Erb
W = u2 ct2 + u3 ct3

=

1 2 2 1 2
1 3
2
2
c 2 − c3 + u 2 − u 3 + w3 − w2
2
2
2

(

)

(

)

(

)

The energy supplied to the rotor blades is the absolute kinetic energy in the jet at the entry plus
the kinetic energy change within the rotor blades.



Erb =

1 2 1 2
1 3
2
2
c2 + w3 − w2 + u2 − u3
2
2
2

(

)

(

)

For axial machines, u = u2 = u3

ε = ηb =

(c

2
2

) (
(

2
2
2
− c3 + w3 − w2
2
2
2
c 2 + w3 − w2

)

)

Maximum utilization factor for a single impulse stage.

u (ct 2 + ct 3 )
ε=
1 2
c2
2
After rearranging the terms, we have

η b = ε = 4 (σ sin α 2 − σ 2 )
This shows that the utilization factor is a function of the blade-to-gas speed ratio and the nozzle
angle.



Elementary theory of axial flow turbine

Fig.7.2 Typical representations of velocity triangles



The above Figures show the velocity triangles for one axial flow turbine stage and the
nomenclature employed. The gas enters the row of nozzle blades (These are also known as 'stator
blades' and 'nozzle guide vanes') with a static pressure and temperature, P1, T1 and a velocity C1
is expanded to P2,T2 and leaves with an increased velocity C2 at an angle α2. The rotor blade inlet
angle will be chosen to suit the direction β2 of the gas velocity V2 relative to the blade at inlet.
β2and V2 are found by vectorial subtraction of the blade speed U from the absolute velocity C2.
After being deflected, and usually further expanded, in the rotor blade passages, the gas leaves at
P3, T3 with relative velocity V3 at angle β3. Vectorial addition of U yields the magnitude and
direction of the gas velocity at exit from the stage, C3 and α3. α3 is known as the swirl angle.

dimensional effects.



Vortex theory
It was pointed out earlier that the shape of the velocity triangles must vary from root to tip of the blade
because the blade speed U increases with radius. Another reason is that the whirl component in the flow
at outlet from the nozzles causes the static pressure and temperature to vary across the annulus. With a
uniform pressure at inlet, or at least with a much smaller variation because the whirl component is
smaller, it is clear that the pressure drop across the nozzle will vary giving rise to a corresponding
variation in efflux velocity C2. Twisted blading designed to take account of the changing gas angles is
called vortex blading.
It has been common steam turbine practice, except in low-pressure blading where the blades are
very long, to design on conditions at the mean diameter, keep the blade angles constant from root to tip,
and assume that no additional loss is incurred by the variation in incidence along the blade caused by the
changing gas angles. Comparative tests have been conducted by the earlier researchers on a single-stage
gas turbine of radius ratio 1-37, using in turn blades of constant angle and vortex blading. The results
showed that any improvement in efficiency obtained with vortex blading was within the margin of
experimental error. This contrasts with similar tests on a 6-stage axial compressor, by another researcher,
which showed a distinct improvement from the use of vortex blading. This was, however, not so

much an improvement in efficiency (of about 1-5 per cent) as in the delay of the onset of surging
which of course does not arise in accelerating flow. It appears, therefore, that steam turbine
designers have been correct in not applying vortex theory except when absolutely necessary at
the LP end. They have to consider the additional cost of twisted blades for the very large number
of rows of blading required, and they know that the Rankine cycle is relatively insensitive to
component losses. Conversely, it is not surprising that the gas turbine designer, struggling to
achieve the highest possible component efficiency, has consistently used some form of
vortex blading which it is felt intuitively must give a better performance however small.
Vortex theory has been outlined earlier by Cohen and others where it was shown that if
the elements of fluid are to be in radial equilibrium, an increase in static pressure from
root to tip is necessary whenever there is a whirl component of velocity. Figure 7.8 shows
(see below) why the gas turbine designer cannot talk of impulse or 50 per cent reaction stages.
The proportion of the stage pressure or temperature drop which occurs in the rotor must increase
from root to tip. Although Fig. 7.8 refers to a single-stage turbine with axial inlet velocity and no
swirl at outlet, the whirl component at inlet and outlet of a repeating stage will be small
compared with CW2- the reaction will therefore still increase from root to tip, if somewhat less
markedly.



Choice of blade profile, pitch and chord
The next step is to choose stator and rotor blade shapes which will accept the gas incident upon
the leading edge, and deflect the gas through the required angle with the minimum loss. An
overall blade loss coefficient Y (or A) must account for the following sources of friction loss.
(a)

Profile loss—associated with boundary layer growth over the blade profile (including
separation loss under adverse conditions of extreme angles of incidence or high inlet
Mach number).

(b)

Annulus loss—associated with boundary layer growth on the inner and outer walls of the
annulus.

(c)

Secondary flow loss—arising from secondary flows which are always present when a
wall boundary layer is turned through an angle by an adjacent curved surface.

(d)

Tip clearance loss—near the rotor blade tip the gas does not follow the intended path,
fails to contribute its quota of work output, and interacts with the outer wall boundary
layer.

The profile loss coefficient Yp is measured directly in cascade tests similar to those described for
compressor blading. Losses (b) and (c) cannot easily be separated, and they are accounted for by
a secondary loss coefficient Ys.



The tip clearance loss coefficient, which normally arises only for rotor blades, will be denoted by
Yk. Thus the total loss coefficient Y comprises the accurately measured two-dimensional loss Yp,
plus the three-dimensional loss (Ys+Yk) which must be deduced from turbine stage test results.
All that is necessary for our present purpose for finding the choice of blade profile is limited to
the knowledge of the sources of loss.

Figure 7.11 shows a conventional steam turbine blade profile constructed from circular arcs and
straight lines. Gas turbines have until recently used profiles closely resembling this, although
specified by aerofoil terminology.



Note that the blade profile will be completely determined when (a) the pitch/width ratio (s/w) is
established, and (b) both the camber line angle α' and blade thickness/pitch ratio have been
calculated for various values of x between 0 and 1.



Turbine Performance
The performance of turbine is limited principally by two factors: compressibility and
stress. Compressibility limits the mass flow that can pass through a given turbine and, stress
limits the wheel speed U. The work per stage depends on the square of the wheel speed.
However, the performance of the engine depends very strongly on the maximum temperature. Of
course, as the maximum temperature increases, the allowable stress level diminishes; hence in
the design of the engine there must be a compromise between maximum temperature and
maximum rotor tip speed U.
For given pressure ratio and adiabatic efficiency, the turbine work per unit mass is proportional
to the inlet stagnation temperature. Since, in addition, the turbine work in a jet or turboshaft
engine is commonly two or three times the useful energy output of the engine, a 1% increase in
turbine inlet temperature can produce a 2% or 3% increase in engine output. This considerable
advantage has supplied the incentive for the adoption of fairly elaborate methods for cooling the
turbine nozzle and rotor blades.

Estimation of stage performance
The last step in the process of arriving at the preliminary design of a turbine stage is to check
that the design is likely to result in values of nozzle loss coefficient and stage efficiency which
were assumed at the outset. If not, the design calculations may be repeated with more probable
values of loss coefficient and efficiency. When satisfactory agreement has been reached, the
final design may be laid out on the drawing board and accurate stressing calculations can be
performed. Before proceeding to describe a method of estimating the design point performance
of a stage, however, the main factors limiting the choice of design, which we have noted during
the course of the worked example, will be summarized. The reason we considered a turbine for a
turbojet engine was simply that we would thereby be working near those limits to keep size and
weight to a minimum. The designer of an industrial gas turbine has a somewhat easier task: he
will be using lower temperatures and stresses to obtain a longer working life, and this means
lower mean blade speeds, more stages, and much less stringentaerodynamic limitations. A power
turbine, not mechanically coupled to the gas generator, is another case where much less difficulty
will be encountered in arriving at a satisfactory solution. The choice of gear ratio between the
power turbine and driven component is normally at the disposal of the turbine designer, and thus
the rotational speed can be varied to suit the turbine, instead of the compressor as we have
assumed here.



The cooled turbine

Figure 7.29 illustrates the methods of blade cooling that have received serious attention and
research effort. Apart from the use of spray cooling for thrust boosting in turbojet engines, the
liquid systems have not proved to be practicable. There are difficulties associated with



channelling the liquid to and from the blades—whether as primary coolant for forced convection
or free convection open thermosyphon systems, or as secondary coolant for closed thermosyphon
systems. It is impossible to eliminate corrosion or the formation of deposits in open systems, and
very difficult to provide adequate secondary surface cooling area at the base of the blades for
closed systems. The only method used successfully in production engines has been internal,
forced convection, air cooling. With 1-5-2 per cent of the air mass flow used for cooling per
blade row, the blade temperature can be reduced by between 200 and 300 °C. Using current
alloys, this permits turbine inlet temperatures of more than 1650 К to be used. The blades are
either cast, using cores to form the cooling passages, or forged with holes of any desired shape
produced by electrochemical or laser drilling.

Figure 7.30 shows the type of turbine rotor blade introduced in the 1980s. The next step forward
is likely to be achieved by transpiration cooling, where the cooling air is forced through a porous
blade wall. This method is by far the most economical in cooling air, because not only does it
remove heat from the wall more uniformly, but the effusing layer of air insulates the outer
surface from the hot gas stream and so reduces the rate of heat transfer to the blade. Successful
application awaits further development of suitable porous materials and techniques of blade
manufacture. We are here speaking mainly of rotor blade cooling because this presents the most
difficult problem. Nevertheless it should not be forgotten that, with high gas temperatures,
oxidation becomes as significant a limiting factor as creep, and it is therefore equally important
to cool even relatively unstressed components such as nozzle blades and annulus walls.



Figure 7.31 (a) illustrates the principal features of nozzle blade cooling. The air is introduced
in such a way as to provide jet impingement cooling of the inside surface of the very hot leading
edge. The spent air leaves through slots or holes in the blade surface (to provide some film
cooling) or in the trailing edge.

FIG. 7.31 (a) Turbine nozzle cooling [(b) courtesy Rolls-Royce]



Figure 7.35: Shows a typical temperature distribution at the mid-span of
a blade designed to operate with Tg= 1500 К and Tсг = 320 К.

It may be noted that the final design calculation for a cooled blade will involve an estimation of
the two-dimensional temperature distribution over the blade cross-section at several values of
l/L. Finite difference methods are used to solve the differential equations, and conduction within
the blade is taken into account. Figure 7.35 shows a typical temperature distribution at the midspan of a blade designed to operate with Tg= 1500 К and Гсг = 320 К. It emphasizes one of the
main problems of blade cooling, i.e. that of obtaining adequate cooling at the trailing edge.
Finally, an estimation will be made of the thermal stresses incurred with due allowance for
redistribution of stress by creep: with cooled blades the thermal stresses can dominate the gas
bending stresses and be comparable with the centrifugal tensile stresses.
Finally, mention must be made of an alternative approach to the high- temperature turbine—the
use of ceramic materials which obviates the need for elaborate cooling passages. Much effort has
been expended on the development of silicon nitride and silicon carbide materials for small
turbine rotors (both axial and radial) in which it would be difficult to incorporate cooling
passages. Adequate reliability and life are difficult to achieve, but demonstrator engines have
been ran for short periods. Ceramic rotor blades are being investigated for use in stationary gas
turbines for powers up to about 5 MW, and experimental trials are expected in the late 1990s.
The use of ceramic turbines in production engines, however, remains an elusive goal three
decades after optimistic forecasts about their introduction.

Blade Cooling
Blade cooling is the most effective way of maintaining high operating temperatures making use
of the available material. Blade cooling may be classified based on the cooling site as external
cooling and internal cooling. Another classification based on the cooling medium is liquid
cooling and air cooling.



External Cooling
The external surface of the gas turbine blade is cooled by making use of compressed air from the
compressor.
Other methods of external cooling are film cooling and transpiration cooling.
Internal Cooling
Internal cooling of blades is achieved by passing air or liquid through internal cooling passages
from hub towards the blade tip. The cooling of the blades is achieved by conduction and
convection.
Hollow blades can also be manufactured with a core and internal cooling passage. Based on the
cooling medium employed, blade cooling may be classified into liquid cooling and air cooling.

Requirements for Efficient Blade Cooling
In a conventional cooled blade, cooling is obtained due to convection by passing cooling air
through internal passages within the blade. The success in obtaining the large reduction in metal
temperature at the expense of a small quantity of cooling flow is governed by the skill in
devising and machining the cooling passages. Because the internal cooling relies on the cooling
air scrubbing against the cooling surface, the internal surface area must be large and the velocity
of the cooling air must be high. This implies that the cross-sectional flow area of the passage
must be small.
The design of the blade internal geometry for cooling is more complex because of the various
aerodynamic, heat transfer, stress and mechanical design criteria that must be satisfied. The most
successful designs have incorporated radial passages through which cooling air passes, escaping
at the tip.

The radial flow turbine
In a radial flow turbine, gas flow with a high tangential velocity is directed inwards and leaves
the rotor with as small a whirl velocity as practicable near the axis of rotation. The result is that
the turbine looks very similar to the centrifugal compressor, but with a ring of nozzle vanes
replacing the diffuser vanes as in Fig. 7.37. Also, as shown there would normally be a diffuser at
the outlet to reduce the exhaust velocity to a negligible value.



Turbine and Compressor Matching
The problem of matching turbine and compressor performance has great importance for jet
engines, which must operate under conditions involving large variations in thrust, inlet pressure,
and temperature, and flight Mach number. Matching the components of turbofan and turboprop
engines involves similar considerations and procedures.
Essentially the matching problem is simple, though the computation can be length. The
steady-state engine performance at each speed is determined by two conditions: continuity of
flow and a power balance. The turbine mass flow must be the sum of the compressor mass flow
and the fuel flow, minus compressor bleed flow. Also the power output of the turbine must be
equal to that demanded by the compressor.
In principle, the matching computations could proceed as follows:
1. Select operating speed
2. Assume turbine inlet temperature
3. Assume compressor pressure ratio
4. Calculate compressor work per unit mass
5. Calculate turbine pressure ratio required to produce this work
6. Check to see if compressor mass flow plus fuel flow equals turbine mass flow; if not,
assume a new value of compressor pressure ratio and repeat steps 4, 5, and 6 until
continuity is satisfied.
7. Now calculate the pressure ratio across the jet nozzle from the pressure ratios across the
diffuser, compressor, combustor, and turbine.
8. Calculate the area of jet nozzle outlet necessary to pass the turbine mass flow calculated
in step 6 with pressure ratio calculated in step 7 and the stagnation temperature
calculated. If the calculated area does not equal the actual exit area, assume a new value
of turbine inlet temperature (step-2) and repeat the entire procedure.



The designer will try to match turbine and compressor so that the compressor is operating
near its peak efficiency through the entire range of operation, as shown in the below
figure, where the operating line (i.e., the locus of stead-state matching condition) runs
through the centers of the islands defined by the constant-efficiency lines.



The essence of compressor-turbine matching is to find a speed at which the turbine will run
delivering power to the compressor and permit excess power in the form of adequate jet pressure
for expansion through the nozzle or additional turbine stages from which power can be derived
to run a propeller or helicopter rotor as the case may be.



Problems
In a single-stage impulse turbine the nozzle discharges the fluid on to the blades at an angle of
650 to the axial direction and the fluid leaves the blades with an absolute velocity of 300 m/s at
an angle of 300 to the axial direction. If the blades have equal inlet and outlet angles and there is
no axial thrust, estimate the blade angle, power produced per kg/s of the fluid and blade
efficiency.

Solution:

Since the axial thrust is zero,
Ca3 = Ca2 = Ca
w3 = w2



ca3 = ca2 = ca = ca3 x cos α3
= 300 x cos 30 = 259.8 m/s
c2 = ca2/cos α2 = 259.8/cos 65 = 614.7 m/s
u = ct2 – wt2 = wt3 - ct3
c2 sin α2 - ca2 tan β2 = ca3 tan β3 – c3 sin α3
Since ca2 = ca3 = ca and β2 = β3 = β
2ca tan β = c2 sin α2 + c3 sin α3
tan β = (614.7 x sin 65 + 300 x sin 30) / 2 x 259.8
= 1.3609
β = 53.7 0
β2 = β3 = 53.7 0
u = c2 sin α2 - ca2 tan β2
= 614.7 x sin 65 – 259.8 x tan 53.7
= 203.43 m/s
ct2 = c2 sin α2
= 614.7 x sin 65
= 557.1 m/s
ct3 = c3 sin α3



= 300 x sin 30
= 150 m/s
WT = 203.43 x (557.1 + 150) x 10-3
= 144 kJ/kg
σ = u/c2 = 203.43 / 614.7 = 0.33
Blade efficiency = 4 (σ sin α2 - σ2)
= 4 x (0.33 x sin 65 – 0.332) = 0.761
= 76.1 %



Aircraft Engine Performance Parameters

Uninstalled thrust of a jet engine (single inlet and single exhaust) is given by

Uninstalled thrust of a jet engine (single inlet and single exhaust) is given by

It is most desirable to expand the exhaust gas to the ambient pressure, which gives



In this case, the uninstalled thrust equation becomes,

The installed thrust T is equal to the uninstalled thrust F minus the inlet drag Dinlet and minus
nozzle drag Dnozzle , or
T = F – Dinlet - Dnozzle

Problem:
An advanced fighter engine operating at Mach 0.8 and 10 km altitude has the following
unistalled performance data and uses a fuel with low heating value 42,800 kJ/kg:
Uninstalled thrust = 50 kN
Mass flow rate of air = 45 kg/sec
Mass flow rate of fuel = 2.65 kg/sec
Determine the specific thrust, thrust specific fuel consumption, exit velocity, thermal efficiency,
propulsive efficiency, and overall efficiency (assume exit pressure equal to ambient pressure).
Find the installed thrust when the total drag is equal to 10% of the uninstalled thrust.

Solution:



Fs = 50/45 = 1.1111kN/(kg/sec)
= 1111.1 m/s
TSFC

= 2.65 / 50
= 0.053 (kg/sec)/kN
= 53 mg/N-sec

V0

= Mo ao
= 239. 6 m/sec

Using the above equation exit velocity,
Ve is obtained as 1275.6 m/s



Power output of the engine = 37.475 x 106 W
Power input to the engine through fuel = 113.42 x 106 W
Propulsive power or Thrust Power = 50,000 x 239.6
Thermal efficiency = 37.475 x 106 / 113.42 x 106
= 33.04 %
Propulsive Efficiency = 50,000 x 239.6 / 37,475 x 106
= 31.97 %
Overall efficiency = 50,000 x 239.6 / 113.42 x 106
= 10.56 %
For additional numerical problems please refer the following books
1. Mathur, M., and Sharma, R.P., “Gas Turbines and Jet and Rocket Propulsion”,
Standard Publishers, New Delhi, 1988.
2. Ganesan, V., Gas Turbines, Tata McGraw-Hill Publishing Company Limited,
New Delhi. Second Edn. 2003.
Additional reading
1. Hill, P.G. & Peterson, C.R. “Mechanics & Thermodynamics of Propulsion” Addison –
Wesley Longman INC, 1999.
2. Cohen, H., Rogers, G.F.C. and Saravanamuttoo, H.I.H., “Gas Turbine Theory”, Longman
Co., ELBS Ed., 1989.



Unit-2
RAMJET PROPULSION
Operating principle – Sub critical, critical and supercritical operation – Combustion in ramjet
engine – Ramjet performance – Sample ramjet design calculations – Introduction to scramjet –
Preliminary concepts in supersonic combustion – Integral ramrocket- Numerical problems.

Ramjets
Introduction

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Ramjets can be thought of as propulsive devices evolved out of turbojets.
Ramjets operates well only at high speeds, typically between M = 2.0 and 4.0.
The combustion mode being not very different from that of an afterburner, the specific
fuel consumption is comparable to that of afterburner.
The ramjet, unlike turbojet and turbofan does not produce any thrust at zero speed.
Ramjets are mostly contemplated for use in military applications.



SCRAM JET ENGINES

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A scram jet engine is an engine that is much lighter than a conventional jet engine, can
propel an object at speeds of over 5000 miles per hour and has no moving parts.
If you could get it to work, the trip from London to Sydney would only take two hours!
This technology would also be very useful to launch small satellites.
The engine runs on oxygen, which it gets from the atmosphere, and a small amount of
hydrogen.
The engine would save a fantastic amount on the cost of fuel.
This technology has been around since the 1950s but the problem is the motor will only
become efficient at five times the speed of sound or Mach 5.
Because of this the plane would need two engines, an engine capable of getting it to
Mach 5 and a Scram Jet.

A ramjet engine

A scramjet engine



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A ramjet has no moving parts and achieves compression of intake air by the forward
speed of the air vehicle.
Air entering the intake of a supersonic aircraft is slowed by aerodynamic diffusion
created by the inlet and diffuser to velocities comparable to those in a turbojet augmenter.
The expansion of hot gases after fuel injection and combustion accelerates the exhaust air
to a velocity higher than that at the inlet and creates positive push.
Scramjet is an acronym for Supersonic Combustion Ramjet.
The scramjet differs from the ramjet is that combustion takes place at supersonic air
velocities through the engine.
It is mechanically simple, but vastly more complex aerodynamically than a jet engine.
Hydrogen is normally the fuel used.
A scramjet (supersonic combustion ramjet) is a variation of a ramjet with the key
difference being that the flow in the combustor is supersonic.
At higher speeds it is necessary to combust supersonically to maximize the efficiency of
the combustion process.
Projections for the top speed of a scramjet engine (without additional oxidizer input) vary
between Mach 12 and Mach 24 (orbital velocity), but the X-30 research gave Mach 17
due to combustion rate issues.
By way of contrast, the fastest conventional air-breathing, manned vehicles, such as the
U.S. Air Force SR-71, achieve slightly more than Mach 3.2 and rockets achieved Mach
30+ during Apollo.
Like a ramjet, a scramjet essentially consists of a constricted tube through which
inlet air is compressed by the high speed of the vehicle, fuel is combusted, and then
the exhaust jet leaves at higher speed than the inlet air.
Also like a ramjet, there are few or no moving parts. In particular there is no high speed
turbine as in a turbofan or turbojet engine that can be a major point of failure.
A scramjet requires supersonic airflow through the engine, thus, similar to a ramjet,
scramjets have a minimum functional speed. This speed is uncertain due to the low
number of working scramjets, relative youth of the field, and the largely classified nature
of research using complete scramjet engines.
However it is likely to be at least Mach 5 for a pure scramjet, with higher Mach numbers
7-9 more likely. Thus scramjets require acceleration to hypersonic speed via other means.
A hybrid ramjet/scramjet would have a lower minimum functional Mach number, and
some sources indicate the NASA X-43A research vehicle is a hybrid design.
Recent tests of prototypes have used a booster rocket to obtain the necessary velocity.
Air breathing engines should have significantly better specific impulse while within
the atmosphere than rocket engines.
However scramjets have weight and complexity issues that must be considered. While
very short suborbital scramjets test flights have been successfully performed, perhaps



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significantly no flown scramjet has ever been successfully designed to survive a flight
test.
The viability of scramjet vehicles is hotly contested in aerospace and space vehicle
circles, in part because many of the parameters which would eventually define the
efficiency of such a vehicle remain uncertain.
This has led to grandiose claims from both sides, which have been intensified by the large
amount of funding involved in any hypersonic testing. Some notable aerospace gurus
such as Henry Spencer and Jim Oberg have gone so far as calling orbital scramjets 'the
hardest way to reach orbit', or even 'scramjets' due to the extreme technical challenges
involved.
Major, well funded projects, like the X-30 were cancelled before producing any working
hardware.
The scramjet is a proposed solution to both of these problems, by modifications of the
ramjet design. The main change is that the blockage inside the engine is reduced, so that
the air isn't slowed down as much. This means that the air is cooler, so that the fuel can
burn properly. Unfortunately the higher speed of the air means that the fuel has to mix
and burn in a very short time, which is difficult to achieve.
To keep the combustion of the fuel going at the same rate, the pressure and temperature
in the engine need to be kept constant. Unfortunately, the blockages which were removed
from the ramjet were useful to control the air in the engine, and so the scramjet is forced
to fly at a particular speed for each altitude. This is called a "constant dynamic pressure
path" because the wind that the scramjet feels in its face is constant, making the scramjet
fly faster at higher altitude and slower at lower altitude.
The inside of a very simple scramjet would look like two kitchen funnels attached by
their small ends. The first funnel is the intake, and the air is pushed through, becoming
compressed and hot. In the small section, where the two funnels join, fuel is added, and
the combustion makes the gas become even hotter and more compressed. Finally, the
second funnel is a nozzle, like the nozzle of a rocket, and thrust is produced.
Note that most artists' impressions of scramjet-powered vehicle designs depict waveriders
where the underside of the vehicle forms the intake and nozzle of the engine. This means
that the intake and nozzle of the engine are asymmetric and contribute directly to the lift
of the aircraft. A waverider is the required form for a hypersonic lifting body
A scramjet is a type of engine which is designed to operate at the high speeds normally
associated with rocket propulsion.
It differs from a classic rocket by using air collected from the atmosphere to burn its fuel,
as opposed to an oxidizer carried with the vehicle.
Normal jet engines and ramjet engines also use air collected from the atmosphere in this
way.
The problem is that collecting air from the atmosphere causes drag, which increases
quickly as the speed increases.



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Also, at high speed, the air collected becomes so hot that the fuel no longer burns
properly.
Theory
All scramjet engines have fuel injectors, a combustion chamber, a thrust nozzle and an
inlet, which compresses the incoming air.
Sometimes engines also include a region which acts as a flame holder, although the high
stagnation temperatures mean that an area of focused waves may be used, rather than a
discrete engine part as seen in turbine engines.
Other engines use pyrophoric fuel additives, such as silane, to avoid such issues.
An isolator between the inlet and combustion chamber is often included to improve the
homogeneity of the flow in the combustor and to extend the operating range of the
engine.
A scramjet is reminiscent of a ramjet.
In a typical ramjet, the supersonic inflow of the engine is decelerated at the inlet to
subsonic speeds and then reaccelerated through a nozzle to supersonic speeds to produce
thrust. This deceleration, which is produced by a normal shock, creates a total pressure
loss which limits the upper operating point of a ramjet engine.
For a scramjet, the kinetic energy of the freestream air entering the scramjet engine is
large compared to the energy released by the reaction of the oxygen content of the air
with a fuel (say hydrogen).
Thus the heat released from combustion at Mach 25 is around 10% of the total enthalpy
of the working fluid.
Depending on the fuel, the kinetic energy of the air and the potential combustion heat
release will be equal at around Mach 8.
Thus the design of a scramjet engine is as much about minimizing drag as maximizing
thrust.
This high speed makes the control of the flow within the combustion chamber more
difficult. Since the flow is supersonic, no upstream influence propagates within the
freestream of the combustion chamber.
Thus throttling of the entrance to the thrust nozzle is not a usable control technique.
In effect, a block of gas entering the combustion chamber must mix with fuel and have
sufficient time for initiation and reaction, all the while travelling supersonically through
the combustion chamber, before the burned gas is expanded through the thrust nozzle.
This places stringent requirements on the pressure and temperature of the flow, and
requires that the fuel injection and mixing be extremely efficient.
Usable dynamic pressures lie in the range 20 to 200 kPa (0.2-2 bar), where

•

where
q is the dynamic pressure of the gas



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ρ (rho) is the density of the gas
v is the velocity of the gas
Fuel injection and management is also potentially complex.
One possibility would be that the fuel is pressurized to 100 bar by a turbo pump, heated
by the fuselage, sent through the turbine and accelerated to higher speeds than the air by a
nozzle.
The air and fuel stream are crossed in a comb like structure, which generates a large
interface.
Turbulence due to the higher speed of the fuel lead to additional mixing. Complex fuels
like kerosine need a long engine to complete combustion.
The minimum Mach number at which a scramjet can operate is limited by the fact that
the compressed flow must be hot enough to burn the fuel, and of high enough pressure
that the reaction is finished before the air moves out the back of the engine.
Additionally, in order to be called a scramjet, the compressed flow must still be
supersonic after combustion.
Here two limits must be observed:
Firstly, since when a supersonic flow is compressed it slows down, the level of
compression must be low enough (or the initial speed high enough) not to slow down the
gas below Mach 1.
If the gas within a scramjet goes below Mach 1 the engine will "choke", transitioning to
subsonic flow in the combustion chamber.
This effect is well known amongst experimenters on scramjets since the waves caused by
choking are easily observable.
Additionally, the sudden increase in pressure and temperature in the engine can lead to an
acceleration of the combustion, leading to the combustion chamber exploding.
Secondly, the heating of the gas by combustion causes the speed of sound in the gas
to increase (and the Mach number to decrease) even though the gas is still traveling
at the same speed. Forcing the speed of air flow in the combustion chamber under
Mach 1 in this way is called "thermal choking".
It is clear that a pure scramjet can operate at Mach numbers of 6-8, but in the lower
limit, it depends on the definition of a scramjet.
Certainly there are designs where a ramjet transforms into a scramjet over the Mach 3-6
range (Dual-mode scramjets). In this range however, the engine is still receiving
significant thrust from subsonic combustion of "ramjet" type.
The high cost of flight testing and the unavailability of ground facilities have hindered
scramjet development.
A large amount of the experimental work on scramjets has been undertaken in cryogenic
facilities, direct-connect tests, or burners, each of which simulates one aspect of the
engine operation.



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Further, vitiated facilities, storage heated facilities, arc facilities and the various types of
shock tunnels each have limitations which have prevented perfect simulation of scramjet
operation.
The HyShot flight test showed the relevance of the 1:1 simulation of conditions in the T4
and HEG shock tunnels, despite having cold models and a short test time.
The NASA-CIAM tests provided similar verification for CIAM's C-16 V/K facility and
the Hyper-X project is expected to provide similar verification for the Langley AHSTF ,
CHSTF and 8 ft HTT.
Computational fluid dynamics has only recently reached a position to make reasonable
computations in solving scramjet operation problems.
Boundary layer modeling, turbulent mixing, two-phase flow, flow separation, and realgas aerothermodynamics continue to be problems on the cutting edge of CFD.
Additionally, the modeling of kinetic-limited combustion with very fast-reacting species
such as hydrogen makes severe demands on computing resources.
Reaction schemes are numerically stiff, having typical times as low as 10-19 seconds,
requiring reduced reaction schemes.
Much of scramjet experimentation remains classified. Several groups including the US
Navy with the SCRAM engine between 1968-1974, and the Hyper-X program with the
X-43A have claimed successful demonstrations of scramjet technology. Since these
results have not been published openly, they remain unverified and a final design method
of scramjet engines still does not exist.
The final application of a scramjet engine is likely to be in conjunction with engines
which can operate outside the scramjet's operating range.
Dual-mode scramjets combine subsonic combustion with supersonic combustion for
operation at lower speeds, and rocket-based combined cycle (RBCC) engines supplement
a traditional rocket's propulsion with a scramjet, allowing for additional oxidizer to be
added to the scramjet flow.
RBCCs offer a possibility to extend a scramjet's operating range to higher speeds or
lower intake dynamic pressures than would otherwise be possible.

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Advantages and disadvantages of scramjets
Special cooling and materials
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Unlike a rocket that quickly passes mostly vertically through the atmosphere or a turbojet
or ramjet that flies at much lower speeds, a hypersonic airbreathing vehicle optimally
flies a "depressed trajectory", staying within the atmosphere at hypersonic speeds.
Because scramjets have only mediocre thrust-to-weight ratios, acceleration would be
limited. Therefore time in the atmosphere at hypersonic speed would be considerable,
possibly 15-30 minutes.



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Similar to a reentering space vehicle, heat insulation from atmospheric friction would be
a formidable task. The time in the atmosphere would be greater than that for a typical
space capsule, but less than that of the space shuttle.
Therefore studies often plan on "active cooling", where coolant circulating throughout the
vehicle skin prevents it from disintegrating from the fiery atmospheric friction.
Active cooling could require more weight and complexity. There is also safety concern
since it's an active system.
Often, however, the coolant is the fuel itself, much in the same way that modern rockets
use their own fuel and oxidizer as coolant for their engines.
Both scramjets and conventional rockets are at risk in the event of a cooling failure.

Half an engine
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The typical waverider scramjet concept involves, effectively, only half an engine. The
shockwave of the vehicle itself compresses the inlet gasses, forming the first half of the
engine. Likewise, only fuel (the light component) needs tankage, pumps, etc. This greatly
reduces craft mass and construction effort, but the resultant engine is still very much
heavier than an equivalent rocket or conventional turbojet engine of similar thrust.

Simplicity of design
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Scramjets have few to no moving parts. Most of their body consists of continuous
surfaces. With simple fuel pumps, reduced total components, and the reentry system
being the craft itself, scramjet development tends to be more of a materials and modelling
problem than anything else.

Additional propulsion requirements
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A scramjet cannot produce efficient thrust unless boosted to high speed, around Mach 5,
depending on design, although, as mentioned earlier, it could act as a ramjet at low
speeds. A horizontal take-off aircraft would need conventional turbofan or rocket engines
to take off, sufficiently large to move a heavy craft. Also needed would be fuel for those
engines, plus all engine associated mounting structure and control systems. Turbofan
engines are heavy and cannot easily exceed about Mach 2-3, so another propulsion
method would be needed to reach scramjet operating speed. That could be ramjets or
rockets. Those would also need their own separate fuel supply, structure, and systems.
Many proposals instead call for a first stage of droppable solid rocket boosters, which
greatly simplifies the design.



Pulsejet

Pulsejet is a constant volume combustion device which is quite efficient only at low speeds and
uses unsteady combustion for its operation. Once the system is started, it works by taking in air
and fuel and combustion them during a part of the cycle and exhausting it during the next part of
the cycle. In order to promote and sustain the operation, a flapper device of metal or plastic, in
recent times, is used in front end.

Supersonic Diffuser
Super sonic diffuser may be divided into two separate parts: the supersonic inlet and the
subsonic diffuser. Although this division is a convenient one, it must be remembered that the
phenomena in the supersonic and subsonic parts of the diffuser can, and often do, interact.
It should be remembered that the higher the Mach number, the greater will be our percentage
loss in pressure across a normal shock. Thus, at very high mach numbers, there is an appreciable
difference between (1) isentropic compression through out and (2) compression with a normal
shock.
The limitations imposed by the losses associated with a normal shock at higher Mach numbers
stimulated the development of a modified simple inlet design which incorporates a spike or
wedge in the nose section of the diffuser.
The modified design utilizes the spike or wedge to produce an oblique shock at the nose
section, and, the mach number after an oblique shock are greater than one. Consequently, in
addition to the oblique shock, we have a normal shock near the minimum area section. The



compression after the normal shock is of the standard subsonic diffuser type; that is, an increase
in area decreases the velocity.
It might be asked why a diffuser which has two shock waves, namely, an oblique and a normal
shock, would give better results than a simple inlet which has only one normal shock. The reason
for this is that the losses across a series of weak shock are less than the losses across one or
several strong shocks. This means that the losses across the normal shock which follows the
oblique shock are considerably less than the losses across a normal shock in the free stream.
Increasing the number of oblique shocks before the normal shock reduces the losses through
the shock system. It must be noted that the complexity of the inlet also increases as the number
shocks increases. In addition to the number of shocks, the pressure losses are also function of the
shock arrangement. It may be noted that the maximum total pressure recovery occurs when the
total pressure recovery is the same across each of oblique shocks, and very nearly equal to that
across the final normal shock.

Mode of Supersonic Diffuser Operation
The three basic modes operation frequently referred to are subcritical operation, critical
operation, and supercritical operation. All these three inlets are operated at the design Mach
number, MD, which by definition, means that the conical shock or conical shock extended will
intersect the cowl lip.
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At the subcritical operation, the normal shock is external and subsonic velocities exit at
the cowl.
For this condition mass-flow ratio based on capture area is less than one; spillage
exists; the inlet is not swallowing air at maximum capacity; pressure recovery is low
since some of the air goes through a single, near normal shock; inlet drag is high
because of the intense shock; operation is generally unstable and conducive to a
condition called “buzz” (normal shock moves in and out of the inlet at relatively high
frequencies). An important instability that occurs during the subcritical operation of
most supersonic inlets. This phenomenon, known as “buzz”, consists of a rapid
oscillation of the inlet shock and flow pattern; the resultant internal disturbance is very
detrimental to engine performance. In a ramjet, for instance, the onset of buzz usually
extinguishes combustion. Although the pulses of the shock system are similar, the
interval between pulses is not constant; hence buzz cannot be considered a periodic
phenomenon. Although it is not thoroughly understood, buzz has been shown to be a
function of conditions only at , and immediately downstream of, the inlet.
In general subcritical operation is unsatisfactory and should be avoided.
As the flow resistance downstream of the diffuser is increased, the mass-flow ratio can
be reduced to its limit value of 0 at which point no flow exits.
For critical operation, both maximum mass flow and ram recovery are attained for the
design Mach number; thus condition represents the optimum performance condition. It
has the disadvantage, however, of being, marginally unstable in actual applications



because small changes in angles of attack or yaw or boundary layer separation can
induce the critical mode of operation across the threshold into the subcritical regime.
Consequently, for actual operation it is usually better to operate the inlet in a more
stable condition, the supercritical regime.

Typical modes of inlet operation

The three basic modes operation frequently referred to aircraft inlets are subcritical operation,
critical operation, and supercritical operation, which are shown schematically for a typical case
in the above figure. With entirely diverging internal flow such as this, the normal shock position
is determined by a downstream flow restriction rather than by the inlet geometry. Hence
operating mode is sensitive to variations in exhaust-nozzle area and fuel flow rate. Subcritical
operation entails “spilling” of flow and a normal shock upstream of the inlet. “Low” and “high”
subcritical operations differ only in the extent of spilling. Supercritical operation occurs at the
same mass flow as critical operation, but with increased losses, since the normal shock occurs at
a higher Mach number. All these three inlets are operated at the design Mach number, MD, which
by definition, means that the conical shock or conical shock extended will intersect the cowl lip.



Ramjet Performance



The ramjet has the virtue of maximum simplicity, with no need for turbomachinery, and
maximum tolerance to high-temperature operation and minimum mass-per-unit thrust at suitable
flight Mach numbers. The ramjet also has its limitations. As well as being generally incapable of
steady operation at subsonic Mach numbers, it has an upper Mach number limit. For the
conventional ramjet (in which the supersonic inlet air is slowed to subsonic speeds to provide
stable combustion prior to the nozzle expansion), there is a limiting Mach number of about 6,
above which the temperature of the air entering the combustor is so high that combustion cannot
be completed. Most of the chemical energy of combustion is nonusefully transformed into
dissociation reactions that on expansion do not provide the exhaust velocity needed for
satisfactory ramjet performance. To avoid this problem, substantial research has been, and is still
being, focused on the supersonic combustion ramjet (SCRAMJET). The difference between this
and the conventional ramjet is that combustion is to take place in a supersonic stream. Fuel must
be injected into the supersonic stream (without causing disruptive shock waves) and must mix
and burn in a millisecond or so. Conventional fuels do not ignite quickly enough, and gaseous
hydrogen seems the most likely candidate. Design of the fuel injector is a formidable challenge;
so is the problem of cooling a vehicle designed to operate at Mach numbers of 4 or higher.
Hydrogen could conceivably serve for structural cooling as well as for engine fuel.
It will be clear from this discussion that future designs for supersonic (or even hypersonic)
aircraft must cope with the design challenges of a whole range of flight Mach numbers.



Supersonic Combustion
The losses associated with subsonic ramjet combustion can be substantial. If ramjets are to be
applied to hypersonic flight, additional problems arise because of extremely high temperature at
the entrance to the combustion chamber. This not only makes vehicle cooling very difficult, but
it leads to severe combustion loss due to dissociation.
Figure shows the air temperature reached after adiabatic deceleration from a high-altitude
ambient temperature of 220 K and from flight Mach number M to a chamber pressure of either 1
or 10 atm. For hypersonic flight (e.g. for M > 8) the temperature of the air in the chamber is quite
dependent on the pressure: The higher the pressure, the less dissociation and the higher the
temperature of the mixture. The temperature of the combustion products is likewise pressure
dependent.
Figure shows, for a combustion pressure of 10 atm and a flight Mach number of 10, there
is no temperature rise due to combustion; all of the combustion energy is absorbed by
dissociation. One sees from the above Figure, the strange result that, at sufficiently high Mach
number, the temperature of the combustion products can be lower than that of the incoming air.
Consideration of the speed with which the fuel and air can be converted into dissociation
products may show that there is sufficient residence time in the combustion chamber to approach
equilibrium composition. But during the subsequent expansion in the nozzle, one cannot take
equilibrium composition for granted. It is quite possible that the expansion will be too rapid for
the composition to readjust, after each step of temperature and pressure reduction, to a new
equilibrium composition. If the expansion extremely rapid, the mixture may be effectively
“frozen” with the initial (high-temperature) composition. This would mean that little of the
combustion energy of the fuel (for the M = 10 case) would be available for acceleration of the
combustion products to produce thrust. The chemical kinetics of the recombination processes in
the nozzle would, in general, have a strong effect on the thrust and the propulsion efficiency of
the engine.
Some researchers have proposed the concept of the supersonic combustion as a way to avoid
this dissociation loss as well as the stagnation pressure losses associated with deceleration in
supersonic-to-subsonic inlets. With supersonic combustion, fluid temperatures are relatively low,
and this decreases the dissociation loss because dissociation depends on static rather than
stagnation temperature. Wall heat transfer, in contrast, depends essentially on stagnation
temperature, so the wall-cooling problem is not removed by employing supersonic combustion.
The stagnation pressure loss due to supersonic heating depends on the extent to which the fluid is
being accelerated while combustion is taking place.
The use of supersonic combustion requires fuel to be injected into, and mixed with, a
supersonic stream without excessive shock losses.



The main advantages of the ramjet engine are;
1.
2.
3.
4.
5.

High temperature can be employed
In the absence of rotating machinery its construction is very simple and cheap
It can operate effectively at high supersonic Mach numbers
It is not very sensitive to the quality of fuel
It provides high thrust per unit weight and frontal area



Ramjet engine’s Main disadvantages are;
1.
2.
3.
4.

It requires a launching device at supersonic speed
It is unsuitable for subsonic flight
It has low thermal efficiency and high TSFC
Its maximum operating altitude is limited

Ideal Efficiency
Various process occurring in the ramjet engine can be represented by an open circuit Brayton
cycle. This cycle is considered here with the following assumptions:
1. Steady one-dimensional flow
2. Isentropic compression and expansion, ∆s = 0, ∆P0 = 0
3. Perfect gas
4. Constant pressure heat addition in the combustion chamber, P2 = P3
5. Very low Mach number in the combustion chamber.
P2 ≈ P02 ≈ P03
T2 ≈ T02 ≈ T03
Compression and expansion process here are thermodynamically different from turbo jet
engine. These process here experience only energy transformation; there is no energy
transfer such as compressor and turbine work within the engine. Thrust work is obtained
from the energy supplied in the fuel during process 2-3. Heat is rejected during process 41 outside the engine. However, the ideal efficiency of the ramjet engine is still given by
Equation,

1
1
η i = 1 − = 1 − (γ −1) / γ
t
r
Here, the temperature ratio, with the above assumption is given by

t =

T2
T
T
γ −1 2
= 02 = 01 = 1 +
Mi
T1
T1
T1
2



Substituting the value of t from the above Equation to the previous equation we get,

γ −1
ηi = 1 −

ηi =

M 12

1
2
=
γ −1 2
γ −1 2
1+
M1
1+
M1
2
2

1
= f (M 1 )
2 1
1+
γ − 1 M 12

Though the actual thermal efficiency of the ramjet engine will be much lower than the
value given by the above equation it demonstrates an important characteristic i.e., the
efficiency increases with the flight Mach number and has a high value (76.19 % at M1 =
4) at higher operating Mach numbers.
Other performance parameters and efficiencies defined for air-breathing engines are also
applicable for the ram jet engine.



The thermal efficiency or the Air standard Efficiency of the ideal cycle 1-2s-3-4s is given by,
= work / heat supplied
= 1 – Qr/Qs
= 1 – (T4s – T1)/(T3-T2s)
The pressure ratio in the compressor and turbine is same,
i.e., r = P2/P1 = P3/P4
Therefore the corresponding temperature ratios are given by,

( γ −1) / γ

t=

P 
T2 s
T
= 3 = r (γ −1) / γ =  2 
P 
T1
T4 s
 1

η AS

P 
= 3 
P 
 4

( γ −1) / γ

1
1
= 1 − = 1 − (γ −1) / γ
t
r

Numerical Problem
Q. A ramjet

engine operates at M = 1.5 at an altitude of 6500 m. The diameter of the

inlet diffuser at entry is 50 cm and the stagnation temperature at the nozzle entry is 1600
K. The calorific value of the fuel used is 40 MJ/kg. The properties of the combustion
gases are same as those of air (γ = 1.4, R = 287 J/kg K). The velocity of air at the diffuser
exit is negligible.
Calculate (a) the efficiency of the ideal cycle (b) flight speed (c) air flow rate (d) diffuser
pressure ratio (e) fuel-air ratio (f) nozzle pressure ratio (g) nozzle jet Mach number (h)
propulsive efficiency (i) and thrust. Assue the following values; ηD = 0.90, ηB = 0.98, ηj
= 0.96, stagnation pressure loss in the combustion chamber = 0.02P02.



At Z = 6500 m the properties of air are
T1 = 245.90 K, p1 = 0.440 bar, a1 = 414.5 m/s
Ρ = 0.624 kg/m3
(a) Ideal cycle efficiency

ηi =

1
2 1
1+
γ − 1 M 12

= 0.310 Ans.
(b) M1 = u/a1
U = M1 a1 = 1.5 x 314.5 = 471.75 m/s
Flight speed = 1698.3 kmph Ans.
( C) Area of cross section of the diffuser inlet
A1 = π d2/4 = π 0.52/4 = 0.1963 m2



m a = ρ1uA1
= 0.624 X 471.48 X 0.1963
Air flow rate = 57.752 kg/s Ans.
(d) For negligible velocity at the diffuser exit,
P02 = P2

( γ −1) / γ

 P2 
 
−1
P 
ηD =  1 
γ −1 2
M1
2
ηD = 0.9, M1 = 1.5
P2/P1 = 3.2875

Ans.

P2 = 3.2875 x 0.44 = 1.446

(e)

T01
γ −1 2
= 1+
M 1 = 1.45
T1
2
= 1.45 x 245.9 = 356.55 K

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m a C p (T03 − T02 ) = η B m f Q f
•

f =

mf
•

= C p (T03 − T02 ) / η B Q f

ma
f = 1.005 (1600-356.55)/0.98 x 40000



Fuel air ratio = 0.03188 Ans

(f) P03 = P02 – 0.02 P02 = 0.98 P02
= 0.98 x 1.446 = 1.417 bar
Nozzle pressure ratio,

P03 1.417
=
= 3.22 Ans
P4
0.440
(g) The Mach number at the nozzle exit for a pressure ratio of 3.22 in an isentropic expansion
would be
M4s = 1.41; however, on account of irreversible expansion (ηj = 0.96) the exit
velocity and Mach number will be slightly lower.

T04
γ −1 2
=1+
M 4 s = 1 + 0.2 x 1.412 = 1.3976
T4 s
2
T4s = 1600/1.3976 = 1144.82 K
T04 – T4 = ηj (T04-T4s)
= 0.96 (1600-1144.82)
= 1600 – 436.973 = 1163.027 K
T04 = T4 + C24/2Cp
C4 = 937.185 m/s
a4 = (1.4 x 287 x 1163.027)0.5
= 683.596 m/s
Nozzle jet Mach number,
M4 = C4/a4 = 937.185/683.596 = 1.371 Ans
(h) σ = u/c4 = 471.48/937.185 = 0.503
ηp = 2σ/(1+ σ) = 2 x 0.503 /(1+0.503)



Propulsive efficiency = 0.6693 Ans
(i)

•

m f = 57.752 x 0.03188 = 1.841 kg / s
•

•

•

m = ma + m f = 57.752 + 1.841 = 59.593 kg / s
•

•

F = m C4 − m a u
= (59.593 x 937.185 – 57.752 x 471.75) 10-3
Thrust = 28.614 kN Ans

Ram rocket
Air-augmented rockets

(also known as rocket-ejector, ramrocket, ducted
rocket, integral rocket/ramjets, or ejector ramjets) use the supersonic exhaust of some kind of
rocket engine to further compress air collected by ram effect during flight to use as additional
working mass, leading to greater effective thrust for any given amount of fuel than either the
rocket or a ramjet alone.
They represent a hybrid class of rocket/ramjet engines, similar to a ramjet, but able to give useful
thrust from zero speed, and are also able in some cases to operate outside the atmosphere, with
fuel efficiency not worse than both a comparable ramjet or rocket at every point.

Operation
A normal chemical rocket engine carries oxidizer and a fuel, sometimes pre-mixed, as in a solid
rocket, which are then burned. The heat generated greatly increases the temperature of the
mixture, which is then exhausted through a nozzle where it expands and cools. The exhaust is
directed rearward through the nozzle, thereby producing a thrust forward. In this conventional
design, the fuel/oxidizer mixture is both the working mass and energy source that accelerates it.
One method of increasing the overall performance of the system is to collect either the fuel or the
oxidizer during flight. Fuel is hard to come by in the atmosphere, but oxidizer in the form of
gaseous oxygen makes up 20% of the air and there are a number of designs that take advantage
of this fact. These sorts of systems have been explored in the LACE (liquid air cycle engine)
concept.



Another idea is to collect the working mass instead. With an air-augmented rocket, an otherwise
conventional rocket engine is mounted in the center of a long tube, open at the front. As the
rocket moves through the atmosphere the air enters the front of the tube, where it is compressed
via the ram effect. As it travels down the tube it is further compressed and mixed with the fuelrich exhaust from the rocket engine, which heats the air much as a combustor would in a ramjet.
In this way a fairly small rocket can be used to accelerate a much larger working mass than
normally, leading to significantly higher thrust within the atmosphere.
A liquid air cycle engine (LACE) is a spacecraft propulsion engine that attempts to gain
efficiency by gathering part of its oxidizer from the atmosphere. In a LOX/LH2 bipropellant
rocket the liquid oxygen needed for combustion is the majority of the weight of the spacecraft on
lift-off, so if some of this can be collected from the air on the way, it might dramatically lower
the take-off weight of the spacecraft.

Principle of operation
LACE works by compressing and then quickly liquefying the air. Compression is achieved
through the ram-air effect in an intake similar to that found on a high-speed aircraft like
Concorde, where intake ramps create shock waves that compress the air. The LACE design then
blows the compressed air over a heat exchanger, in which the liquid hydrogen fuel is flowing.
This rapidly cools the air, and the various constituents quickly liquefy. By careful mechanical
arrangement the liquid oxygen can be removed from the other parts of the air, notably water,
nitrogen and carbon dioxide, at which point it can be fed into the engine as normal. The
hydrogen is so much lighter than oxygen that the now-warm hydrogen is often dumped
overboard instead of being re-used as fuel, at a net gain.
One issue with the LACE system is that in order to appreciably reduce the mass of the oxygen
carried at launch, a LACE vehicle needs to spend more time in the lower atmosphere where it
can collect enough oxygen to supply the engines. This leads to greatly increased vehicle heating
and drag, which offset somewhat the savings in oxidizer weight, but this in turn is offset by
higher Isp (Specific impulse) permitting a lifting trajectory which greatly reduces gravity losses.
More significantly the LACE system is far heavier than a rocket engine, and the performance of
launch vehicles of all types is particularly affected by dry mass, rather than any oxidizer mass
which would be burnt off over the course of the flight.

Additional Reading:
1.
2.
3.

4.

Hill, P.G. & Peterson, C.R. “Mechanics & Thermodynamics of Propulsion” Addison – Wesley
Longman INC, 1999.
Cohen, H., Rogers, G.F.C. and Saravanamuttoo, H.I.H., “Gas Turbine Theory”, Longman Co.,
ELBS Ed., 1989.
Gorden, C.V., “Aero thermodynamics of Gas Turbine and Rocket Propulsion”, AIAA Education
Series, New York, 1989.
Mathur, M., and Sharma, R.P., “Gas Turbines and Jet and Rocket Propulsion”, Standard
Publishers, New Delhi, 1988.



Unit-3
FUNDAMENTALS OF ROCKET PROPULSION
Operating principle – Specific impulse of a rocket – internal ballistics- Rocket nozzle
classification – Rocket performance considerations – Numerical Problems.

Rockets – Special Features and Applications
Historical Reference
•

•
•
•
•

•
•
•

The basic principles of all propulsive devices lie with the laws of motion due to Newton
(17th Century AD). These laws are phenomenological and therefore one can expect that
even before Newton there may have existed many devices working on the principles of
reaction.
Rockets working directly on the principle of reaction are perhaps the simplest of the
propulsive engines.
The reciprocating engines and gas turbine engines are relatively more complex.
The Chinese are credited with the invention of rockets probably in 12-14th century AD.
Indians used the rockets as effective weapons in late 18th century against British and in
19th century, the rockets became a part of the warfare in Europe. But it was only in the
early part of the present century that man has recognized the full potential of rocket
owing to the interests in space travel/satellite technology and like.
Tsiolkovsky (USSR 1903) Goddard (USA, 1912) and Oberth (1921) are the pioneers of
modern rocketry.
The liquid propellant rocket owe their genesis to these people.
The German V-2 rockets (25 tons, 65 sec, LOX-Alchol) and the post-second World war
progress in rocketry are too familiar to all.

Principle
All the conventional propulsion systems work by causing a change of momentum in a working
fluid in a direction opposite to the intended motion. Rockets fall under the category of direct
acting engines – since the energy liberated by the chemical process is directly used to obtain
thrust. Being non-air breathing devices the basic component of a rocket are
(i) Combustion chamber where exothermic processes produces gases at high temperature
and pressure, and
(ii) Nozzle, which accelerate the fluid to high velocities and discharge them into surrounding
atmosphere thereby deriving the desired force or thrust.



Some Special Features
The non-air breathing nature of rockets makes them very distinct among the propulsive devices.
(a) The reaction system does not depend on the surrounding atmosphere. There are no
velocity limitations and altitude ceiling.
(b) Since it has to carry its own oxidizer required for combustion reaction, the specific
propellant consumption is very high. Rockets consume approximately 15kg/kg-hr of
propellant compared to about 1 kg/kg-hr of fuel by turbojet engine.
(c) High pressure operation is possible and hence the ratio of energy liberation per unit
volume (and also unit weight of hardware) is very high.
(d) Main part of the rockets contains no moving element. Hence there is no constraint on
internal aerodynamics and the reliability is high. This also implies quick response times,
which makes them ideal control components.
With the above features, it is clear that the rockets are the most suitable power plants for
(i) High altitude and space applications where atmospheric oxygen is not available,
eg. Launch vehicles and satellite control rockets.
(ii) All applications where high thrust are required for short duration: missiles, boosters,
JATO etc.

Rockets in Space Applications
There are a variety of rockets when it comes to launching and satellite control. Many of these are
non-chemical in nature but are restricted to extremely low thrust levels.
Sl
No

Type

Order of
Magnitude of
Thrust (N)

F/W

Operational
Time

Isp
(sec)

Applications

10-5

10-4

Years

∞

Satellite Altitude
control

Solar sail
(not a rocket in
fact)
Electric Prop.
(Electro thermal,
Electro Static,
Electro
Magnetic)
Stored cold gas
(N2, NH3 etc.)

10-6 - 10-2

10-5-10-3

Years

150 - 6000

Satellite control,
stabilization, orbit
maneuver

10-2 - 10-1

~ 10-3

Years

50 - 100

-do-

4

Nuclear Rocket

upto 105

20-30

Minute to
hours

800

5

Chemical Rocket
(Solid, Liquid
and Hybrid)

upto 107

upto 80

Seconds to
minutes@

150-450

1

2

3

Interplanetary and
space travel
Launch vehicles,
Missiles, Control
rockets, Sounding
rockets, JATO etc

@ shuttle main engine operate for about 8 min at a time but over 7 hrs cumulatively.



Classification of Chemical Rockets
Depending on the context, the chemical rockets are classified in many ways as follows:
(a)
(b)
(c)
(d)

Type of propellant: Solid, Liquid (mono propellant / bipropellant and hybrid rockets)
Application: Launch vehicle, ABM’s, JATO’s, ICBM, IRBM, SAM etc.
Size of Unit (and thrust level sometimes): 10 ton, 100 kg etc.
Type of subsystem: Turbopump fed, clustering, grain type etc.

Specific Impulse
•

•

The specific impulse of a rocket, Isp, is the ratio of the thrust to the flow rate of the weight ejected,
that is

where F is thrust,
is the rate of mass flow, and g is the acceleration of gravity at ground
level.
Specific impulse is expressed in seconds. When the thrust and the flow rate remain constant
throughout the burning of the propellant, the specific impulse is the time for which the rocket
engine provides a thrust equal to the weight of the propellant consumed.

•

For a given engine, the specific impulse has different values on the ground and in the vacuum of
space because the ambient pressure is involved in the expression for the thrust. It is therefore
important to state whether specific impulse is the value at sea level or in a vacuum.

•

There are a number of losses within a rocket engine, the main ones being related to the
inefficiency of the chemical reaction (combustion) process, losses due to the nozzle, and losses
due to the pumps.

•

Overall, the losses affect the efficiency of the specific impulse. This is the ratio of the real
specific impulse (at sea level, or in a vacuum) and the theoretical specific impulse obtained with
an ideal nozzle from gases coming from a complete chemical reaction. Calculated values of
specific impulse are several percent higher than those attained in practice.

•

From Equation (2.8) we can substitute

•

Equation (2.24) is very useful when solving Equations (2.18) through (2.21). It is rare we are
given the value of C directly, however rocket engine specific impulse is a commonly given
parameter.

C for F in Equation (2.23), thus obtaining



Internal Ballistics
The parameters that govern the burning rate and mass discharge rate of rocket motors are called
internal ballistic properties; they include
r–

propellant burning rate (velocity of consumption), m/sec or mm/sec or in/sec.

K–

ratio of burning surface to throat area, Ab/At

σp – temperature sensitivity of burning rate, expressed as percent change of burning
rate per degree change in propellant temperature at a particular value of chamber
pressure.

πK - temperature sensitivity of pressure expressed as percent change of chamber
pressure per degree change in propellant temperature at a particular value of K,
and the influences caused by pressure, propellant ingredients, gas velocity, or acceleration.
The subsequent solid propellant rocket parameters are performance parameters; they include
thrust, ideal exhaust velocity, specific impulse, propellant mass fraction, flame temperature,
temperature limits and duration.

Propellant Burning Rate
The rocket motor’s operation and design depend on the combustion characteristics of the
propellant, its burning rate, burning surface, and grain geometry. The branch of applied science
describing these is known as internal ballistics.
Solid propellant burns normal to its surface. The (average) burning rate, r, is defined as the
regression of the burning surface per unit time. For a given propellant, the burning rate is mainly
dependent on the pressure, p, and the initial temperature, Ti, of the propellant. Burning rate is
also a function of propellant composition. For composite propellants it can be increased by
changing the propellant characteristics:
1. Add a burning rate catalyst, often called burning rate modifier (0.1 to 3.0% of propellant)
or increase percentage of existing catalyst.
2. Decrease the oxidizer particle size.
3. Increase oxidizer percentage
4. Increase the heat of combustion of the binder and/or the plasticizer
5. Imbed wires or metal staples in the propellant



Apart from the propellant formulation and propellant manufacturing process, burning ratein a
full-scale motor can be increased by the following
1.
2.
3.
4.
5.

Combustion chamber pressure
Initial temperature of the solid propellant prior to start
Combustion gas temperature
Velocity of the gas flow parallel to the burning surface
Motor motion ( acceleration and spin-induced grain stress)

Burning rate data are usually obtained in three ways – namely, from testing by:
1. Standard strand burners, often called Crawford burners
2. Small-scale ballistic evaluation motors
3. Full-scale motors with good instrumentation
A strand burner is a small pressure vessal (usually with windows) in which a thin strand
or bar of propellant is ignited at one end and burned to the other end. The strand can be
inhibited with an external coating so that it will burn only on the exposed cross-sectional
surface; chamber pressure is simulated by pressurizing the container with inert gas. The
burning rate can be measured by electric signals from embedded wires, by ultrasonic
waves, or by optical means. The burning rate measured on strand burners is usually lower
than that obtained from actual rocket motor firing (by 4 to 12%) because it does not truly
simulate the hot chamber environment of an actual rocket motor. Also small ballistic
evaluation motors usually have a slightly lower burning rate than full-scale large motors,
because of scaling factors.
During development of a new or modified solid propellant, it is tested extensively or
characterized. This includes the testing of the burn rate (in several different ways) under
different temperatures, pressures, impurities, and conditions. It also requires
measurements of physical, chemical, and manufacturing properties, ignitability, aging,
sensitivity to various energy inputs or stimuli (e.g., shock, friction, fires), moister
absorption, compatibility with other materials (liners, insulators, cases), and other
characteristics. It is a lengthy, expensive, often hazardous program with many tests,
samples, and analyses.
The burning rate of propellant in a motor is a function of many parameters, and at any
•

instant governs the mass flow rate

m

of hot gas generated and flowing from the motor

(stable combustion);
•

m

= Ab r ρb

Here Ab is the burning area of the propellant grain, r the burning rate, and ρb the solid
propellant density prior to motor start. The total mass m of effective propellant burned can be
determined by integrating the above equation,



•

∫ m dt

m=

= ρ b ∫ Ab r dt

Where Ab and r vary with time and pressure.
Burning Rate Relation with Pressure
Classical equations relating to burning rate are helpful in preliminary design, data extrapolation,
and understanding the phenomena. Unless otherwise stated, burning rate is expressed for 70oF or
294 K propellant (prior to ignition) burning at a reference chamber pressure of 1000 psia or
6.895 MPa. For most production-type propellant the burning rate is approximated as a function
of chamber pressure, at least for a limited range of chamber pressures, which is given as
r = a Pn
where r, the burn rate, is usually in centimeter per second and chamber pressure P is in MPa; a is
an empirical constant influenced by ambient temperature. Also a is known as the temperature
coefficient and it is NOT dimensionless. The burning rate exponent n, sometimes called the
combustion index, is independent of the initial grain temperature and describes the influence of
chamber pressure on the burning rate.
Burning Rate Relation with Temperature
Temperature affects chemical reaction rates and the initial ambient temperature of a propellant
grain prior to combustion influences burning rate.
The sensitivity of burning rate to propellant temperature can be expressed in the form of
temperature coefficient, the two most common being

1  ∂r 
 ∂ ln r 
 = 

r  ∂T  p
 ∂T  p

σp = 

1  ∂P 
 ∂ ln p 
 = 

P  ∂T  K
 ∂T  K

πK = 

with σp , temperature sensitivity of burning rate and πK, temperature sensitivity of pressure.
The coefficient σp (typically 0.001 – 0.009 / K) for a new propellant is usually calculated from
strand burner test data, and πK (typically 0.067 – 0.278 % / oC) from small-scale or full-scale
motors. Mathematically, these coefficients are the partial derivatives of the natural logarithm of
the burning rate r or the chamber pressure p, respectively, with respect to propellant temperature
T.
The values of πK and σp depend primarily on the nature of the propellant burning rate, the
composition, and the combustion mechanism of the propellant. It is possible to derive a
relationship between the two temperature sensitivities, namely



πK =

1
σp
1− n

This formula is usually valid when the three variables are constant over the chamber pressure
and temperature range.
The temperature sensitivity σp can be also expressed as

 ∂ ln (aP n ) 
1 da
σp = 
 =
a dT
 ∂T
p



Equilibrium chamber pressure

In the above figure the straight line through the origin and point ‘S’ depicts the mass flow
through the nozzle as a function of Pc. At point S there is a balance between mass production and
__

outflux of the mass. At higher pressures (> Pc ) the mass flow through the nozzle is larger than
the production at the burning surface in case n < 1 and the reverse happens for n > 1. Thus if
__

n < 1 the pressure will drop to its steady-state value Pc . Note that when n < 1 even at higher
chamber pressure rocket motor will back to its designed equilibrium chamber pressure and
ensure a stable operation. On the other hand when n>1 these types of situations will possibly lead
to over-pressurization and rupture of the rocket motor or depressurization and flame out.

Erosive Burning
Erosive burning refers to the increase in the propellant burning caused by the high-velocity flow
of combustion gases over the burning propellant surface. It can seriously affect the performance
of solid propellant rocket motors. It occurs primarily in the port passages or perforations of the
grain as the combustion gases flow toward the nozzle; it is more likely to occur ehen the port
passage cross-sectional area A is small relative to the throat area At with a port-to-throat area



ratio of 4 or less. The high velocity near the burning surface and the turbulent mixing in the
boundary layers increase the heat transfer to the solid propellant and thus increase the burning
rate.

Erosive burning increases the mass flow and thus also the chamber pressure and thrust during
the early portion of the burning for a particular motor (see above Fig.). Erosive burning causes
early burnout of the web, usually at the nozzle end, and exposes the insulation and aft closure to
hot combustion gas for a longer period of time; this usually requires more insulation layer
thickness (and more inert mass) to prevent local thermal failure. In designing motors, erosive
burning is either avoided or controlled to be reproducible from one motor to the next.
Total burning rate = steady state burning rate ( aPcn ) + erosive burning

Basic Performance Relations
One basic performance relation derived from the principle of conservation of matter. The
propellant mass burned per unit time has to equal the sum of the change in gas mass per unit time
in the combustion chamber grain cavity and the mass flowing out through the exhaust nozzle per
unit time.

d
k  2 
Ab r ρb = ( ρ1V1 ) + At P


1
dt
RT1  k + 1 


( k +1) /( k −1)


The term on the left side of the equation gives the mass rate of gas generation. The first term on
the right gives the change in propellant mass in the gas volume of the combustion chamber, and
the last term gives the nozzle flow. The burning rate of propellant is r; Ab is the propellant
burning area; ρb is the solid propellant density; ρ1 is the combustion gas density; V1 is the
chamber gas cavity volume, which becomes larger as the propellant is expended; At is the throat
area; P1 is the chamber pressure; T1 is the absolute chamber temperature, which is usually
assumed to be constant; and k is the specific heat ratio of the combustion gases. During startup
the changing mass of propellant in the grain cavity becomes important.

Isentropic Flow through Nozzles
In a converging diverging nozzle a large fraction of the thermal energy of the gases in the
chamber is converted into kinetic energy. As will be explained, the gas pressure and temperature
drop dramatically and gas velocity can reach values in excess of around 3.2 km/sec. This is a
reversible, essentially isentropic flow process.
If a nozzle inner wall has a flow obstruction or a wall protrusion (a piece of weld splatter or
slag), then the kinetic gas energy is locally converted back into thermal energy essentially equal
to the stagnation temperature and stagnation pressure in the chamber. Since this would lead
quickly to a local overheating and failure of the wall, nozzle inner walls have to be smooth
without any protrusion.
Nozzle exit velocity can be derived as,

v2 =

 P
2k
RT1 1 −  2

k −1
  P1







( k −1) / k



 + v12




This relation also holds for any two points within the nozzle. Note that when the chamber section
is large compared to the nozzle throat section, the chamber velocity or nozzle approach velocity
is comparatively small and the v12 can be neglected. The chamber temperature T1 is at the nozzle
inlet and, under isentropic condition, differ little from the stagnation temperature or (for a
chemical rocket) from combustion temperature. This leads to an important simplified expression
of the exhaust velocity v2, which is often used in the analysis.

 P
2k
RT1 1 −  2

k −1
  P1


v2 =






( k −1) / k

( k −1) / k

2k R 'To   P2 
1 −  

k − 1 M   P1 

  


=

Thrust and Thrust Coefficient

•

F = m v 2 + ( p 2 − p3 ) A2

F = C F At P1








Where CF is the thrust coefficient, which can be derived as a function of gas property k, the
nozzle area ratio (A2/At), and the pressure ratio across the nozzle p1/p2 , but independent of
chamber temperature. For any fixed pressure ratio (p1/p3) the thrust coefficient CF and the thrust
F have a peak when p2 = p3. This peak value is known as optimum thrust coefficient.

CF =

2k 2  2 


k −1 k +1

( k +1) /( k −1)

  p  ( k −1) / k 
p − p 3 A2
1 −  2 
 + 2
 
p1
At
  p1 




Effective Exhaust Velocity
In a rocket nozzle the actual exhaust velocity is not uniform over the entire exit cross-section and
does not represent the entire thrust magnitude. The velocity profile is difficult to measure
accurately. For convenience a uniform axial velocity ‘c’ is assumed which allows a onedimensional description of the problem. This effective exhaust velocity ‘c’ is the average
equivalent velocity at which propellant is ejected from the vehicle. It is defined as
c = I sp g o =

F
•

m

It is usually given in meters per second.
The concept of weight relates to the gravitational attraction at or near sea level, but in space or
outer satellite orbits, “weight” signifies the mass multiplied by an arbitrary constant, namely go.
In system international (SI) or metric system of units Isp can be expressed simply in “seconds”,
because of the use of the constant go.

Specific Propellant Consumption
Specific propellant consumption is the reciprocal of the specific impulse.

Mass Ratio
The mass ratio of a vehicle or a particular vehicle stage is defined to be the final mass mf (after
rocket operation has consumed all usable propellant) divided by initial mass mo (before rocket
operation).



This applies to a single or multi-stage vehicle. The final mass mf is the mass of the vehicle after
the rocket has ceased to operate when all the useful propellant mass mp has been consumed and
ejected. The final vehicle mass mf includes all those components that are not useful propellant
and may include guidance devices, navigation gear, payload (e.g., scientific instruments or a
military warhead), flight control systems, communication devices, power supplies, tank
structure, residual or unusable propellant, and all the propulsion hardware. In some vehicles it
can also include wings, fins, a crew, life support systems, reentry shields, landing gears etc.
Typical value of Mass ratio can range from 60% for tactical missiles to less than 10 % for
unmanned launch vehicle stages. This mass ratio is an important parameter in analyzing flight
performance. Note that when mass-ratio is applied to a single stage of a multi-stage rocket, then
its upper stages become the “payload”

Propellant Mass Fraction, ζ
Propellant mass fraction ‘ζ’ is defined as the ratio of propellant mass ‘mp’ to the initial mass ‘mo’

ζ =

mp
mo

mo = mf + mp

Characteristic Velocity
The characteristic velocity has been used frequently in the rocket propulsion literature. It is
represented by a symbol C*. It is defined as,

C∗ =

p1 At
•

m
The characteristic velocity is used in comparing the relative performance of different chemical
rocket propulsion system designs and propellants. It is basically a function of the propellant
•

characteristics. It is easily determined from data of m , p1, and At. It relates to the efficiency of
the combustion and is essentially independent of nozzle characteristics. However, the specific
impulse and the effective exhaust velocities are functions of the nozzle geometry, such as the
nozzle area ratio.



Problems:
Q1.
A rocket projectile has the following characteristics:
Initial mass = 200kg
Mass after rocket operation = 130 kg
Payload, nonpropulsive structure, etc., = 110 kg
Rocket operation duration = 3.0 sec
Average specific impulse of propellant = 240 sec
Determine the vehicle’s (i) mass ratio, (ii) propellant mass fraction, (iii) propellant flow rate, (iv)
thrust, (v) thrust-to-weight ratio, (vi) acceleration of the vehicle, (vii) effective exhaust velocity,
(viii) total impulse, and (ix) the impulse to weight ratio.

Solution:
(i) Mass ratio of vehicle, mf/mp = 130/200 = 0.65
Mass ratio of rocket system = mf/mo = (130-110)/(200-110) = 20/90 = 0.222
(ii) Propellant mass fraction = (mo – mf)/mo = (90-20)/90 = 0.778
(iii)Propellant mass flow rate = 70/3 = 23.3 kg/sec
•

(iv) Thrust = I sp m g o = 240 x 23.3 x 9.81 = 54.857 N
(v) Thrust-to-weight ratio of the vehicle is
Initial value
Final value

= 54,857 / (200 x 9.81) = 28
= 54,857 / (130 x 9.81) = 43

(vi)

Maximum acceleration of the vehicle is 43 x 9.81 = 421 m/sec2

(vii)

The effective exhaust velocity is
c = Isp go = 240 x 9.81 = 2354 m/sec

(viii) Total impulse = Isp w = 240 x 70 x 9.81 = 164, 808 N-sec
This result can also be obtained by multiplying the thrust by the duration.
(ix) The impulse to weight ratio of the propulsion system is
= 164,808 / [(200-110) x 9.81] = 187



Q2.

The following measurements were made in a sea level test of a solid propellant rocket
motor:
Burn duration = 40 sec
Initial mass before test = 1210 kg
Mass of rocket motor after test = 215 kg
Average thrust = 62,250 N
Chamber pressure = 7.00 MPa
Nozzle exit pressure = 0.070 MPa
Nozzle throat diameter = 0.855 m
Nozzle exit diameter = 0.2703 m
•

Determine m, v 2 , c ∗ , c and I sp at sea level, and c and Isp at 1000 and 25,000 m altitude.
Assume an invariant thrust and mass flow rate and negligible short start and stop
transients.

Solution:
Mass flow rate = (initial motor mass – final motor mass)/burn time
= (1210 – 215) / 40 = 24.9 kg/sec
The nozzle areas at the throat and exit are
At = π D2/4 = π x 0.08552 /4 = 0.00574 m2
A2 = π D2/4 = π x 0.27032 /4 = 0.0574 m2
The actual exhaust velocity

v2 =

( F − ( p 2 − p3 ) A2 )
•

m
= (62,250 – (0.070-0.1013) 106 x 0.0574) / 24.9
= 2572 m/sec

C∗ =

p1 At
•

m
= 7.00 x 106 x 0.00574/24.9 = 1613 m/sec
Isp = 62,250 / (24.9 x 9.81) = 255 sec
c = 255 x 9.81 = 2500 m/sec
For altitudes of 1000 and 25, 000 m the ambient pressure (see atmospheric table) is 0.898 and
0.00255 MPa.



c = v2 +

( p2 − p3 ) A2
•

m
At 1000 m altitude,
c = 2572 + (0.070-0.898) x 106 x 0.0574/24.9 = 2527 m/sec
Isp = 2527/9.81 = 258 sec
At 25,000 m altitude,
c = 2572 + (0.070-0.00255) x 106 x 0.0574/24.9 = 2727 m/sec
Isp = 2727/9.81 = 278 sec



Rocket Nozzles
Purpose:
The nozzle is the component of a rocket or air-breathing engine that produces thrust. This is
accomplished by converting the thermal energy of the hot chamber gases into kinetic energy and
directing that energy along the nozzle's axis, as illustrated below.

Simple representation of a rocket nozzle
Although simplified, this figure illustrates how a rocket nozzle works. The propellant is
composed of a fuel, typically liquid hydrogen (H 2), and an oxidizer, typically liquid oxygen (O
(mdot) where the fuel
2). The propellant is pumped into a combustion chamber at some rate
and oxidizer are mixed and burned. The exhaust gases from this process are pushed into the
throat region of the nozzle. Since the throat is of less cross-sectional area than the rest of the
engine, the gases are compressed to a high pressure. The nozzle itself gradually increases in
cross-sectional area allowing the gases to expand. As the gases do so, they push against the walls
of the nozzle creating thrust.
Mathematically, the ultimate purpose of the nozzle is to expand the gases as efficiently as
possible so as to maximize the exit velocity (v exit). This process will maximize the thrust (F)
produced by the system since the two are directly related by the equation



where
F = thrust force
= mass flow rate
v exit = exhaust gas velocity at the nozzle exit
p exit = pressure of the exhaust gases at the nozzle exit
p

= ambient pressure of the atmosphere

A exit = cross-sectional area of the nozzle exit

Expansion Area Ratio:
In theory, the only important parameter in rocket nozzle design is the expansion area ratio (), or
the ratio of exit area (A exit) to throat area (A throat).

Fixing all other variables (primarily the chamber pressure), there exists only one such ratio that
optimizes overall system performance for a given altitude (or ambient pressure). However, a
rocket typically does not travel at only one altitude. Thus, an engineer must be aware of the
trajectory over which a rocket is to travel so that an expansion ratio that maximizes performance
over a range of ambient pressures can be selected.
Nevertheless, other factors must also be considered that tend to alter the design from this
expansion ratio-based optimum. Some of the issues designers must deal with are nozzle weight,
length, manufacturability, cooling (heat transfer), and aerodynamic characteristics.

Typical temperatures (T) and pressures (p) and speeds (v) in a De Laval Nozzle



Maximum thrust for a rocket engine is achieved by maximizing the momentum contribution of
the equation without incurring penalties from over expanding the exhaust. This occurs when Pe =
Pamb. Since ambient pressure changes with altitude, most rocket engines spend very little time
operating at peak efficiency.

If the pressure of the exhaust jet varies from atmospheric pressure, nozzles can be said to be
underexpanded, ambient or overexpanded. If under or overexpanded then loss of efficiency
occurs, grossly overexpanded nozzles lose less efficiency, but the exhaust jet is usually unstable.
Rockets become progressively more underexpanded as they gain altitude. Note that almost all
rocket engines will be momentarily grossly overexpanded during startup in an atmosphere.

Rocket Nozzle Shapes
Not all rocket nozzles are alike, and the shape selected usually depends on the application.
This section discusses the basic characteristics of the major classes of nozzles used today.

Nozzle Comparisons:
To date three major types of nozzles, the cone, the bell or contoured, and the annular or plug,
have been employed. Each class satisfies the design criteria to varying degrees. Examples of
these nozzle types can be seen below.



Size comparison of optimal cone, bell, and radial nozzles for a given set
of conditions
Conical Nozzle:
The conical nozzle was used often in early rocket applications because of its simplicity and
ease of construction. The cone gets its name from the fact that the walls diverge at a constant
angle. A small angle produces greater thrust, because it maximizes the axial component of
exit velocity and produces a high specific impulse (a measure of rocket efficiency). The
penalty, however, is a longer and heavier nozzle that is more complex to build. At the other
extreme, size and weight are minimized by a large nozzle wall angle. Unfortunately, large
angles reduce performance at low altitude because the high ambient pressure causes
overexpansion and flow separation.

Bell Nozzle:
The bell, the most commonly used nozzle shape, offers significant advantages over the
conical nozzle, both in size and performance. Referring to the above figure, note that the bell
consists of two sections. Near the throat, the nozzle diverges at a relatively large angle but the
degree of diveregence tapers off further downstream. Near the nozzle exit, the diveregence
angle is very small. In this way, the bell is a compromise between the two extremes of the
conical nozzle since it minimizes weight while maximizing performance. The most important
design issue is to contour the nozzle to avoid oblique shocks and maximize performance.
However, we must remember that the final bell shape will only be the optimum at one
particular altitude.



Annular Nozzles:
The annular nozzle, also sometimes known as the plug or "altitude-compensating" nozzle, is
the least employed of those discussed due to its greater complexity. The term "annular" refers
to the fact that combustion occurs along a ring, or annulus, around the base of the nozzle.
"Plug" refers to the centerbody that blocks the flow from what would be the center portion of
a traditional nozzle. "Altitude-compensating" is sometimes used to describe these nozzles
since that is their primary advantage, a quality that will be further explored later.
Before describing the various forms of annular nozzles, it is useful to mention some key
differences in design parameters from the conical or bell nozzles. The expansion area ratio
for a traditional nozzle has already been discussed. When considering an annular nozzle, the
area of the centerbody (A plug) must also be taken into account.

Another parameter particular to this type of nozzle is the annular diameter ratio, D p / D t, or
the ratio of the centerbody diameter to that of the throat. The ratio is used as a measure of the
nozzle geometry for comparison with other plug nozzle shapes. Typical values of this ratio
appear in the above figure.

Annular Nozzles I
Having introduced the three principal families of nozzle shapes, we will now look more closely
at the two major subclasses of annular, or plug, nozzles.

Radial Out-Flow Nozzles:
Two major types of plug nozzles have been developed to date. They are distinguished by the
method in which they expand the exhaust, outward or inward. The radial out-flow nozzle was the
subject of much research in the late 1960s and early 1970s. Examples of this type are the
expansion-deflection (E-D), reverse-flow (R-F), and horizontal-flow (H-F) nozzles shown in the
figure above.
The name of each of these nozzles indicates how it functions. The expansion-deflection nozzle
works much like a bell nozzle since the exhaust gases are forced into a converging throat region
of low area before expanding in a bell-shaped nozzle. However, the flow is deflected by a plug,
or centerbody, that forces the gases away from the center of the nozzle. Thus, the E-D is a radial
out-flow nozzle.
The reverse-flow nozzle gets its name because the fuel is injected from underneath, but the
exhaust gases are rotated 180° thereby reversing their direction. Similarly, the fuel in the
horizontal-flow nozzle is injected sideways, but the exhaust is rotated 90°.



Judging by the amount of literature obtained on this subject, little work has been done on the R-F
and H-F nozzles, and they will not be considered further. The E-D, on the other hand, has been
one of the most studied forms of annular nozzles. While similar in nature to the bell nozzle, the
most notable difference is the addition of a centerbody. As shown below, this "plug" may be
located upstream of, downstream of, or in the throat, with each location resulting in better
performance for a given set of operating conditions.

Comparison of centerbody locations in Expansion-Deflection
nozzles [from Conley et al, 1984]
The purpose of the centerbody is to force the flow to remain attached to, or to stick to, the nozzle
walls, as illustrated in the following figure.



Expansion-deflection nozzle flow behavior at low altitude
[from Sutton, 1992]
This behavior is desirable at low altitudes because the atmospheric pressure is high and may be
greater than the pressure of the exhaust gases. When this occurs, the exhaust is forced inward and
no longer exerts force on the nozzle walls, so thrust is decreased and the rocket becomes less
efficient. The centerbody, however, increases the pressure of the exhaust gases by squeezing the
gases into a smaller area thereby virtually eliminating any loss in thrust at low altitude.

Annular Nozzles II
Having introduced the three principal families of nozzle shapes and discussed the radial out-flow
nozzle, we will now look more closely at the second class of annular nozzles.

Radial In-Flow Nozzles:
The second major variety of annular nozzles is the radial in-flow type, exemplified by the spike
shown above.
This type of nozzle, named for the prominent spike centerbody, is often described as a bell
turned inside out. However, the nozzle shown above is only one of many possible spike
configurations. Variations of this design, shown below, include
(a) a traditional curved spike with completely external supersonic expansion
(b) a similar shape in which part of the expansion occurs internally
(c) a design similar to the expansion-deflection nozzle in which all expansion occurs
internally.



Comparison of spike nozzles with (a) external expansion, (b) internal-external expansion, and
(c) internal expansion [from Berman and Crimp, 1961]
Note that each of the above spike nozzles features a curved, pointed spike, the most ideal shape.
This spike shape allows the exhaust gases to expand through an isentropic, or constant entropy,
process. In so doing, the nozzle efficiency is maximized and no energy is lost because of
turbulent mixing in the exhaust flow. While the isentropic spike may be most efficient, it also
tends to be prohibitively long and heavy. However, theoretical studies have shown that replacing
the curved shape by a much shorter and easier to construct cone results in very little performance
loss. The following graph illustrates that the thrust decreases by less than 1% for cone halfangles up to 30°. Furthermore, the graph gives an indication of how much the spike length can be
reduced by employing a cone-shaped spike.

Aerospike Nozzles
A further subclass of the radial in-flow family of spike nozzles is known as the aerospike.

Aerospike Nozzles:
Previously, we discussed methods of reducing the length of a spike nozzle centerbody by
replacing the ideal spike with a conical spike. While this method does indeed result in a much
shorter nozzle length, we can go even further by removing the pointed spike altogether and
replacing it with a flat base. This configuration is known as a truncated spike, an example of
which is shown below.



Example of a truncated, conical spike [from Berman and Crimp, 1961]
As any fluid dynamicist recognizes, the significant disadvantage of the "flat" plug is that a
turbulent wake forms aft of the base at high altitudes resulting in high base drag and reduced
efficiency. However, this problem can be greatly alleviated in an improved version of the
truncated spike that introduces a "base bleed," or secondary subsonic flow, into the region aft of
the base.

Example of an aerospike nozzle with a subsonic, recirculating flow
[from Hill and Peterson, 1992]



The circulation of this secondary flow and its interaction with the engine exhaust creates an
"aerodynamic spike" that behaves much like the ideal, isentropic spike. In addition, the
secondary flow re-circulates upward pushing on the base to produce additional thrust. It is this
artificial aerodynamic spike for which the aerospike nozzle is named.

Linear Aerospike:
All of the nozzles we have studied thus far have been annular, or circular when viewed from
below. Still another variation of the aerospike nozzle is not an annular nozzle at all. A second
approach, pioneered by the Rocketdyne company (now a division of Boeing) in the 1970s, places
the combustion chambers in a line along two sides of the nozzle:

Rocketdyne RS-2200 linear aerospike engine [from Flinn, 1996]
This approach results in a more versatile design allowing the use of lower-cost modular
combustors. These modules can be combined in varying configurations depending on the
application.



Aerospike Flowfield:
The exact nature of the exhaust flowfield behind an aerospike nozzle is currently the subject of
much research. The most notable features of a typical aerospike nozzle flowfield are shown in
more detail below.

Flowfield characteristics of an aerospike nozzle [from Ruf and McConnaughey, 1997]
The primary exhaust can be seen expanding against the centerbody and then around the corner of
the base region. The interaction of this flow with the re-circulating base bleed creates an inner
shear layer. The outer boundary of the exhaust plume is free to expand to ambient pressure.
Expansion waves can be seen emanating from the thruster exit lip, and these waves reflect from
the centerbody contour to the free jet boundary. Compression waves are then reflected back and
may merge to form the envelope shock seen in the primary exhaust.
At low altitude (high ambient pressure), the free boundary remains close to the nozzle (see
below) causing the compression waves to reflect onto the centerbody and shear layer themselves.
The waves impacting the centerbody increase pressure on the surface, thereby increasing the
centerbody component of thrust. The waves impacting the shear layer, on the other hand,
increase the circulation of the base flow thereby increasing the base component of thrust.



Aerospike nozzle behavior during flight [from Rocketdyne, 1999]
•

Thrust vectoring: Because the combustion chambers can be controlled individually, the
vehicle can be maneuvered using differential thrust vectoring. This eliminates the need
for the heavy gimbals and actuators used to vary the direction of traditional nozzles.

Aerospike thrust vectoring control [from Rocketdyne, 1999]

Additional Reading
1.

Sutton, G.P., “Rocket Propulsion Elements”, John Wiley & Sons Inc., New York, 7th
Edn., 2001.



Unit-4
CHEMICAL ROCKETS
Solid propellant rockets – Selection criteria of solid propellants – Important hardware
components of solid rockets – Propellant grain design considerations – Liquid propellant rockets
– Selection of liquid propellants – Thrust control in liquid rockets – Cooling in liquid rockets –
Limitations of hybrid rockets – Relative advantages of liquid rockets over solid rocketsNumerical Problems.

Introduction to Propulsion
Definitions and Basic Relations
•

Fluid dynamics of compressible flows is generally referred to as Gas dynamics. This deals with an
unified analysis of dynamics and thermodynamics of compressible flows.

•

Convectional fluid mechanics analyses are inadequate for high speed flows of gases and vapours
due to non-compressibility approach.

•

Therefore in the application like high speed aerodynamics, rocket and missile propulsion, steam
and gas turbines, and high speed turbocompressors compressible fluid dynamics is used to
obtain solutions of a number of design problems.

•

The properties of fluid which are generally considered in compressible flow problems are
temperature, pressure, density, internal energy, enthalpy, entropy and viscosity.

•

A major portion covered by the fluid dynamics of compressible flows deals with the relation
between force, mass and velocity.

•

The following laws are frequently used in dealing with a variety of compressible flow problems:

•
•
•
•
•
•
•
•

(i) First law of thermodynamics
(Energy equation).
(ii) Second law of thermodynamics
(Entropy relation)
(iii) Law of conservation of mass
(Continuity equation)
(iv) Newton’s second law of motion
(Momentum equation)



Goal: Create a Force to Propel a Vehicle
Two options:
Take mass stored in a vehicle and throw it
reaction force to propel the vehicle.

1)

Propellant --->

burn --->

backwards (rocket propulsion). Use the

expand through nozzle

(chem. energy) (thermal energy) (kinetic energy & momentum)

2) Seize mass from the surroundings and set the mass in motion backwards. Use the reaction
force to propel vehicle (air-breathing propulsion).
•

Continuously:
a) Draw in air.
b) Compress it.
c) Add fuel and burn (convert chemical energy to thermal energy).
d) Expand through a turbine to drive compressor (extract work).

e.1)
Then expand in a nozzle to convert thermal energy to kinetic
& momentum (turbojet).

energy

e.2)
Or expand in a second turbine (extract work), use this to drive a
shaft for a fan (turbofan), or a propeller (turboshaft). The fan or
propeller
impart k.e. & mom. to the air.
*Remember:
•

Overall goal: take at Vo (flight speed), throw it out at Vo + DV



•

Flying model rockets is a relatively safe and inexpensive way for students to learn the basics of
forces and the response of a vehicle to external forces. Like an airplane, a model rocket is
subjected to the forces of weight, thrust, and aerodynamics during its flight.

•

On this slide we show the parts of a single stage model rocket. We have laid the rocket on its
side and cut a hole in the body tube so that we can see what is inside. Beginning at the far right,
the body of the rocket is a green cardboard tube with black fins attached at the rear. The fins
can be made of either plastic or balsa wood and are used to provide stability during flight.
Model rockets use small, pre-packaged, solid fuel engines The engine is used only once, and
then is replaced with a new engine for the next flight. Engines come in a variety of sizes and can
be purchased at hobby stores and at some toy stores.



We live in a world that is defined by three spatial dimensions and one time dimension. Objects move
within this domain in two ways. An object translates, or changes location, from one point to another.
And an object rotates, or changes its attitude. In general, the motion of any object involves both
translation and rotation. The translations are in direct response to external forces. The rotations are in
direct response to external torques or moments (twisting forces).
•

The motion of a rocket is particularly complex because the rotations and translations are
coupled together; a rotation affects the magnitude and direction of the forces which affect
translations.

•

To understand and describe the motion of a rocket, we usually try to break down the complex
problem into a series of easier problems.

•

We can, for instance, assume that the rocket translates from one point to another as if all the
mass of the rocket were collected into a single point called the center of gravity.

•

We can describe the motion of the center of gravity by using Newton's laws of motion.

•

In general, there are four forces acting on the rocket; the weight, thrust, drag and lift.



•

The thrust of the engine is transmitted to the body of the rocket through the engine mount.

•

This part is fixed to the rocket and can be made of heavy cardboard or wood.

•

There is a hole through the engine mount to allow the ejection charge of the engine to
pressurize the body tube at the end of the coasting phase and eject the nose cone and the
recovery system.

•

Recovery wadding is inserted between the engine mount and the recovery system to prevent
the hot gas of the ejection charge from damaging the recovery system.

•

The recovery wadding is sold with the engine.

•

The recovery system consists of a parachute (or a streamer) and some lines to connect the
parachute to the nose cone.

•

Parachutes and streamers are made of thin sheets of plastic.

•

The nose cone can be made of balsa wood, or plastic, and may be either solid or hollow. The
nose cone is inserted into the body tube before flight.



•

An elastic shock cord is connected to both the body tube and the nose cone and is used to keep
all the parts of the rocket together during recovery.

•

The launch lugs are small tubes (straws) which are attached to the body tube.

•

The launch rail is inserted through these tubes to provide stability to the rocket during launch.



Temperature Variation in the Atmosphere



SOLID ROCKETS
Specific Impulse: 100-400 sec
Thrust: 103-107 N
•
•
•
•

Solid rockets are the simplest and earliest types of rocket propulsion dating back to the
first rockets used by the Chinese.
Solid rockets are filled with a solid mixture of a propellant and an oxidizer. Little else is
actually required for these rockets.
The designs are very simple and therefore very reliable.
The main drawback of solid rockets is that once ignited, they burn until all of the fuel is
gone. Because of this, they aren't used often in space where propulsion systems are
usually required to be turned on and off many times. However, they are good for getting
things into space. In fact, the space shuttles use solid rocket boosters (SRBs) during
takeoff.

•
Quick Fact : The SRBs are the largest solid-propellant motors ever flown and the first
designed for reuse. Each is 149.16 feet long and 12.17 feet in diameter.

MONOPROPELLANT ROCKETS

•

Thrust: 0.1-100 N
Monopropellant rockets are simple propulsion systems that rely on special chemicals
which, when energized, decompose. This decomposition creates both the fuel and an
oxidizer (which allows the fuel to burn), which then react with each other. Because they
only use a single propellant, monopropellant rockets are quite simple and reliable.
Unfortunately, they are not very efficient. They are mainly used to make small
adjustments such as attitude control. Main propulsion systems usually use some other
technology.

BIPROPELLANT ROCKETS
Thrust: 0.1-107 N
•

Bipropellant rockets separate the fuel and oxidizer and mix them in the chamber where
they burn. Bipropellant rockets are widely used and more efficient than monopropellant
rockets. The reaction given in the lesson on chemistry gives an example of a
fuel(H2)/oxidizer(O2) combination. It's actually a very good combination in that it
releases a large amount of energy. It's the combination used by the space shuttle's main
engines. Unfortunately, large tanks kept at extremely low temperatures are required to



carry them. In fact, the main purpose of the giant red external tank attached to the space
shuttle on take-off is to carry enough fuel to get the space shuttle into space.
The main drawback of bipropellant rockets is that they are more complex than solid or
monopropellant rockets. The fuel and oxidizer have to be stored separately and fed together in
exactly the right ratios to achieve maximum efficiency. Despite the extra complexity,
bipropellant rockets are still one of the preferred systems for primary propulsion

ROCKET PROPULSION
Isaac Newton stated in his third law of motion that "for every action there is an equal and
opposite reaction." It is upon this principle that a rocket operates. Propellants are combined
in a combustion chamber where they chemically react to form hot gases which are then
accelerated and ejected at high velocity through a nozzle, thereby imparting momentum to
the engine. The thrust force of a rocket motor is the reaction experienced by the motor
structure due to ejection of the high velocity matter. This is the same phenomenon which
pushes a garden hose backward as water flows from the nozzle, or makes a gun recoil when
fired.

Thrust
Thrust is the force that propels a rocket or spacecraft
and is measured in pounds, kilograms or Newtons.
Physically speaking, it is the result of pressure which
is exerted on the wall of the combustion chamber.
The figure to the right shows a combustion chamber
with an opening, the nozzle, through which gas can
escape. The pressure distribution within the chamber
is asymmetric; that is, inside the chamber the
pressure varies little, but near the nozzle it decreases
somewhat. The force due to gas pressure on the
bottom of the chamber is not compensated for from
the outside. The resultant force F due to the internal
and external pressure difference, the thrust, is
opposite to the direction of the gas jet. It pushes the
chamber upwards.
To create high speed exhaust gases, the necessary
high temperatures and pressures of combustion are
obtained by using a very energetic fuel and by having
the molecular weight of the exhaust gases as low as
possible. It is also necessary to reduce the pressure
of the gas as much as possible inside the nozzle by
creating a large section ratio. The section ratio, or expansion ratio, is defined as the area of
the exit Ae divided by the area of the throat At.



The thrust F is the resultant of the forces due to the pressures exerted on the inner and
outer walls by the combustion gases and the surrounding atmosphere, taking the boundary
between the inner and outer surfaces as the cross section of the exit of the nozzle. As we
shall see in the next section, applying the principle of the conservation of momentum gives

where q is the rate of the ejected mass flow, Pa the pressure of the ambient atmosphere, Pe
the pressure of the exhaust gases and Ve their ejection speed. Thrust is specified either at
sea level or in a vacuum.

Conservation of Momentum
The linear momentum (p), or simply momentum, of a particle is the product of its mass and
its velocity. That is,

Newton expressed his second law of motion in terms of momentum, which can be stated as
"the resultant of the forces acting on a particle is equal to the rate of change of the linear
momentum of the particle". In symbolic form this becomes

which is equivalent to the expression F=ma.
If we have a system of particles, the total momentum P of the system is the sum of the
momenta of the individual particles. When the resultant external force acting on a system is
zero, the total linear momentum of the system remains constant. This is called the principle
of conservation of linear momentum. Let's now see how this principle is applied to rocket
mechanics.
Consider a rocket drifting in gravity free space. The rocket's engine is fired for time t and,
during this period, ejects gases at a constant rate and at a constant speed relative to the
rocket (exhaust velocity). Assume there are no external forces, such as gravity or air
resistance.
The figure below-left (a) shows the situation at time t. The rocket and fuel have a total
mass M and the combination is moving with velocity v as seen from a particular frame of
reference. At a time t later the configuration has changed to that shown below-right (b). A
mass M has been ejected from the rocket and is moving with velocity u as seen by the
observer. The rocket is reduced to mass M- M and the velocity v of the rocket is changed to
v+ v.



Because there are no external forces, dP/dt=0. We can write, for the time interval

t

where P2 is the final system momentum, figure (b), and P1 is the initial system momentum,
figure (a). We write

If we let t approach zero, v/ t approaches dv/dt, the acceleration of the body. The
quantity M is the mass ejected in t; this leads to a decrease in the mass M of the original
body. Since dM/dt, the change in mass of the body with time, is negative in this case, in the
limit the quantity M/ t is replaced by -dM/dt. The quantity u-(v+ v) is Vrel, the relative
velocity of the ejected mass with respect to the rocket. With these changes, equation (1.4)
can be written as

The right-hand term depends on the characteristics of the rocket and, like the left-hand
term, has the dimensions of a force. This force is called the thrust, and is the reaction force
exerted on the rocket by the mass that leaves it. The rocket designer can make the thrust
as large as possible by designing the rocket to eject mass as rapidly as possible (dM/dt
large) and with the highest possible relative speed (Vrel large).
In rocketry, the basic thrust equation is written as

where q is the rate of the ejected mass flow, Ve is the exhaust gas ejection speed, Pe is the
pressure of the exhaust gases at the nozzle exit, Pa is the pressure of the ambient
atmosphere, and Ae is the area of the nozzle exit. The product qVe, which we derived above
(Vrel x dM/dt), is called the momentum, or velocity, thrust. The product (Pe-Pa)Ae, called
the pressure thrust, is the result of unbalanced pressure forces at the nozzle exit. As we
shall see latter, maximum thrust occurs when Pe=Pa.



PROBLEM 1.1
A spacecraft's engine ejects mass at a rate of 30 kg/s with an exhaust
velocity of
3,100 m/s. The pressure at the nozzle exit is 5 kPa and the exit area is 0.7
m2.
What is the thrust of the engine in a vacuum?

SOLUTION,
Given:

q = 30 kg/s
Ve = 3,100 m/s
Ae = 0.7 m2
Pe = 5 kPa = 5,000 N/m2
Pa = 0

Equation (1.6),
F = q x Ve + (Pe - Pa) x Ae
F = 30 x 3,100 + (5,000 - 0) x 0.7
F = 96,500 N

Equation (1.6) may be simplified by the definition of an effective exhaust gas velocity, C,
defined as

Equation (1.6) then reduces to

Impulse & Momentum
In the preceding section we saw that Newton's second law may be expressed in the form

Multiplying both sides by dt and integrating from a time t1 to a time t2, we write



The integral is a vector known as the linear impulse, or simply the impulse, of the force F
during the time interval considered. The equation expresses that, when a particle is acted
upon by a force F during a given time interval, the final momentum p2 of the particle may
be obtained by adding its initial momentum p1 and the impulse of the force F during the
interval of time.
When several forces act on a particle, the impulse of each of the forces must be considered.
When a problem involves a system of particles, we may add vectorially the momenta of all
the particles and the impulses of all the forces involved. When can then write

For a time interval

t, we may write equation (1.10) in the form

Let us now see how we can apply the principle of impulse and momentum to rocket
mechanics.
Consider a rocket of initial mass M which it launched vertically at time t=0. The fuel is
consumed at a constant rate q and is expelled at a constant speed Ve relative to the rocket.
At time t, the mass of the rocket shell and remaining fuel is M-qt, and the velocity is v.
During the time interval t, a mass of fuel q t is expelled. Denoting by u the absolute
velocity of the expelled fuel, we apply the principle of impulse and momentum between time
t and time t+ t. Please note, this derivation neglects the effect of air resistance.

We write

We divide through by t and replace u-(v+ v) with Ve, the velocity of the expelled mass
relative to the rocket. As t approaches zero, we obtain

Separating variables and integrating from t=0, v=0 to t=t, v=v, we obtain



which equals

The term -gt in equation (1.15) is the result of Earth's gravity pulling on the rocket. For a
rocket drifting in space, -gt is not applicable and can be omitted. Furthermore, it is more
appropriate to express the resulting velocity as a change in velocity, or V. Equation (1.15)
thus becomes

PROBLEM 1.2
The spacecraft in problem 1.1 has an initial mass of 30,000 kg.
change
in velocity if the spacecraft burns its engine for one minute?

What is the

SOLUTION,
Given:

M = 30,000 kg
q = 30 kg/s
Ve = 3,100 m/s
t = 60 s

Equation (1.16),
V = Ve x LN[ M / (M - qt) ]
V = 3,100 x LN[ 30,000 / (30,000 - (30 x 60)) ]
V = 192 m/s

Note that M represents the initial mass of the rocket and M-qt the final mass. Therefore,
equation (1.16) is often written as

where mo/mf is called the mass ratio. Equation (1.17) is also known as Tsiolkovsky's rocket
equation, named after Russian rocket pioneer Konstantin E. Tsiolkovsky (1857-1935) who
first derived it.
In practical application, the variable Ve is usually replaced by the effective exhaust gas
velocity, C. Equation (1.17) therefore becomes



Alternatively, we can write

where e is a mathematical constant approximately equal to 2.71828.

PROBLEM 1.3
A spacecraft's dry mass is 75,000 kg and the effective exhaust gas velocity
of its
main engine is 3,100 m/s. How much propellant must be carried if the
propulsion system
is to produce a total v of 700 m/s?

SOLUTION,
Given:

Mf = 75,000 kg
C = 3,100 m/s
V = 700 m/s

Equation (1.20),
Mo = Mf x e^( V / C)
Mo = 75,000 x e^(700 / 3,100)
Mo = 94,000 kg
Propellant mass,
Mp = Mo - Mf
Mp = 94,000 - 75,000
Mp = 19,000 kg
For many spacecraft maneuvers it is necessary to calculate the duration of an engine burn
required to achieve a specific change in velocity. Rearranging variables, we have


PROBLEM 1.4
A 5,000 kg spacecraft is in Earth orbit traveling at a velocity of 7,790 m/s.
Its engine is burned to accelerate it to a velocity of 12,000 m/s placing it
on an escape trajectory. The engine expels mass at a rate of 10 kg/s and an
effective velocity of 3,000 m/s. Calculate the duration of the burn.

SOLUTION,
Given:

M = 5,000 kg
q = 10 kg/s
C = 3,000 m/s
V = 12,000 - 7,790 = 4,210 m/s

Equation (1.21),
t = M / q x [ 1 - 1 / e^( V / C) ]
t = 5,000 / 10 x [ 1 - 1 / e^(4,210 / 3,000) ]
t = 377 s

Combustion & Exhaust Velocity
The combustion process involves the oxidation of co

The optimum mixture ratio is typically that which will deliver the highest engine
performance (measured by specific impulse), however in some situations a different O/F
ratio results in a better overall system. For a volume-constrained vehicle with a low-density
fuel such as liquid hydrogen, significant reductions in vehicle size can be achieved by
shifting to a higher O/F ratio. In that case, the losses in performance are more than
compensated for by the reduced fuel tankage requirement. Also consider the example of
bipropellant systems using NTO/MMH, where a mixture ratio of 1.67 results in fuel and
oxidizer tanks of equal size. Equal sizing simplifies tank manufacturing, system packaging,
and integration.
As we have seen previously, impulse thrust is equal to the product of the propellant mass
flow rate and the exhaust gas ejection speed. The ideal exhaust velocity is given by

where k is the specific heat ratio, R' is the universal gas constant (8,314.51 N-m/kg mol-K
in SI units, or 49,720 ft-lb/slug mol-oR in U.S. units), Tc is the combustion temperature, M
is the average molecular weight of the exhaust gases, Pc is the combustion chamber
pressure, and Pe is the pressure at the nozzle exit.
Specific heat ratio(2) varies depending on the composition and temperature of the exhaust
gases, but it is usually about 1.2. The thermodynamics involved in calculating combustion
temperatures are quite complicated, however, flame temperatures generally range from
about 2,500 to 3,600 oC (4,500-6,500 oF). Chamber pressures can range from about about
7 to 250 atmospheres. Pe should be equal to the ambient pressure at which the engine will
operate, more on this later. See below the charts providing optimum mixture ratio,
adiabatic flame temperature, gas molecular weight, and specific heat ratio for some
common rocket propellants.
From equation (1.22) we see that high chamber temperature and pressure, and low exhaust
gas molecular weight results in high ejection velocity, thus high thrust. Based on this
criterion, we can see why liquid hydrogen is very desirable as a rocket fuel.

Liquid Oxygen & Liquid Hydrogen
Optimum Mixture Ratio
Unlike other propellants, the optimum mixture ratio for liquid oxygen and liquid hydrogen is
not necessarily that which will produce the maximum specific impulse. Because of the
extremely low density of liquid hydrogen, the propellant volume decreases significantly at
higher mixture ratios. Maximum specific impulse typically occurs at a mixture ratio of
around 3.5, however by increasing the mixture ratio



Adiabatic Flame Temperature



Gas Molecular Weight

Specific Heat Ratio



•

Molecular weight equals the sum of the atomic weights of
the atoms in the molecule. For NaCl, the atomic weight of
sodium is 23, of chlorine is 35 and a molecule contains one
sodium and one chlorine, so 23 + 35 = 58, the molecular
weight of NaCl. The formula for glucose ( a very common
sugar) is C6H12O6. The subscripts to the right mean that it
contains 6 atoms of carbon, 12 atoms of hydrogen, and
6 atoms of oxygen. The atomic weight for carbon is 12, for
hydrogen is 1, and for oxygen is 16, so the molecular
weight of glucose can be calculated thus:
---------------------------------------------------------Element
Atomic
Weight
No. of Atoms
Total Weight
----------------------------------------------------------C
12
6
6 × 12 = 72
H
1
12
12 × 1 = 12
O
16
6
6 × 16 = 96

--------------------------------------------------------------Total Molecular Weight
= 180

PROPELLANT COMBUSTION CHARTS
How To Use These Charts
For each of the propellant combinations shown above, four graphs have been provided.
These graphs can be used to estimate (1) the optimum mixture ratio of the combustion
reactants, (2) the adiabatic flame temperature of the combustion reaction, (3) the average
molecular weight of the combustion products, and (4) the specific heat ratio of the
combustion products. This data is necessary to determine the velocity of the exhaust gases
expelled from a rocket engine, which in turn determines the engine's thrust. Adiabatic flame
temperature and gas molecular weight have been calculated using the freeware program
STANJAN.



Mixture Ratio is the ratio of oxidizer mass t
o fuel mass. We define the optimum mixture ratio as that which will produce the highest
specific impulse for the given reactants. A propellant's optimum mixture ratio is a function
of the pressures at which the rocket engine will operate. An engine with a high combustion
chamber pressure and a low nozzle exit pressure, i.e. a large section ratio, will have the
highest optimum mixture ratio.
Below we see a graph of optimum mixture ratio versus combustion chamber pressure for
liquid oxygen and kerosene at two different nozzle exit pressures (Pe). To use this graph,
select the desired chamber pressure across the bottom axis of the graph and draw a vertical
line. When the vertical line intersects the curve for the desired exit pressure, draw a
horizontal line to the left and read the corresponding mixture ratio off the vertical axis of
the graph. If an exit pressure other than those shown is desired, estimate the position of
the exit pressure curve by interpolating between those given. For instance, the curve for a
Pe of 0.7 atmosphere lies approximately one-third the distance from the Pe = 1.0 curve to
the Pe = 0.1 curve. In the given example we've selected a combustion chamber pressure of
75 atmospheres and a nozzle exit pressure of 1 atmosphere, which gives us an optimum
mixture ratio of 2.30.



Gas Molecular Weight
The exhaust gas molecular weight is the average molar weight of the combustion products,
that is, the mass of the exhaust gas divided by the number of moles.
Below is a graph of gas molecular weight versus combustion chamber pressure for liquid
oxygen and kerosene at three different mixture ratios. To use this graph, select the desired
pressure across the bottom axis of the graph and draw a vertical line. When the vertical line
intersects the curve for the desired mixture ratio, draw a horizontal line to the left and read
the corresponding gas molecular weight off the vertical axis of the graph. For mixture ratios
other than those shown, estimate by interpolating between the given curves. In the
provided example we've selected a pressure of 75 atmospheres and a mixture ratio of 2.30,
which gives us an average gas molecular weight of about 21.65.
The gas molecular weights shown below are taken at the combustion chamber. The
molecular weight will increase slightly as the gas expands and cools while moving toward
the nozzle exit.



Liquid Oxygen & Liquid Methane




Liquid Oxygen & Kerosene*
* n-Dodecane, C12H26




PROBLEM 1.5
A rocket engine burning liquid oxygen and kerosene operates at a mixture
ratio of 2.26 and a combustion chamber pressure of 50 atmospheres. If the


where F is thrust, q is the rate of mass flow, and g is the acceleration of gravity at ground
level.
Specific impulse is expressed in seconds. When the thrust and the flow rate remain constant
throughout the burning of the propellant, the specific impulse is the time for which the
rocket engine provides a thrust equal to the weight of the propellant consumed.
For a given engine, the specific impulse has different values on the ground and in the
vacuum of space because the ambient pressure is involved in the expression for the thrust.
It is therefore important to state whether specific impulse is the value at sea level or in a
vacuum.
There are a number of losses within a rocket engine, the main ones being related to the
inefficiency of the chemical reaction (combustion) process, losses due to the nozzle, and
losses due to the pumps. Overall, the losses affect the efficiency of the specific impulse.
This is the ratio of the real specific impulse (at sea level, or in a vacuum) and the theoretical
specific impulse obtained with an ideal nozzle from gases coming from a complete chemical
reaction. Calculated values of specific impulse are several percent higher than those
attained in practice.

PROBLEM 1.6
A rocket engine produces a thrust of 1,000 kN at sea level with a propellant
flow
rate of 400 kg/s. Calculate the specific impulse.

SOLUTION,
Given:

F = 1,000,000 N
q = 400 kg/s

Equation (1.23),
Isp = F / (q x g)
Isp = 1,000,000 / (400 x 9.80665)
Isp = 255 s (sea level)

From Equation (1.8) we can substitute qC for F in Equation (1.23), thus obtaining

Equation (1.24) is very useful when solving Equations (1.18) through (1.21). It is rare we
are given the value of C directly, however rocket engine specific impulse is a commonly
given parameter from which we can easily calculate C.


Engines & Nozzles
A typical rocket motor consists of the combustion chamber, the nozzle, and the injector, as
shown in the figure below. The combustion chamber is where the burning of propellants
takes place at high pressure. The chamber must be strong enough to contain the high
pressure generated by, and the high temperature resulting from, the combustion process.
Because of the high temperature and heat transfer, the chamber and nozzle are usually
cooled. The chamber must also be of sufficient length to ensure complete combustion before
the gases enter the nozzle.


The figure above-right shows three different exhaust nozzles. The most efficient nozzle (1)
is contoured to the exhaust stream, allowing the escaping gas to expand just enough to fill
the nozzle. A nozzle that lets the gas expand too much (2), or too little (3), wastes the
energy and thrust potential of the exhaust system.
The nozzle throat area, At, can be found if the total propellant flow rate is known and the
propellants and operating conditions have been selected. Assuming perfect gas law theory,
we have

where q is the propellant mass flow rate, Pt is the gas pressure at the nozzle throat, Tt is
the gas temperature at the nozzle throat, R' is the universal gas constant, and k is the
specific heat ratio. Pt and Tt are given by

where Pc is the combustion chamber pressure and Tc is the combustion chamber flame
temperature.

PROBLEM 1.7
A rocket engine uses the same propellant, mixture ratio, and combustion
chamber
pressure as that in problem 1.5. If the propellant flow rate is 500 kg/s,
calculate
the area of the exhaust nozzle throat.

SOLUTION,
Given:

Pc = 50 x 0.101325 = 5.066 MPa
Tc = 3,470<SUP.O< sup> K
M = 21.40
k = 1.221
q = 500 kg/s

Equation (1.26),
Pt = Pc x [1 + (k - 1) / 2]-k/(k-1)
Pt = 5.066 x [1 + (1.221 - 1) / 2]-1.221/(1.221-1)
Pt = 2.839 MPa = 2.839x106 N/m2


Equation (1.27),
Tt = Tc / (1 + (k - 1) / 2)
Tt = 3,470 / (1 + (1.221 - 1) / 2)
Tt = 3,125 K
Equation (1.25),
At = (q / Pt) x SQRT[ (R' x Tt) / (M x k) ]
At = (500 / 2.839x106) x SQRT[ (8,314.51 x 3,125) / (21.40 x 1.221) ]
At = 0.1756 m2
The hot gases must be expanded in the diverging section of the nozzle to obtain maximum
thrust. The pressure of these gases will decrease as energy is used to accelerate the gas.
We must find that area of the nozzle where the gas pressure is equal to the outside
atmospheric pressure. This area will then be the nozzle exit area.
Mach number Nm is the ratio of the gas velocity to the local speed of sound. The Mach
number at the nozzle exit is given by the perfect gas expansion expression


Equation (1.28),
Nm2 = (2 / (k - 1)) x [(Pc / Pa)(k-1)/k - 1]
Nm2 = (2 / (1.221 - 1)) x [(5.066 / 0.0795)(1.221-1)/1.221 - 1]
Nm2 = 10.15
Nm = (10.15)1/2 = 3.185
Equation (1.29),
Ae = (At / Nm) x [(1 + (k - 1) / 2 x Nm2)/((k + 1) / 2)](k+1)/(2(k-1))
Ae = (0.1756 / 3.185) x [(1 + (1.221 - 1) / 2 x 10.15)/((1.221 + 1) /
2)](1.221+1)/(2(1.221-1))
Ae = 1.426 m2
Section Ratio,
Ae / At = 1.426 / 0.1756 = 8.12

For launch vehicles (particularly first stages) where the ambient pressure varies during the
burn period, trajectory computations are performed to determine the optimum exit
pressure. However, an additional constraint is the maximum allowable diameter for the
nozzle exit cone, which in some cases is the limiting constraint. This is especially true on
stages other than the first, where the nozzle diameter may not be larger than the outer
diameter of the stage below. For space engines, where the ambient pressure is zero, thrust
always increases as nozzle expansion ratio increases. On these engines, the nozzle
expansion ratio is generally increased until the additional weight of the longer nozzle costs
more performance than the extra thrust it generates.

Rocket Nozzle Design:
Optimizing Expansion for Maximum Thrust
A rocket engine is a device in which propellants are burned in a combustion chamber and
the resulting high pressure gases are expanded through a specially shaped nozzle to
produce thrust. The function of the nozzle is to convert the chemical-thermal energy
generated in the combustion chamber into kinetic energy. The nozzle converts the slow
moving, high pressure, high temperature gas in the combustion chamber into high velocity
gas of lower pressure and temperature. Gas velocities from 2 to 4.5 kilometers per second
can be obtained in rocket nozzles. The nozzles which perform this feat are called DeLaval
nozzles (after the inventor) and consist of a convergent and divergent section. The
minimum flow area between the convergent and divergent section is called the nozzle
throat. The flow area at the end of the divergent section is called the nozzle exit area.
Hot exhaust gases expand in the diverging section of the nozzle. The pressure of these
gases will decrease as energy is used to accelerate the gas to high velocity. The nozzle is
usually made long enough (or the exit area great enough) such that the pressure in the
combustion chamber is reduced at the nozzle exit to the pressure existing outside the
nozzle. It is under this condition that thrust is maximum and the nozzle is said to be
adapted, also called optimum or correct expansion. To understand this we must examine
the basic thrust equation:


where F = Thrust
q = Propellant mass flow rate
Ve = Velocity of exhaust gases
Pe = Pressure at nozzle exit
Pa = Ambient pressure
Ae = Area of nozzle exit
The product qVe is called the momentum, or velocity, thrust and the product (Pe-Pa)Ae is
called the pressure thrust. As we have seen, Ve and Pe are inversely proportional, that is,
as one increases the other decreases. If a nozzle is under-extended we have Pe>Pa and Ve
is small. For an over-extended nozzle we have Pe<Pa and Ve is large. Thus, momentum
thrust and pressure thrust are inversely proportional and, as we shall see, maximum thrust
occurs when Pe=Pa.
Let us now consider an example. Assume we have a rocket engine equipped with an
extendible nozzle. The engine is test fired in an environment with a constant ambient
pressure. During the burn, the nozzle is extended from its fully retracted position to its fully
extended position. At some point between fully retracted and fully extended Pe=Pa (see
figure below).


The gas pressure and temperature at the nozzle throat is less than in the combustion
chamber due to the loss of thermal energy in accelerating the gas to the local speed of
sound at the throat. Therefore, we calculate the pressure and temperature at the nozzle
throat,
-k/(k-1)

Pt = Pc x [1 + (k - 1) / 2] -1.20/(1.20-1)
Pt = 5 x [1 + (1.20 - 1) / 2]
6
2
Pt = 2.82 MPa = 2.82x10 N/m
Tt = Tc x [1 / (1 + (k - 1) / 2)]
Tt = 3,600 x [1 / (1 + (1.20 - 1) / 2)]
Tt = 3,273 K
The area at the nozzle throat is given by
At = (q / Pt) x SQRT[ (R' x Tt) / (M x k) ]
6
At = (100 / 2.82x10 ) x SQRT[ (8,314 x 3,273) / (24 x 1.20) ]
2
At = 0.0345 m
The hot gases must now be expanded in the diverging section of the nozzle to obtain
maximum thrust. The Mach number at the nozzle exit is given by
2

Nm2 =
Nm2 =
Nm =
Nm =

(k-1)/k

(2 / (k - 1)) x [(Pc / Pa)
- 1]
(1.20-1)/1.20
(2 / (1.20 - 1)) x [(5 / 0.05)
- 1]
11.54
1/2
= 3.40
(11.54)

The nozzle exit area corresponding to the exit Mach number is given by
2

2)]

(k+1)/(2(k-1))

Ae = (At / Nm) x [(1 + (k - 1) / 2 x Nm )/((k + 1) / 2)]
Ae = (0.0345 / 3.40) x [(1 + (1.20 - 1) / 2 x 11.54)/((1.20 + 1) /
(1.20+1)/(2(1.20-1))
Ae = 0.409 m

2

The velocity of the exhaust gases at the nozzle exit is given by
(k-1)/k

) ]
Ve = SQRT[ (2 x k / (k - 1)) x (R' x Tc / M) x (1 - (Pe / Pc)
Ve = SQRT[ (2 x 1.20 / (1.20 - 1)) x (8,314 x 3,600 / 24) x (1 - (0.05 /
(1.20-1)/1.20
5)
) ]
Ve = 2,832 m/s
Finally, we calculate the thrust,
6
6
F = 100 x 2,832 + (0.05x10 - 0.05x10 ) x 0.409
F = 283,200 N

Let's now consider what happens when the nozzle is under-extended, that is Pe>Pa. If we
assume Pe=Pa x 2, we have
Pe = 0.05 x 2 = 0.10 MPa
At = 0.0345 m
2

2

Nm = (2 / (1.20 - 1)) x [(5 / 0.10)

(1.20-1)/1.20

- 1]



As can be easily seen, thrust is maximum when Pa/Pe=1, or when Pe=Pa.

Power Cycles
Liquid bipropellant rocket engines can be categorized according to their power cycles, that
is, how power is derived to feed propellants to the main combustion chamber. Described
below are some of the more common types.
Gas-generator cycle: The gas-generator cycle, also called open cycle, taps off a small
amount of fuel and oxidizer from the main flow (typically 3 to 7 percent) to feed a burner
called a gas generator. The hot gas from this generator passes through a turbine to
generate power for the pumps that send propellants to the combustion chamber. The hot
gas is then either dumped overboard or sent into the main nozzle downstream. Increasing
the flow of propellants into the gas generator increases the speed of the turbine, which
increases the flow of propellants into the main combustion chamber, and hence, the amount
of thrust produced. The gas generator must burn propellants at a less-than-optimal mixture
ratio to keep the temperature low for the turbine blades. Thus, the cycle is appropriate for
moderate power requirements but not high-power systems, which would have to divert a
large portion of the main flow to the less efficient gas-generator flow.
As in most rocket engines, some of the propellant in a gas generator cycle is used to cool
the nozzle and combustion chamber, increasing efficiency and allowing higher engine
temperature.


can achieve higher chamber pressures than the closed expander cycle although at lower
efficiency because of the overboard flow.

Regenerative cooling is the most widely used
method of cooling a thrust chamber and is
accomplished by flowing high-velocity coolant over
the back side of the chamber hot gas wall to
convectively cool the hot gas liner. The coolant
with the heat input from cooling the liner is then
discharged into the injector and utilized as a
propellant.
Earlier thrust chamber designs, such as the V-2
and Redstone, had low chamber pressure, low
heat flux and low coolant pressure requirements,
which could be satisfied by a simplified "double
wall chamber" design with regenerative and film
cooling.
For
subsequent
rocket
engine
applications, however, chamber pressures were
increased and the cooling requirements became
more difficult to satisfy. It became necessary to
design new coolant configurations that were more
efficient structurally and had improved heat
transfer characteristics.
This led to the design of "tubular wall" thrust chambers, by far the most widely used design
approach for the vast majority of large rocket engine applications. These chamber designs
have been successfully used for the Thor, Jupiter, Atlas, H-1, J-2, F-1, RS-27 and several
other Air Force and NASA rocket engine applications. The primary advantage of the design
is its light weight and the large experience base that has accrued. But as chamber pressures
and hot gas wall heat fluxes have continued to increase (>100 atm), still more effective
methods have been needed.
One solution has been "channel wall" thrust chambers, so named because the hot gas wall
cooling is accomplished by flowing coolant through rectangular channels, which are
machined or formed into a hot gas liner fabricated from a high-conductivity material, such
as copper or a copper alloy. A prime example of a channel wall combustion chamber is the
SSME, which operates at 204 atmospheres nominal chamber pressure at 3,600 K for a
duration of 520 seconds. Heat transfer and structural characteristics are excellent.
In addition to the regeneratively cooled designs mentioned above, other thrust chamber
designs have been fabricated for rocket engines using dump cooling, film cooling,
transpiration cooling, ablative liners and radiation cooling. Although regeneratively cooled
combustion chambers have proven to be the best approach for cooling large liquid rocket
engines, other methods of cooling have also been successfully used for cooling thrust
chamber assemblies. Examples include:
Dump cooling, which is similar to regenerative cooling because the coolant flows through
small passages over the back side of the thrust chamber wall. The difference, however, is
that after cooling the thrust chamber, the coolant is discharged overboard through openings
at the aft end of the divergent nozzle. This method has limited application because of the
performance loss resulting from dumping the coolant overboard. To date, dump cooling has
not been used in an actual application.


Film cooling provides protection from excessive heat by introducing a thin film of coolant
or propellant through orifices around the injector periphery or through manifolded orifices in
the chamber wall near the injector or chamber throat region. This method is typically used
in high heat flux regions and in combination with regenerative cooling.
Transpiration cooling provides coolant (either gaseous or liquid propellant) through a
porous chamber wall at a rate sufficient to maintain the chamber hot gas wall to the desired
temperature. The technique is really a special case of film cooling.
With ablative cooling, combustion gas-side wall material is sacrificed by melting,
vaporization and chemical changes to dissipate heat. As a result, relatively cool gases flow
over the wall surface, thus lowering the boundary-layer temperature and assisting the
cooling process.
With radiation cooling, heat is radiated from the outer surface of the combustion chamber
or nozzle extension wall. Radiation cooling is typically used for small thrust chambers with a
high-temperature wall material (refractory) and in low-heat flux regions, such as a nozzle
extension.

Solid Rocket Motors
Solid rockets motors store propellants in solid form. The fuel is typically powdered
aluminum and the oxidizer is ammonium perchlorate. A synthetic rubber binder such as
polybutadiene holds the fuel and oxidizer powders together. Though lower performing than
liquid propellant rockets, the operational simplicity of a solid rocket motor often makes it
the propulsion system of choice.
Solid Fuel Geometry
A solid fuel's geometry determines the area and contours of its exposed surfaces, and thus
its burn pattern. There are two main types of solid fuel blocks used in the space industry.
These are cylindrical blocks, with combustion at a front, or surface, and cylindrical blocks
with internal combustion. In the first case, the front of the flame travels in layers from the
nozzle end of the block towards the top of the casing. This so-called end burner produces
constant thrust throughout the burn. In the second, more usual case, the combustion
surface develops along the length of a central channel. Sometimes the channel has a star
shaped, or other, geometry to moderate the growth of this surface.

The shape of the fuel block for a rocket is chosen for the particular type of mission it will
perform. Since the combustion of the block progresses from its free surface, as this surface
grows, geometrical considerations determine whether the thrust increases, decreases or
stays constant.


Burn Rate
The burning surface of a rocket propellant grain recedes in a direction perpendicular to this
burning surface. The rate of regression, typically measured in millimeters per second (or
inches per second), is termed burn rate. This rate can differ significantly for different
propellants, or for one particular propellant, depending on various operating conditions as
well as formulation. Knowing quantitatively the burning rate of a propellant, and how it
changes under various conditions, is of fundamental importance in the successful design of
a solid rocket motor.
Propellant burning rate is influenced by certain factors, the most significant being:
combustion chamber pressure, initial temperature of the propellant grain, velocity of the
combustion gases flowing parallel to the burning surface, local static pressure, and motor
acceleration and spin. These factors are discussed below.
•

Burn rate is profoundly affected by chamber pressure. The usual representation of
the pressure dependence on burn rate is the Saint-R


a grain L/D ratio of 6. A greater Aport/At ratio should be used for grains with larger
L/D ratios.
•

•

In an operating rocket motor, there is a pressure drop along the axis of the
combustion chamber, a drop that is physically necessary to accelerate the increasing
mass flow of combustion products toward the nozzle. The static pressure is greatest
where gas flow is zero, that is, at the front of the motor. Since burn rate is
dependant upon the local pressure, the rate should be greatest at this location.
However, this effect is relatively minor and is usually offset by the counter-effect of
erosive burning.
Burning rate is enhanced by acceleration of the motor. Whether the acceleration is a
result of longitudinal force (e.g. thrust) or spin, burning surfaces that form an angle
of about 60-90o with the acceleration vector are prone to increased burn rate.

It is sometimes desirable to modify the burning rate such that it is more suitable to a
certain grain configuration. For example, if one wished to design an end burner grain, which
has a relatively small burning area, it is necessary to have a fast burning propellant. In
other circumstances, a reduced burning rate may be sought after. For example, a motor
may have a large L/D ratio to generate sufficiently high thrust, or it may be necessary for a
particular design to restrict the diameter of the motor. The web would be consequently thin,
resulting in short burn duration. Reducing the burning rate would be beneficial.
There are a number of ways of modifying the burning rate: decrease the oxidizer particle
size, increase or reduce the percentage of oxidizer, adding a burn rate catalyst or
suppressant, and operate the motor at a lower or higher chamber pressure. These factors
are discussed below.
•

•

•

•

The effect of the oxidizer particle size on burn rate seems to be influenced by the
type of oxidizer. Propellants that use ammonium perchlorate (AP) as the oxidizer
have a burn rate that is significantly affected by AP particle size. This most likely
results from the decomposition of AP being the rate-determining step in the
combustion process.
The burn rate of most propellants is strongly influenced by the oxidizer/fuel ratio.
Unfortunately, modifying the burn rate by this means is quite restrictive, as the
performance of the propellant, as well as mechanical properties, are also greatly
affected by the O/F ratio.
Certainly the best and most effective means of increasing the burn rate is the
addition of a catalyst to the propellant mixture. A catalyst is a chemical compound
that is added in small quantities for the sole purpose of tailoring the burning rate. A
burn rate suppressant is an additive that has the opposite effect to that of a catalyst
-- it is used to decrease the burn rate.
For a propellant that follows the Saint-Robert's burn rate law, designing a rocket
motor to operate at a lower chamber pressure will provide for a lower burning rate.
Due to the nonlinearity of the pressure-burn rate relationship, it may be necessary to
significantly reduce the operating pressure to get the desired burning rate. The
obvious drawback is reduced motor performance, as specific impulse similarly decays
with reducing chamber pressure.



Product Generation Rate
The rate at which combustion products are generated is expressed in terms of the
regression speed of the grain. The product generation rate integrated over the port surface
area is

where q is the combustion product generation rate at the propellant surface, p is the solid
propellant density, Ab is the area of the burning surface, and r is the propellant burn rate.
It is important to note that the combustion products may consist of both gaseous and
condensed-phase mass. The condensed-phase, which manifests itself as smoke, may be
either solid or liquid particles. Only the gaseous products contribute to pressure
development. The condensed-phase certainly does, however, contribute to the thrust of the
rocket motor, due to its mass and velocity.

PROBLEM 1.9
A solid rocket motor burns along the face of a central cylindrical channel 10
meters long and 1 meter in diameter. The propellant has a burn rate
coefficient of 5.5, a pressure exponent of 0.4, and a density of 1.77 g/ml.
Calculate the burn rate and the product generation rate when the chamber
pressure is 5.0 MPa.

SOLUTION,
Given:

a = 5.5
n = 0.4
Pc = 5.0 MPa
p = 1.77 g/ml
Ab =
x 1 x 10 = 31.416 m2

Equation (1.30),
r = a x Pcn
r = 5.5 x 5.00.4 = 10.47 mm/s
Equation (1.31),
q = p x Ab x r
q = 1.77 x 31.416 x 10.
3



with associated burn rate variation. Other factors may play a role, however, such as nozzle
throat erosion and erosive burn rate augmentation.

Monopropellant Engines
By far the most widely used type of propulsion for spacecraft attitude and velocity control is
monopropellant hydrazine. Its excellent handling characteristics, relative stability under
normal storage conditions, and clean decomposition products have made it the standard.
The general sequence of operations in a hydrazine thruster is:
•

•
•

•

•

When the attitude control system signals for thruster operation, an electric solenoid
valve opens allowing hydrazine to flow. The action may be pulsed (as short as 5 ms)
or long duration (steady state).
The pressure in the propellant tank forces liquid hydrazine into the injector. It enters
as a spray into the thrust chamber and contacts the catalyst beds.
The catalyst bed consists of alumina pellets impregnated with iridium. Incoming
hydrazine heats to its vaporizing point by contact with the catalyst bed and with the
hot gases leaving the catalyst particles. The temperature of the hydrazine rises to a
point where the rate of its decomposition becomes so high that the chemical
reactions are self-sustaining.
By controlling the flow variables and the geometry of the catalyst chamber, a
designer can tailor the proportion of chemical products, the exhaust temperature,
the molecular weight, and thus the enthalpy for a given application. For a thruster
application where specific impulse is paramount, the designer attempts to provide
30-40% ammonia dissociation, which is about the lowest percentage that can be
maintained reliably. For gas-generator application, where lower temperature gases
are usually desired, the designer provides for higher levels of ammonia dissociation.
Finally, in a space thruster, the hydrazine decomposition products leave the catalyst
bed and exit from the chamber through a high expansion ratio exhaust nozzle to
produce thrust.

Monopropellant hydrazine thrusters typically produce a specific impulse of about 230 to 240
seconds.
Other suitable propellants for catalytic decomposition engines are hydrogen peroxide and
nitrous oxide, however the performance is considerably lower than that obtained with
hydrazine - specific impulse of about 150 s with H2O2 and about 170 s with N2O.
Monopropellant systems have successfully provided orbit maintenance and attitude control
functions, but lack the performance to provide weight-efficient large V maneuvers required
for orbit insertion. Bipropellant systems are attractive because they can provide all three
functions with one higher performance system, but they are more complex than the
common solid rocket and monopropellant combined systems. A third alternative are dual
mode systems. These systems are hybrid designs that use hydrazine both as a fuel for high
performance bipropellant engines and as a monopropellant with conventional low-thrust
catalytic thrusters. The hydrazine is fed to both the bipropellant engines and the
monopropellant thrusters from a common fuel tank.
Cold gas propulsion is just a controlled, pressurized gas source and a nozzle. It represents
the simplest form of rocket engine. Cold gas has many applications where simplicity and/or


the need to avoid hot gases are more important than high performance. The Manned
Maneuvering Unit used by astronauts is an example of such a system.

Staging
Multistage rockets allow improved payload capability for vehicles with a high
V
requirement such as launch vehicles or interplanetary spacecraft. In a multistage rocket,
propellant is stored in smaller, separate tanks rather than a larger single tank as in a singlestage rocket. Since each tank is discarded when empty, energy is not expended to
accelerate the empty tanks, so a higher total V is obtained. Alternatively, a larger payload
mass can be accelerated to the same total V. For convenience, the separate tanks are
usually bundled with their own engines, with each discardable unit called a stage.
Multistage rocket performance is described by the same rocket equation as single-stage
rockets, but must be determined on a stage-by-stage basis. The velocity increment, Vi, for
each stage is calculated as before,

where moi represents the total vehicle mass when stage i is ignited, and mfi is the total
vehicle mass when stage i is burned out but not yet discarded. It is important to realize that
the payload mass for any stage consists of the mass of all subsequent stages plus the
ultimate payload itself. The velocity increment for the vehicle is then the sum of those for
the individual stages where n is the total number of stages.

PROBLEM 1.10
A two-stage rocket has the following masses: 1st-stage propellant mass
120,000 kg,
1st-stage dry mass 9,000 kg, 2nd-stage propellant mass 30,000 kg, 2nd-stage
dry mass
3,000 kg, and payload mass 3,000 kg. The specific impulses of the 1st and
2nd stages
are 260 s and 320 s respectively. Calculate the rocket's total V.

SOLUTION,
Given:

Mo1 = 120,000 + 9,000 + 30,000 + 3,000 + 3,000 = 165,000 kg
Mf1 = 9,000 + 30,000 + 3,000 + 3,000 = 45,000 kg
Isp1 = 260 s
Mo2 = 30,000 + 3,000 + 3,000 = 36,000 kg
Mf2 = 3,000 + 3,000 = 6,000 kg
Isp2 = 320 s


C1 = Isp1g
C1 = 260 x 9.80665 = 2,550 m/s
C2 = Isp2g
C2 = 320 x 9.80665 = 3,138 m/s
Equation (1.33),
V1 = C1 x LN[ Mo1 / Mf1 ]
V1 = 2,550 x LN[ 165,000 / 45,000 ]
V1 = 3,313 m/s
V2 = C2 x LN[ Mo2 / Mf2 ]
V2 = 3,138 x LN[ 36,000 / 6,000 ]
V2 = 5,623 m/s
Equation (1.34),
VTotal = V1 + V2
VTotal = 3,313 + 5,623
VTotal = 8,936 m/s

We define the payload fraction as the ratio of payload mass to initial mass, or mpl/mo.
For a multistage vehicle with dissimilar stages, the overall vehicle payload fraction depends
on how the V requirement is partitioned among stages. Payload fractions will be reduced if
the V is partitioned suboptimally. The optimal distribution may be determined by trial and
error. A V distribution is postulated and the resulting payload fraction calculated. The V
distribution is varied until the payload fraction is maximized. Once the V distribution is
selected, vehicle sizing is accomplished by starting with the uppermost or final stage (whose
payload is the actual deliverable payload) and calculating the initial mass of this assembly.
This assembly then forms the payload for the previous stage and the process repeats until
V
all stages are sized. Results reveal that to maximize payload fraction for a given
requirement:
1.
Stages
with
higher
Isp
should
be
above
stages
2.
More
V
should
be
provided
by
the
stages
with
3.
Each
succeeding
stage
should
be
smaller
than
4. Similar stages should provide the same V.


with
the
its

lower
Isp.
higher
Isp.
predecessor.


Solid Rocket Components
The key inert components of solid propellant rocket motors are the motor case, nozzle, and
igniter case. Thrust vector control (TVC) mechanism also a component of many rocket motors.
Motor Case:
The case not only contains the propellant grain, but also serves as a highly loaded pressure
vessel. Case design is usually governed by a combination of motor and vehicle requirements.
Besides constituting the structural body of the rocket motor with its nozzle, propellant grain, and
so on, the case frequently serves also as the primary structure of the missile or launch vehicle.
Different types of loads and their sources must be considered at the beginning of a case design.
In addition, the environmental conditions peculiar to a specific motor and its usage must be
carefully considered. Typically, these conditions include the following; (1) temperature (internal
heating, temperature cycling during storage, or thermal stress and strains); (2) corrosion
(moisture/chemical, galvanic, stress corrosion etc.); (3) space conditions: vacuum or radiation.
Three classes of materials have been used: high-strength metals (such as steel, aluminum, or
titanium alloys), wound-filament reinforced plastics, and a combination of these.
Rocket Motor Case Loads
(Ref: G.P.Sutton)
Origin of Load
Internal pressure
Axial thrust
Motor nozzle
Thrust vector control actuators
Thrust termination equipment
Aerodynamic control surface or wings
mounted to case
Staging
Flight maneuvering
Vehicle mass and wind forces on launch pad
Dynamic loads from vehicle oscillations
Ground transport, Ground handling, including
lifting
Earthquakes (large motors)

Type of Load/Stress
Tension biaxial, vibration
Axial, vibration
Axial, bending, shear
Biaxial, bending
Tension, compression, bending, shear, torsion
Bending, shear
Axial, bending, shear, torsion
Tension, compression, bending, shear, torsion,
vibration



Nozzles
Nozzles for solid propellant rockets can be classified into five categories.
1. Fixed nozzle; simple and used in small missiles
2. Movable nozzle : provide thrust vector control for the flight.
3. Submerged nozzle: it reduces the overall motor length by inserting the significant portion
of the nozzle structure into the combustion chamber.
4. Extendible nozzle: it improves specific impulse. Nozzle area ratio is enlarged by
mechanically adding a nozzle cone extension piece.
5. Blast-Tube-Mounted nozzle: Used in missiles. The blast tube allows the rocket motor’s
center of gravity (CG) to be close to or ahead of the vehicle CG. This limits the CG travel
during motor burn and makes flight stabilization much easier.
Design and Construction
Almost all solid rocket nozzles are ablatively cooled. The general construction of a solid
rocket nozzle features steel or aluminium shells (housings) that are designed to carry
structural loads (motor operating pressure and nozzle TVC actuator load are the biggest), and
composite ablative liners which are bonded to the housings. Solid rocket nozzles are
designed to ensure that the thickness of ablative liners is sufficient to maintain the liner-tohousing adhesive bond line below the temperature that would degrade the adhesive structural
properties during the motor operation.
The construction of nozzle ranges from simple single-piece non-movable graphite nozzles
to complex multipiece nozzles capable of moving to control the direction of the thrust vector.
Igniter hardware
There are generally two types:
•
•

Pyrotechnic igniters and
pyrogen igniters.

In industrial practice, pyrotechnic igniters are defined as igniters using solid explosives or
energetic propellant-likw chemical formulations (usually small pellets of propellant which
give a large burning surface and a short burning time) as the heat-producing material.

Pyrogen igniter is basically a small rocket motor that is used to ignite a large rocket
motor. The pyrogen is not designed to produce thrust. All use one or more nozzle orifices,
both sonic and supersonic types, and most use conventional rocket motor gra8 0 Td [(a)3.15789(t)-2.53658(



ROCKET PROPELLANTS
Propellant is the chemical mixture burned to produce thrust in rockets and consists of a fuel
and an oxidizer. A fuel is a substance which burns when combined with oxygen producing
gas for propulsion. An oxidizer is an agent that releases oxygen for combination with a fuel.
The ratio of oxidizer to fuel is called the mixture ratio. Propellants are classified according to
their state - liquid, solid, or hybrid.
The gauge for rating the efficiency of rocket propellants is specific impulse, stated in
seconds. Specific impulse indicates how many pounds (or kilograms) of thrust are obtained
by the consumption of one pound (or kilogram) of propellant in one second. Specific impulse
is characteristic of the type of propellant, however, its exact value will vary to some extent
with the operating conditions and design of the rocket engine.

Liquid Propellants
In a liquid propellant rocket, the fuel and oxidizer are stored in separate tanks, and are fed
through a system of pipes, valves, and turbopumps to a combustion chamber where they
are combined and burned to produce thrust. Liquid propellant engines are more complex
than their solid propellant counterparts, however, they offer several advantages. By
controlling the flow of propellant to the combustion chamber, the engine can be throttled,
stopped, or restarted.
A good liquid propellant is one with a high specific impulse or, stated another way, one with
a high speed of exhaust gas ejection. This implies a high combustion temperature and
exhaust gases with small molecular weights. However, there is another important factor
which must be taken into consideration: the density of the propellant. Using low density
propellants means that larger storage tanks will be required, thus increasing the mass of
the launch vehicle. Storage temperature is also important. A propellant with a low storage
temperature, i.e. a cryogenic, will require thermal insulation, thus further increasing the
mass of the launcher. The toxicity of the propellant is likewise important. Safety hazards
exist when handling, transporting, and storing highly toxic compounds. Also, some
propellants are very corrosive, however, materials that are resistant to certain propellants
have been identified for use in rocket construction.
Liquid propellants used in rocketry can be classified into three types: petroleum, cryogens,
and hypergols.
Petroleum fuels are those refined from crude oil and are a mixture of complex
hydrocarbons, i.e. organic compounds containing only carbon and hydrogen. The petroleum
used as rocket fuel is a type of highly refined kerosene, called RP-1 in the United States.
Petroleum fuels are usually used in combination with liquid oxygen as the oxidizer. Kerosene
delivers a specific impulse considerably less than cryogenic fuels, but it is generally better
than hypergolic propellants.
Specifications for RP-1 where first issued in the United States in 1957 when the need for a
clean burning petroleum rocket fuel was recognized. Prior experimentation with jet fuels
produced tarry residue in the engine cooling passages and excessive soot, coke and other
deposits in the gas generator. Even with the new specifications, kerosene-burning engines
still produce enough residues that their operational lifetimes are limited.



Liquid oxygen and RP-1 are used as the propellant in the first-stage boosters of the Atlas
and Delta II launch vehicles. It also powered the first-stages of the Saturn 1B and Saturn V
rockets.
Cryogenic propellants are liquefied gases stored at very low temperatures, most frequently
liquid hydrogen (LH2) as the fuel and liquid oxygen (LO2 or LOX) as the oxidizer. Hydrogen
remains liquid at temperatures of -253 oC (-423 oF) and oxygen remains in a liquid state at
temperatures of -183 oC (-297 oF) .
Because of the low temperatures of cryogenic propellants, they are difficult to store over
long periods of time. For this reason, they are less desirable for use in military rockets that
must be kept launch ready for months at a time. Furthermore, liquid hydrogen has a very
low density (0.071 g/ml) and, therefore, requires a storage volume many times greater
than other fuels. Despite these drawbacks, the high efficiency of liquid oxygen/liquid
hydrogen makes these problems worth coping with when reaction time and storability are
not too critical. Liquid hydrogen delivers a specific impulse about 30%-40% higher than
most other rocket fuels.
Liquid oxygen and liquid hydrogen are used as the propellant in the high efficiency main
engines of the Space Shuttle. LOX/LH2 also powered the upper stages of the Saturn V and
Saturn 1B rockets, as well as the Centaur upper stage, the United States' first LOX/LH2
rocket (1962).
Another cryogenic fuel with desirable properties for space propulsion systems is liquid
methane (-162 oC). When burned with liquid oxygen, methane is higher performing than
state-of-the-art storable propellants but without the volume increase common with LOX/LH2
systems, which results in an overall lower vehicle mass as compared to common hypergolic
propellants. LOX/methane is also clean burning and non-toxic. Future missions to Mars will
likely use methane fuel because it can be manufactured partly from Martian in-situ
resources. LOX/methane has no flight history and very limited ground-test history.
Liquid fluorine (-188 oC) burning engines have also been developed and fired successfully.
Fluorine is not only extremely toxic; it is a super-oxidizer that reacts, usually violently, with
almost everything except nitrogen, the lighter noble gases, and substances that have
already been fluorinated. Despite these drawbacks, fluorine produces very impressive
engine performance. It can also be mixed with liquid oxygen to improve the performance of
LOX-burning engines; the resulting mixture is called FLOX. Because of fluorine's high
toxicity, it has been largely abandoned by most space-faring nations.
Some fluorine containing compounds, such as chlorine pentafluoride, have also been
considered for use as an 'oxidizer' in deep-space applications.
Hypergolic propellants are fuels and oxidizers which ignite spontaneously on contact with
each other and require no ignition source. The easy start and restart capability of hypergols
make them ideal for spacecraft maneuvering systems. Also, since hypergols remain liquid at
normal temperatures, they do not pose the storage problems of cryogenic propellants.
hypergols are highly toxic and must be handled with extreme care.
Hypergolic fuels commonly include hydrazine, monomethyl hydrazine (MMH) and
unsymmetrical dimethyl hydrazine (UDMH). Hydrazine gives the best performance as a
rocket fuel, but it has a high freezing point and is too unstable for use as a coolant. MMH is
more stable and gives the best performance when freezing point is an issue, such as


spacecraft propulsion applications. UDMH has the lowest freezing point and has enough
thermal stability to be used in large regeneratively cooled engines. Consequently, UDMH is
often used in launch vehicle applications even thou


Solid Propellants
Solid propellant motors are the simplest of all rocket designs. They consist of a casing,
usually steel, filled with a mixture of solid compounds (fuel and oxidizer) which burn at a
rapid rate, expelling hot gases from a nozzle to produce thrust. When ignited, a solid
propellant burns from the center out towards the sides of the casing. The shape of the
center channel determines the rate and pattern of the burn, thus providing a means to
control thrust. Unlike liquid propellant engines, solid propellant motors can not be shut
down. Once ignited, they will burn until all the propellant is exhausted.
There are two families of solids propellants: homogeneous and composite. Both types
are dense, stable at ordinary temperatures, and easily storable.
Homogeneous propellants are either simple base or double base. A simple base propellant
consists of a single compound, usually nitrocellulose, which has both an oxidation capacity
and a reduction capacity. Double base propellants usually consist of nitrocellulose and
nitroglycerine, to which a plasticiser is added. Homogeneous propellants do not usually
have specific impulses greater than about 210 seconds under normal conditions. Their main
asset is that they do not produce traceable fumes and are, therefore, commonly used in
tactical weapons. They are also often used to perform subsidiary functions such as
jettisoning spent parts or separating one stage from another.
Modern composite propellants are heterogeneous powders (mixtures) which use a
crystallized or finely ground mineral salt as an oxidizer, often ammonium perchlorate, which
constitutes between 60% and 90% of the mass of the propellant. The fuel itself is
generally aluminum. The propellant is held together by a polymeric binder, usually
polyurethane or polybutadienes, which is also consumed as fuel. Additional compounds
are sometimes included, such as a catalyst to help increase the burning rate, or other
agents to make the powder easier to manufacture. The final product is rubberlike substance
with the consistency of a hard rubber eraser.
Composite propellants are often identified by the type of polymeric binder used. The two
most common binders are polybutadiene acrylic acid acrylonitrile (PBAN) and hydroxyterminator polybutadiene (HTPB). PBAN formulations give a slightly higher specific impulse,
density, and burn rate than equivalent formulations using HTPB. However, PBAN propellant
is the more difficult to mix and process and requires an elevated curing temperature. HTPB
binder is stronger and more flexible than PBAN binder. Both PBAN and HTPB formulations
result in propellants that deliver excellent performance, have good mechanical properties,
and offer potentially long burn times.
Solid propellant motors have a variety of uses. Small solids often power the final stage of a
launch vehicle, or attach to payloads to boost them to higher orbits. Medium solids such as
the Payload Assist Module (PAM) and the Inertial Upper Stage (IUS) provide the added
boost to place satellites into geosynchronous orbit or on planetary trajectories.
The Titan, Delta, and Space Shuttle launch vehicles use strap-on solid propellant rockets to
provide added thrust at liftoff. The Space Shuttle uses the largest solid rocket motors ever
built and flown. Each booster contains 500,000 kg (1,100,000 pounds) of propellant and can
produce up to 14,680,000 Newtons (3,300,000 pounds) of thrust.


Hybrid Propellants

Hybrid propellant engines represent an intermediate group between solid and liquid
propellant engines. One of the substances is solid, usually the fuel, while the other, usually
the oxidizer, is liquid. The liquid is injected into the solid, whose fuel reservoir also serves as
the combustion chamber. The main advantage of such engines is that they have high
performance, similar to that of solid propellants, but the combustion can be moderated,
stopped, or even restarted. It is difficult to make use of this concept for vary large thrusts,
and thus, hybrid propellant engines are rarely VESFVE) WB05SD5)hWB05S5==E)tWBFS&EF=E)hWB=SVD0

ROCKET PROPELLANT PERFORMANCE
Combustion chamber pressure, Pc = 68 atm (1000 PSI) ... Nozzle exit pressure, Pe = 1 atm
Oxidizer

Fuel

Hypergolic Mixture Ratio


An Introduction to Hybrid Rockets

Hybrid Rocket Engines are those which use liquid oxidizer and a solid fuel. Below figure shows
typical elements of an Hybrid Rocket Engine.
The liquid oxidizer is atomized and sprayed over the fuel block. In hypergolic systems, only gas
phase reactions occur. The oxidizer content of the hot product gases decreases along the port and
the length of the grain.
•
•
•

Two of the issues in this combustion process are
(i) mixing of the oxidizer rich and fuel rich gases across the diffusion flame occurs much
later than the length of the fuel grain and
(ii) fuel regression rate is small.

The first issue is resolved by adding mixing devices and second issue is solved by adding a
certain amount of oxidizer into the fuel.



•

Hybrid rocket engines retain the advantage of controllability like liquid rockets. The
added safety is an attraction for use of hybrid rockets in situations calling for safety
similar to civil aircraft operations. There may be possibilities for their use in single stageto-orbit vehicles providing low cost access to space.

When considering different methods of propelling an aerospace vehicle, it must be realized that
there is an overall hierarchy of engines that produce a desired thrust. There are air-breathing
engines, which include most sub-orbital vehicles such as airplanes and jets, and then there are
spacecraft engines.
Among spacecraft engines there are two general types, those being electric propulsion and
chemical propulsion. Electric motors are very efficient and make excellent use of fuel, but
provide very little thrust. Chemical rockets, however, are powerful enough to launch payloads
from the ground into orbit.
In chemical rockets, the idea is to combine two substances, a fuel and an oxidizer, in some
mixing region. The chemical energy associated with combining these two substances is
transferred to the total flow as thermal (kinetic) energy. This high-energy flow can then be
expanded out a nozzle to provide thrust for the attached vehicle.
One major issue involved is apparent, for we need to what substance are best usable as oxidizer
and fuel. However, the even larger question is : what is the best way to mix the fuel and
oxidizer? The two long-standing answers to this question involve liquid and solid rockets.
However, a third response to this question seems to be feasible these days, and that answer
involves hybrid rockets.
To review, liquid rockets utilize liquid fuel and liquid oxidizer stored in tanks. By either pressure
feeding or by mechanically pumping the propellants from their tanks, they are forced into a
mixing chamber where chemical combustion occurs. These types of systems generally provide
good thrust and can be thrust-controlled (throttled). In addition, they tend to be the most efficient
of high-thrust engines. However, the complexity of these systems is also high. There are stopvalves, pressure regulators, injectors, turbopump machinery and all sorts of “plumbing”. When
considering that there needs to be redundancies on all of these systems in order to make a
reliable motor, it easy to see that the overall cost and weight of liquid rockets will be excessive.
In addition, due to the liquid nature of the propellants involved, there can also be storage
problems.
Solid rockets are somewhat different in nature, but also have a specific set of advantages and
drawbacks. In solid rocket motors, the fuel and oxidizer are chemically premixed to form a solid
fuel grain. By simply igniting this substance, the oxidizer and fuel in the solid react and produce
the high-energy combustion gases desired. A variety of designs for the central burning port of the
solid fuel can be created so as to produce the desired thrust performance. Solid rockets provide
good thrust and are the most simple systems available. On the down side, they also are fairly
inefficient fuel burners and cannot be throttled. In some cases there may also be explosion
dangers since the oxidizer and fuel are not separated.
It appears necessary to obtain some "optimal" solution to this dilemma. On the one hand, we
have a high-thrust rocket engine with good performance but high complexity and cost, while on
the other hand to get low complexity we must accept lower performance as well. It is at this
point where hybrid rockets become an attractive alternative. Hybrid rockets combine elements


from both types of rockets. In a hybrid rocket, a gaseous or liquid oxidizer is stored in a tank
separate from a solid fuel grain. The fuel grain is placed inside a pressure chamber which lies
between an oxidizer injector and the exit nozzle. The solid grain is hollowed out in the same
fashion to produce a combustion port, very similar to that of a solid rocket motor type system.
Unless the fuel is hypergolic (spontaneously combustible in the presence of an oxidizer), the fuel
must be initially ignited in order to vaporize some of the fuel into a region just above the solid
surface. Then, by injecting the oxidizer at a high mass flow rate and pressure into the pressure
chamber / combustion port area, the oxidizer and fuel are free to react in a thin boundary layer
just above the surface of the fuel grain. The high energy released and the high temperature
attained both increase the energy in the flow and sustain the solid fuel vaporization. The
combustion gases pass down the remainder of the combustion port and are expanded via nozzle.
By changing the flow rate of the oxidizer, the total production of combustion gases and the
energy going into them will be changed in a like fashion (increasing or decreasing). This fact
demonstrates that hybrid rockets can be throttled. Given a simple ignition system that would
58(.9590.842-0.9c556417(n)-0.956417( burning prior to injecting the aat
efficiently initiate fuel 1.7465(t)-2..956417(n)53658(e)3.18( )250]-2.)-0.956417(i)3658(.956417(.)-0..15789(0.95


Coasting Flight
Coasting is defined as the free flight of a space vehicle during which the thrust acting on it is
zero.

The thrust is zero after the “burn out” and the rocket coasts. During this flight the rocket
ascends to the maximum altitude and decelerates to zero velocity. Therefore,
u = up - gtc = 0
The coasting time is given by, tc = up / g
The gain in altitude during coasting is given by,

Z c = u ptc −

1 2
gt c
2

Thrust vectoring
•

Thrust vectoring is the ability of an aircraft or rocket or other vehicle to deflect the angle
of its thrust away from the vehicles longitudinal axis.



•

The advantages of thrust vectoring systems on aircraft include improved post stall
performance, the ability (ability to change the body's position, and requires a
combination of balance, coordination, speed, strength, endurance etc.) to operate on
damaged airfields due to reduced takeoff distances and overall enhanced agility.

•

These factors can provide substantial benefits for military aircraft, which are primarily
concerned with manoeuvrability and control.
•

The concept of thrust vectoring is not a new one. The Germans used graphite control
vanes in the exhaust stream of their V-2 ballistic missile in World War II for some
directional control.

•

Thrust vectoring in aircraft though is a relatively new practice and the concept came
under widespread consideration during the cold war.

•

There are several methods employed to produce thrust vectoring.

•

Most current production aircraft with thrust vectoring use turbofan engines with
rotating nozzles or turning vanes to deflect the exhaust stream. This method can deflect
thrust to as much as 90 degrees providing a vertical take off and landing capability.
However for vertical thrust the engine has to be more powerful to overcome the weight
of the aircraft, this means the aircraft requires a bigger heavier engine. As a result of the
increased overall weight of the aircraft the manoeuvrability and agility are reduced in
normal horizontal flight.

•

Another method to produce thrust vectoring is through fluidic thrust vector control. This
is achieved using a static nozzle and a secondary flow between the primary jet and the
nozzle. This method is desirable for its lower weight, mechanical simplicity and lower
radar cross section.
Advantages and Disadvantages of Thrust Vector Control

•

Thrust-vectoring research to date has successfully identified and demonstrated many
potential benefits to high-performance aircraft.

•

These include enhanced aircraft manoeuvrability, performance, survivability, and
stealth.

•

The full extent of these benefits, however, has yet to be realized even with new
generation aircraft because current mechanical thrust-vectoring configurations are
heavy, complex, and expensive.
Countercurrent shear layer enhancement for fluidic thrust vector control



Photo courtesy Pratt & Whitney, A United Technologies Company
F119 engine for F/A-22 Raptor showing the 2 extreme vectoring cases
•

Thrust Vector Control or Thrust Vectoring is a technology that deflects the mean flow of
an engine jet from the centerline in order to transfer some force to the aimed axis. By
that imbalance, a momentum is created and used to control the change of attitude of
the aircraft.

•

Among other things, thrust vectoring greatly improves maneuverability, even at high
angles of attack or low speeds where conventional aerodynamic control surfaces lose all
effectiveness.

•

Thrust Vector Control is currently achieved by complex arrays of mechanical actuators
capable of modifying the geometry of the nozzle and thus defect the flow.

•

This variable geometry greatly increases weight and maintenance to the engine, and
therefore limits the benefits from vectoring the thrust.

•

Fluidic Thrust Vector Control is a technology aiming at the above listed benefits by the
use of fluidic means, implying less complexity and faster dynamic responses.

•

Different concepts have been developed in the last decade to redirect the thrust
without mechanical actuators.

•

Induction to flow separation, countercurrent shear layer, synthetic pulses or skewing of
the sonic line are some of the proven concepts.


•

Countercurrent shear flow control has been established as an effective method for
fluidic thrust vector control.

•

However, hardware integration issues exist and must be overcome in order to make a
viable technology for future aircraft.

•

Recent developments in fluidic thrust vector control have focused on nozzle interior
methods that skew the throat of the nozzle using multiple transverse jets.

Rockets
•

The thrust vector control history first came from rocket. The evolution of the rocket
has made it an indispensable tool in the exploration of space.

•

For centuries, rockets have provided ceremonial and warfare uses starting with the
ancient Chinese, the first to create rockets. But for centuries rockets were in the main
rather small, and their use was confined principally to weaponry, the projection of
lifelines in sea rescue, signalling, and fireworks displays.

•

Not until the 20th century did a clear understanding of the principles of rockets emerge,
and only then did the technology of large rockets begin to evolve. Thus, as far as
spaceflight and space science are concerned, the story of rockets up to the beginning of
the 20th century was largely prologue.

•


•

Early in the 20th century, an American scientist, Robert H. Goddard (1882-1945), he
began to try various types of solid fuels and to measure the exhaust velocities of the
burning gases.

•

Since the earliest days of discovery and experimentation, rockets have evolved from
simple gunpowder devices into giant vehicles capable of travelling into outer space.

•

Rockets have opened the universe to direct exploration by humankind.

•

A third great space pioneer, Hermann Oberth (1894-1989) of Germany, published a
book in 1923 about travel into outer space has led to the development of the V-2
rocket. The V-2 rocket (in Germany called the A-4) was small by comparison to today's
designs.

•

It achieved its great thrust by burning a mixture of liquid oxygen and alcohol at a rate of
about one ton every seven seconds.

•

Once launched, the V-2 was a formidable weapon that could devastate whole city
blocks. Other than that, the V-2 rocket use graphite vanes in the exhaust to achieve the
thrust vector control.



•

The concept of thrust vectoring is not a new one. The Germans used graphite control
vanes in the exhaust stream of their V-2 ballistic missile in World War II for some
directional control. Thrust vectoring in aircraft though is a relatively new practice and
the concept came under widespread consideration during the cold war.

•

There are several methods employed to produce thrust vectoring. Most current
production aircraft with thrust vectoring use turbofan engines with rotating nozzles or
turning vanes to deflect the exhaust stream.

•

This method can deflect thrust to as much as 90 degrees providing a vertical take off
and landing capability. However for vertical thrust the engine has to be more powerful
to overcome the weight of the aircraft, this means the aircraft requires a bigger heavier
engine. As a result of the increased overall weight of the aircraft the manoeuvrability
and agility are reduced in normal horizontal flight.

Thrust vector control in rockets
•

All chemical propulsion systems can be provided with one of several types of thrust
vector control (TVC) mechanisms.

•

Some of these apply either to solid, hybrid, or to liquid propellant rocket propulsion
systems, but most are specific to only one of these propulsion categories.

•

Thrust vector control is effective only while the propulsion system is operating and
creating an exhaust jet. For the flight period, when a rocket propulsion system is not
firing and therefore its TVC is inoperative, a separate mechanism needs to be provided
to the flying vehicle for achieving control over its attitude or flight path.

Hence, there are two types of thrust vector control concept:
(1) for an engine or a motor with a single nozzle; and
(2) for those that have two or more nozzles.

TVC Mechanisms with a single nozzle
•

Mechanical deflection of the nozzle or thrust chamber.

•

Insertion of heat-resistant movable bodies into the exhaust jet; these experience
aerodynamic forces and cause a deflection of a part of the exhaust gas flow.

•

Injection of fluid into the side of the diverging nozzle section, causing an asymmetrical
distortion of the supersonic exhaust flow.

•

Separate thrust-producing devices that are not part of the main flow through nozzle.


TVC Mechanisms
•
•
•
•
•
•
•
•
•
•

Gimbal or hinge - Liquid rockets
Movable nozzle (flexible bearing) – Solid rockets
Movable nozzle (rotary ball with gas seal) – Solid rocket
Jet vanes
- Liqid/Solid
Jet tabs
- Solid
Jetavator
- Solid
Liquid-side injection - Solid/Liquid
Hot gas side injection – Solid/Liquid
Hinged auxiliary thrust chambers for high thrust engine – Liquid
Turbine exhaust gas swivel for large engine - Liquid


Types of rocket engines
Physically powered
Type
water
rocket

Description
Partially filled pressurised
carbonated drinks container with
tail and nose weighting

Advantages
Very simple to
build

Disadvantages
Altitude typically limited to a
few hundred feet or so (world
record is 623 meters/2044 feet)

cold gas A non combusting form, used for
thruster attitude jets

Non
contaminating
exhaust

Extremely low performance

Hot water is stored in a tank at
hot water
high temperature/pressure and
rocket
turns to steam in exhaust

Simple, fairly
safe

Low performance due to heavy
tank

Chemically powered
Type

Description

Advantages

Disadvantages
Once lit, extinguishing it is
difficult although often
possible,
cannot
be
throttled in real time;
handling
issues
from
Simple, often no moving ignitable mixture, lower
Ignitable, self
parts, reasonably good performance than liquid
sustaining solid
mass fraction, reasonable rockets, if grain cracks it
Solid rocket fuel/oxidiser mixture
I . A thrust schedule can can block nozzle with
("grain") with central sp
be designed into the
disastrous results, cracks
hole and nozzle
grain.
burn and widen during
burn. Refuelling grain
harder than simply filling
tanks,
Lower
specific
Impulse
than
Liquid
Rockets.
Some
oxidisers
are
Quite simple, solid fuel monopropellants,
can
Separate oxidiser/fuel,
is essentially inert
explode in own right;
typically oxidiser is
without oxidiser, safer; mechanical failure of solid
Hybrid rocket liquid and kept in a
cracks do not escalate, propellant
can
block
tank, the other solid
throttleable and easy to nozzle, central hole widens
with central hole
switch off.
over burn and negatively
affects mixture ratio.
Simple in concept,
catalysts can be easily
Monopropellant Propellant such as
Hydrazine, Hydrogen throttleable, low
contaminated,
rocket


Peroxide or Nitrous
Oxide, flows over
catalyst and
exothermically
decomposes and hot
gases are emitted
through nozzle

Liquid
Bipropellant
rocket

Dual mode
propulsion
rocket

Tripropellant
rocket

temperatures in
combustion chamber

monopropellants
can
detonate if contaminated or
provoked, Isp is perhaps 1/3
of best liquids

Up to ~99% efficient
Pumps needed for high
Two fluid (typically
combustion with
performance are expensive
liquid) propellants are excellent mixture
to design, huge thermal
introduced through
control, throttleable, can fluxes across combustion
injectors into
be used with turbopumps chamber wall can impact
combustion chamber which permits incredibly reuse,
failure
modes
and burnt
lightweight tanks, can be include major explosions, a
safe with extreme care lot of plumbing is needed.
Rocket takes off as a
bipropellant rocket,
Simplicity and ease of
Lower performance than
then turns to using just
control
bipropellants
one propellant as a
monopropellant
Three different
propellants (usually
hydrogen, hydrocarbon
and liquid oxygen) are
introduced into a
combustion chamber
in variable mi.53536(n)-0.95641lu5789(r)2.417( )-0.478208(l)-2.56417(w)-9.3165.48 422417


added to the airstream
to increase maximum
altitude

dangerous. Much heavier
than simple rockets.

Easily tested on ground.
High thrust/weight ratios
Intake air is chilled to are possible (~14)
very low temperatures together with good fuel
Precooled jet at inlet before passing efficiency over a wide
range of airspeeds, mach
engine / LACE through a ramjet or
(combined cycle turbojet engine. Can be 0-5.5+; this combination
of efficiencies may
with rocket) combined with a
rocket engine for
permit launching to
orbital insertion.
orbit, single stage, or
very rapid
intercontinental travel.

Exists only at the lab
prototyping
stage.
Examples include RB545,
SABRE, ATREX

Electrically powered
Type
Resistojet rocket
(electric heating)

Arcjet rocket
(chemical burning
aided by electrical
discharge)

Description
A monopropellant is
electrically heated by
a filament for extra
performance
Similar to resistojet in
concept but with inert
propellant, except an
arc is used which
allows higher
temperatures

Pulsed plasma
Plasma is used to
thruster (electric
erode a solid
arc heating; emits
propellant
plasma)

Advantages
Disadvantages
Higher Isp than
monopropellant Uses a lot of power and hence
alone, about 40% gives typically low thrust
higher.

1600 seconds Isp

Very low thrust and high power,
performance is similar to Ion
drive.

High Isp , can be
pulsed on and off Low energetic efficiency
for attitude control

similar thrust/weight ratio with
ion drives (worse), thermal
issues, as with ion drives very
Variable specific
Microwave heated
Variable Isp from
high power requirements for
impulse
plasma with magnetic 1000 seconds to
significant thrust, really needs
magnetoplasma
throat/nozzle
10,000 seconds
advanced nuclear reactors, never
rocket
flown, requires low temperatures
for superconductors to work



Solar powered
The Solar thermal rocket would make use of solar power to directly heat reaction mass, and
therefore does not require an electrical generator as most other forms of solar-powered
propulsion do. A solar thermal rocket only has to carry the means of capturing solar energy, such
as concentrators and mirrors. The heated propellant is fed through a conventional rocket nozzle
to produce thrust. The engine thrust is directly related to the surface area of the solar collector
and to the local intensity of the solar radiation.
Type

Description

Advantages
Simple design. Using hydrogen
propellant, 900 seconds of Isp is
comparable to Nuclear Thermal rocket,
Solar Propellant is
without the problems and complexity
thermal heated by
of controlling a fission reaction. Using
rocket solar collector
higher–molecular-weight propellants,
for example water water, lowers
performance.

Disadvantages
Only useful once in space, as
thrust is fairly low, but
hydrogen is not easily stored
in
space,
otherwise
moderate/low Isp if higher–
molecular-mass
propellants
are used

Beam powered
Type

Description

Advantages

Disadvantages
~1 MW of power per kg of payload is
needed to achieve orbit, relatively high
Propellant is heated
accelerations, lasers are blocked by
by light beam (often simple in
clouds, fog, reflected laser light may be
principle, in
light beam laser) aimed at
dangerous, pretty much needs hydrogen
principle very high
powered vehicle from a
monopropellant for good performance
distance, either
exhaust speeds can
rocket
which needs heavy tankage, some
directly or indirectly be achieved
designs are limited to ~600 seconds due
via heat exchanger
to
reemission
of
light
since
propellant/heat exchanger gets white hot
~1 MW of power per kg of payload is
needed to achieve orbit, relatively high
accelerations, microwaves are absorbed
microwaves avoid
to a degree by rain, reflected
microwave Propellant is heated reemission of
microwaves may be dangerous, pretty
by microwave beam energy, so ~900
beam
much needs hydrogen monopropellant
seconds exhaust
powered aimed at vehicle
for good performance which needs
from a distance
speeds might be
rocket
heavy tankage, transmitter diameter is
achieveable
measured in kilometres to achieve a fine
enough beam to hit a vehicle at up to
100 km.


Nuclear powered
Nuclear propulsion includes a wide variety of propulsion methods that use some form of nuclear
reaction as their primary power source. Various types of nuclear propulsion have been proposed,
and some of them tested, for spacecraft applications:
Type
Radioisotope
rocket/"Poodle
thruster"
(radioactive decay
energy)

Description

Advantages

Heat from
about 700-800
radioactive decay
seconds, almost no
is used to heat
moving parts
hydrogen

Disadvantages

low thrust/weight ratio.

Maximum temperature is limited
propellant (typ.
by materials technology, some
Isp can be high,
hydrogen) is
radioactive particles can be
perhaps 900 seconds
Nuclear thermal
passed through a
present in exhaust in some
or more, above unity
rocket (nuclear
nuclear reactor to
designs, nuclear reactor shielding
thrust/weight ratio
fission energy)
heat to high
is heavy, unlikely to be permitted
with some designs
temperature
from surface of the Earth,
thrust/weight ratio is not high.
Nuclear reaction Very hot propellant, difficulties in heating propellant
using a gaseous not limited by
without losing fissionables in
Gas core reactor
state fission
keeping reactor solid, exhaust,
exhaust
inherently
rocket (nuclear
nuclear
reactor in intimate Isp between 1500 and highly
radioactive,
massive
fission energy)
contact with
thermal issues particularly for
3000 seconds but
propellant
with very high thrust nozzle/throat 9809 0 0 1 376.32 458863(r)-7.6513


below Earth's magnetosphere.
Containment
of
antimatter,
Antimatter
Nuclear pulse
production of antimatter in
catalyzed nuclear
propulsion with Smaller sized vehicle
macroscopic
quantities
isn't
pulse propulsion
antimatter assist might be possible
currently feasible. Theoretical
(fission and/or
for smaller bombs
only at this point.
fusion energy)
Fusion rocket
Fusion is used to Very high exhaust
Largely beyond current state of
(nuclear fusion
heat propellant
velocity
the art.
energy)
Problems
with
antimatter
Extremely energetic, production and handling; energy
Antimatter rocket Antimatter
annihilation heats very high theoretical losses in neutrinos, gamma rays,
(annihilation
propellant
exhaust velocity
muons;
thermal
issues.
energy)
Theoretical only at this point



Solid Propellant Rockets
Advantages

Disadvantages

Simple Design (few or no moving parts)

Explosion and fire potential is larger; failure
can be catastrophic

Easy to operate (little preflight checkout)

Many require environmental permit and safety
features for transport on public conveyances

Ready to operate quickly

Under certain conditions
propellants can detonate

Will not leak, spill, or slosh

Cumulative grain damage occurs through
temperature cycling or rough handling; this
limits useful life

Can be stored for 5 to 25 years

If designed for reuse, it requires extensive
factory rework and new propellants

some

solid

Usually, higher overall density; this allows a Requires an ignition system
more compact package, a small vehicle (less
drag)
Can provide TVC, but at increased complexity

Once ignited, cannot change predetermined
thrust or duration

Some propellants have nontoxic, clean exhaust Integrity of grain (cracks, unbounded areas) is
gases, but at a performance penalty
difficult to determine in the field
Some grain and case design can be used with Large boosters take a few seconds to start
several nozzles
Thrust termination devices permit control over Cannot be tested prior to use
total impulse
Can be designed for recovery and reuse

Thermal insulation is required in almost all
rocket motors

Some tactical missile motors have been Needs a safety provision to prevent inadvertent
produced in large quantities
ignition, which would lead to an unplanned
motor firing. Can cause a disaster.



Liquid Propellant Rockets
Advantages

Disadvantages

High specific impulse than solid propellant rockets

Relatively complex design, more
components, more things to go wrong!

Can be randomly throttled and randomly stopped and
restarted.

Cryogenic propellants cannot be stored for long
periods except when tanks are well insulated and
escaping vapours are recondensed. Propellant
loading occurs at the launch stand and requires
cryogenic propellant storage facilities

Thrust-time profile can be randomly controlled; this
allows a reproducible flight trajectory

Spills or leaks of several propellants can be
hazardous, corrosive, toxic, and cause fires, but this
can be minimized with gelled propellants

Cutoff impulse can be controllable with thrust
termination device (better control of vehicle terminal
velocity)

More overall weight for most short-duration, lowtotal-impulse applications.

Can be tested at full thrust on ground or launch pad
prior to flight

Non-hypergolic propellants require an ignition
system

Can be designed for reuse after field services and
checkout

Tanks need to be pressurized by a separate
pressurization system. This can require high pressure
inert gas storage for long periods of time.

Thrust chamber (or some part of the vehicle) can be
cooled and made lightweight

Bullet impact will cause leaks, sometimes a fire, but
usually no detonations; gelled propellants can
minimize or eliminate these hazards.

Storable liquid propellants have been kept in vehicle
for more than 20 years and engine can be ready to
operate quickly.

Usually requires more volume due to lower average
propellant density and relatively inefficient
packaging of engine components

Most propellants have nontoxic exhaust, which is
environmentally acceptable

Sloshing in tank can cause a flight stability problem,
but can be minimized with baffles.

Can modify operating conditions during firing to
prevent some failures that would otherwise result in
the loss of the mission or vehicle

Smoky exhaust (soot) plume can occur with some
hydrocarbon fuels

Can provide component redundancy (e.g., dual check
valves or extra thrust chamber) to enhance reliability

Needs special design provisions for start in zero
gravity

Plume radiation and smoke are usually low

High-thrust unit requires several seconds to start


parts

or

Appendix
Chemical Rocket Systems
The primary rocket engine technology at the present time is the chemical rocket engine, and it is likely
to remain the dominant technology for some time to come. This chapter provides a short introduction
to chemical rocket engine systems.

[1.1] BASIC CONCEPTS OF ROCKET PROPULSION

* All rocket vehicles work on the principle of reaction, or "recoil", which is a consequence of the
law of conservation of momentum. If a cannon fires a cannonball, the cannonball flies away with
a momentum equal to the mass of the cannonball times its velocity. The shot gives the cannon
the same momentum in the opposite direction, and if it were free to move without interference
from friction or other constraint, it would fly backward, with a velocity less than that of the
cannonball by the same factor that the cannon's mas f5.347(3597(h)-0.957028(e)3.15789( )-90.6536( )-0.478208


mass of the exhaust flow and the greater the velocity of that flow, the greater the recoil generated
by the rocket engine, and the greater the thrust.
There are various ways to generate this thrust, though in all cases the result is the same, to expel
a gas at high velocity. Nuclear rocket engines run a fluid through a nuclear reactor. Electric
rocket engines typically accelerate ions to high velocities using electrified grids. Chemical rocket
engines, the subject of this chapter, burn a "fuel" and an "oxidizer", either in a solid mixture or
stored as liquids in separate tanks, and blast the exhaust out a usually bell-shaped ("convergentdivergent" or "con-di") nozzle.
Rocket engine thrust is formally measured in newtons (N) in the metric system; in pounds force
(lbf) in the English system; and sometimes in kilograms force (kgp, where the "p" stands for the
French "puissance / force"). Since the kilogram is a measure of mass, not force, kgp is a little
dubious from the strict physics point of view, but it is equivalent to newtons divided by 9.81, and
at least at one time was a fairly common measure of thrust.
Efficiency of a rocket engine can be measured in terms of exhaust velocity, but since the actual
thrust is also dependent on the mass of the exhaust gas, a more useful measure is "specific
impulse (Isp)", or thrust produced by a unit mass of propellant per second. In metric units, Isp is
defined as "newtons per kilogram of propellant per second", and in English units it is defined as
"pounds thrust per pound of propellant per second". The second definition, by the way, evaluates
to "seconds", and that's normally how specific impulse is described. Specific impulse can be
thought of as an index of the "mass ratio" of a rocket vehicle, or the ratio of payload to vehicle
mass: the higher the specific impulse, the greater the efficiency in terms of the amount of
payload per fuel mass.
However, this is a somewhat narrow definition of "efficiency", a much more practical one being
how much payload can be lifted at a given cost, and in such terms an engine with the highest
specific impulse may not be the most efficient. In addition, high specific impulse does not
necessarily mean high thrust, and in fact as later chapters will show, highly efficient engines with
high values of specific impulse tend to have very low thrust.
* A rocket vehicle obviously consists of some sort of airframe or casing mounting a rocket
engine and providing storage for propellants. Less obviously, it must also carry guidance and
control systems.
Holiday firework rockets simply have a stick or fins to keep them flying straight. Unguided
rocket projectiles used by combat aircraft to attack ground targets or launched as a form of
"barrage" artillery also generally use fins, though they also may have multiple rocket exhausts
canted at an angle around the centerline of the rocket to cause them to spin for stabilization.
For large rocket vehicles, such as long-range missiles or space launch boosters, which are the
focus of this discussion, more sophisticated control schemes are required. While some large
rocket vehicles do have fins, fins are only useful at low altitudes, since they are ineffective once
the vehicle leaves the atmosphere. There are several approaches for control of such large
vehicles:



•

•

•

The early "V-2" missile, built by the Germans in World War II to attack England, used
moveable graphite vanes in the rocket engine exhaust. This caused some loss of thrust,
and so this approach was later abandoned. The V-2 used a gyroscopic control system to
move the vanes. The control system included three gyros, one each for the two horizontal
and one vertical directions, and responded to changes in the rocket's attitude and
movement by changing the direction of the vanes. Modern rocket vehicles have retained
gyroscopic control systems, though they will most likely now be implemented with solidstate "ring laser gyros" instead of rotating gyroscopes.
A more modern flight control scheme is to use a "gimballed" rocket engine, in which the
rocket nozzle can be moved back and forth or side to side to change the vehicle's
direction of flight.
Another modern scheme is to use "verniers", or small auxiliary rocket engines that
produce thrust off to the sides of the vehicle to change flight direction.

Most modern large rocket vehicles are actually assemblages of separate rocket vehicles, known
as "stages", that are stacked on top of each other. A big rocket vehicle contains a large amount of
fuel, and as the fuel is burned up, the vehicle carries more and more useless dead weight. With
"staging", when one stage is exhausted, the next ignites and the first is discarded.
Staging is a tricky operation, in essence trying to launch one rocket vehicle on top of another
while the whole assembly is in flight, and some early long-range missiles used dodges to
simplify the scheme. The original American Atlas missile, for example, used "half staging", with
a three-engine assembly in a skirt at the bottom; two of the engines were discarded along with
the skirt after initial boost. The Soviet R-7 missile / SL-1 booster used "clustering", with four
auxiliary boosters clustered around a similar central "core" booster, the auxiliary boosters being
discarded after initial boost. Both these schemes allowed all the engines to be ignited at take-off,
simplifying launch procedures. They were perfectly practical rocket vehicles, and in fact their
descendants are still in use.
More modern large rocket vehicles use true staging, though they often also use a set of auxiliary
solid-fuel or liquid-fuel "strap-on" boosters attached to the first stage to provide additional thrust.
Each stage is connected to the others by a "shroud", or the case of many Soviet-Russian missiles
and boosters, by an open framework. The open framework has the advantage that the upper stage
can be ignited before the lower stage is discarded, which simplifies the staging process.
The Soviets also came up with an ingenious staging scheme for their R-27 / SS-N-6 submarinelaunched ballistic missile to produce a more compact vehicle, with the engines for the payload
stage actually contained in the fuel tank for the main stage. Pyrotechnics were used to cut open
the tank so the rocket engine could ignite.
* While the lower stages of a multistage rocket vehicle are discarded before the machine leaves
the atmosphere, the upper stages and the spacecraft they carry, if there is a distinction, need to
operate in space. Such "space vehicles" generally need "restartable" rocket engines that can be
turned on or off, which is a somewhat tricky problem because under "zero-gee" conditions the
propellants do not tend to flow to the bottom of the tanks.



fed engines fueled by LOX and propane. LOX tends to be self-pressurizing as it boils off, and
propane becomes self-pressurizing if heated slightly.
Most modern rocket engines use high-speed turbine pumps to drive the propellants into the
combustion chamber at a very fast rate. The turbopumps are turned on with a "starter", an
electrically activated solid-fuel charge that spins up the drive turbine for the turbopumps.
However, even rocket vehicles that use turbopumps still pressurize the propellant tanks, not so
much to drive propellant flow rate as to prevent a void from arising as the tank is vacated, which
would otherwise stifle thrust or even cause the propellant tanks to collapse.
The fuel line is generally wrapped around the engine nozzle, helping to cool the engine and also
"preheat" the fuel, conserving some of the combustion energy that would otherwise be wasted.
This is known as "regenerative" cooling. While regenerative cooling is common now, early
rockets used water cooling, or various types of "heat sinks" -- sets of fins or other structures that
could radiate the heat away.
There is also usually a second set of valves downstream from the turbopumps. These are kept
closed until propellant pressures build up enough to ensure a regular fuel flow into the
combustion chamber. If the propellants were allowed to trickle unevenly into the combustion
chamber, the burn would be irregular and poorly controlled.
For similar reasons, the propellant feed system is usually designed to make sure that oxidizer
flow reaches its proper flow level before fuel does. However, modern liquid fuel rocket engines
are often designed to burn "fuel rich", throwing so much fuel into the combustion chamber that
all of it can't be burned. This may seem inefficient, but it allows an increase in exhaust mass
flow, and so thrust, without raising exhaust temperature. Determining the proper propellant ratio
is a fine art.
The propellants are forced into the combustion chamber using an "injector" system that ensures
they mix properly, which can be visualized as something like a shower spray head. The engine
burn is then initiated with an "igniter" system. Igniter systems can be based on electrical spark
plugs, pyrotechnic charges, electroresistive heating elements, and even small igniter rockets
using hypergolic storable propellants.
The exhaust then pours out the engine nozzle, producing thrust. The input to the nozzle is a
narrow constriction, where the exhaust flows at high pressure and low velocity. As the exhaust
flows down the nozzle it expands, losing pressure but gaining velocity, resulting in greater
momentum transfer to the rocket vehicle.
There is a tradeoff between nozzle size and thrust. If the nozzle is too small, the exhaust will be
robbed of thrust. If the nozzle is too big, the exhaust will separate from the nozzle wall, not only
making the larger size useless but also counterproductive, since it sets up turbulence that robs the
exhaust of thrust. The behavior of the exhaust varies with atmospheric pressure, which of course
falls off as the rocket climbs, and so optimizing the exhaust design is a troublesome matter. It is
also obvious that building a big engine is more difficult and expensive than a small one. As a


compromise, rocket engines were developed that featured multiple clustered "thrust chambers"
but shared the same systems upstream.
* Usually the interval between start of the starter motor and engine ignition is about a second.
Once the propellant is gated into the main combustion chamber, a small amount of it is fed back
towards the turbopump drive turbine and burned in a small secondary combustion chamber to
take over from the starter, which then burns out.
The propellant feed to the secondary combustion chamber must be precisely regulated to ensure
proper turbopump RPM. Liquid fuel rocket engines that have variable thrust have adjustable
valves on these feed lines, while those that have constant thrust simply use a small orifice to limit
fuel rate. Incidentally, the secondary combustion chamber may need an igniter of its own, though
in many cases the starter exhaust into the drive turbine will be hot enough to ignite the liquid
propellants.
To get really elaborate, exhaust from the secondary combustion chamber has several other uses.
First, it is used to drive a lubrication system that keeps the turbopump system oiled and running
smoothly. Since the oil in the lubrication system tends to get hot after a while, it is cooled using a
heat exchanger linked to a loop off the fuel line. The intake of this loop is downstream from the
turbopump, while the output is upstream, to ensure a strong pressure difference and a fast fuel
rate through the heat exchanger to carry off heat without vaporizing the fuel.
Second, the exhaust is fed back to the fuel tank to keep it pressurized. The secondary combustion
chamber burns fuel-rich, which ensures that little or no oxidizer is present in the exhaust that
could cause fuel to combust in the tank, particularly if hypergolic fuels are used. The exhaust
should not be too hot, not because it could ignite the fuel, but because it could vaporize it and
disrupt fuel flow, and so another heat exchanger linked to a loop in the fuel line is used to draw
off the heat.

Pressure is maintained in the oxidizer tank through a separate system thtel13658( )-130.728(i)-2temue13658(


flow to the main combustion chamber shut off propellant flow, and the engine burn halts
immediately.
Of course, a controlled shutdown is absolutely essential in a restartable engine. As mentioned,
ensuring fuel flow in a restartable engine is tricky because the propellants cannot flow down to
the engine, since "down" doesn't exist under weightless conditions. There are several approaches:
•
•

•

The most conceptually obvious scheme is to fit bladders in the propellant tanks that are
filled by compressed gas to force the fluids out.
A somewhat less obvious scheme is to fit a set of screens into the tank, with the mesh
becoming finer as they near the bottom of the tank. Surface tension of the fuel on the
mesh causes the propellant to "wick" towards the bottom of the tank.
A third, even trickier but common, approach is to use a thruster to give the rocket vehicle
a small, short acceleration to cause fuel to flow into the main engine. Ignition of the main
engine sustains the flow, and the thruster is reloaded with propellant during the main
engine burn to prepare it for another restart.

* Modern LOX-hydrocarbon rocket engines burn LOX and kerosene, or more precisely a highly
refined grade of kerosene named "RP-1" or just "RP" for short, which some sources claim stands
for "rocket propellant" and others claim stands for "refined petroleum" -- take your pick. RP
looks and smells like ordinary kerosene, but it is pure and has highly predictable burn and
density characteristics. If a large rocket vehicle were fueled with normal kerosene it might burn,
but not evenly, and the fuel weight could vary by a matter of tonnes, which would make the
performance of the vehicle very unpredictable.
LOX-RP is traditionally one of the most popular liquid-fuel schemes. LOX-RP engines typically
have a specific impulse of about 260 seconds. This will be used as a "baseline" value in the rest
of this document, with specific impulse values given relative to it. This avoids the question of
metric or English units and the less-than-intuitive use of "seconds" as a unit of measure for
rocket efficiency.
LOX-LH2 provides higher specific impulse, about 1.5 times that of LOX-RP, but there is price
for it. LH2 is a low-density fuel, meaning it requires a large tank, and the rocket vehicle has to be
big as well. It also has to be kept very cold, substantially colder than liquid oxygen. The LOX
and LH2 tanks have to be thermally isolated from each other, or the LOX will tend to freeze and
the LH2 to boil.
LOX-kerosene and LOX-LH2 are both "cryogenic" propulsion systems, meaning they require
cooled propellants. Both use cooled LOX oxidizer, while LOX-LH2 also requires even colder
LH2 fuel. Incidentally, some sources refer only to LOX-LH2 as "cryogenic" propulsion, but this
usage seems a bit misleading and will not be used in this document. A rocket vehicle using
cryogenic propellants has to be fueled a relatively short time before launch, or the propellants
will gradually vaporize away. Launch systems for such vehicles cycle the cryogenic propellants
through an external cooling system to keep losses as low as possible, and also include a bleed
valve to keep vaporized propellants from building up in the tanks and possibly rupturing them.



Storable propellants, as the name implies, avoid this problem. They can be loaded into a rocket
vehicle and left indefinitely. One of the earliest storable propellant combinations was
concentrated hydrogen peroxide (HO), known as "high-test peroxide (HTP)", for oxidizer, and
aniline (C6H7N1), a benzene derivative, for fuel.
Since HTP tends to degrade slowly in storage over time, it was generally replaced as an oxidizer
by nitric acid (NHO3), nitrogen tetroxide (N2O4), or combinations of the two. Aniline was
replaced by hydrazine (NH2NH2); unsymmetrical dimethyl hydrazine (UDMH), with the
chemical formula N(CH3)2NH2; or a mix of the two, sometimes called "Aerozine-50". Nitrogen
tetroxide and UDMH are a popular combination, and have a specific impulse only a few percent
less than that of LOX-RP.
Storables have a number of drawbacks. Not only are they usually hypergolic, they are also as a
rule extremely toxic and corrosive. Storable propellant tanks have to be lined with stainless steel,
and workers handling these propellants must wear protective clothing and respirators. There
were cases in both the Soviet and American space programs where space capsules returning to
Earth fired thrusters fueled by storables too persistently, and the fumes overcame the crews,
though nobody was ever done any long-term harm. The US space shuttle's orbital propulsion
system uses storables, and when the orbiter lands, a crew in protective clothing has to go out and
"safe" it before anyone else is allowed to get near. The nasty behavior of storables means higher
cost, and they are also now generally regarded as environmentally unacceptable and avoided
when possible.
Storables were initially used in military missiles that had to be ready to fire on a moment's
notice. Their tanks were permanently fueled, capped by seals that were blown at the moment of
firing. Solid propellants are now preferred for military missiles, though the Soviets stayed with
storables for much longer than the US since they were comfortable with the technology. The
Soviets even used them for submarine-launched missiles, despite the threat posed by such toxic
and violent chemicals in a closed environment. The successor Russian government has found
disposal of large quantities of toxic fuels to be a major environmental headache.
* Storables are still used on spacecraft, such as deep-space probes that will fly through space for
years and make occasional engine burns. Obviously there is no practical way to store cryogenic
propellants for such a long period of time.
Of course, the thruster systems on such spacecraft are also based on storable fuels. Thruster
systems are in general simple, very low thrust, restartable rockets. The most elaborate use
storable propellants, typically N2O4-UDMH, but "monopropellant" thrusters are also used.
These feature a fuel, usually hydrazine, that burns when passed over a catalyst. Monopropellant
thrusters are much simpler and, in principle, more reliable than a bipropellant system, but they
are much less efficient, with a monopropellant hydrazine thruster having a specific impulse less
than 70% that of LOX-RP. Whether bipropellant or monopropellant, the thrusters are fed using a
pressure or electric pump system, as the high propellant flow rates of a turbopump are not
required.


Another scheme occasionally used is the "cold gas" thruster, which is nothing more than a
compressed-gas jet. Cold gas thrusters are not efficient at all, but they are extremely simple and
very safe since no combustibles or combustion is involved. There are a range of more exotic
thruster schemes, which are discussed in a later chapter.

* A wide range of different liquid propellant combinations have been used for liquid rocket
engines, and the combinations listed above are only those that actually went into widespread use.
Unusual fuels include ammonia and ethanol (grain alco986(t)-2.53658(h)-0.9564.53658(i)-2.5-2.53658(s)-0.4


The Atlas intercontinental ballistic missile (ICBM) and booster was powered by three engines
based on the Navaho engine. The half-stage featured two "LR-89" series engines -- which
confusingly shared a turbopump and so could just as well be regarded as a single engine with
two thrust chambers -- and an "LR-105" series engine. The entire engine assembly went through
a series of designations, from the "MA-1" of flight test prototypes to the "MA-5" that was used
in maturity. Liftoff thrust of the full MA-5 engine assembly was about 1,920 kN (195,500 kgp /
431,000 lbf), with the thrust falling to about a third of that when the half-stage was discarded.
The Atlas would never be very useful as a weapon, but it would prove a wildly successful space
launch vehicle.
The "Thor" medium-range missile, which would evolve into the "Delta" series of launch
vehicles, was powered by a single "LR-79" or "MB-3" engine, also with 756 kN (77,000 kgp /
170,000 lbf) thrust and based on the Navaho engine.
The initial version of the "Titan" missile was powered by a different type of engine, the Aerojet
"LR-87-3", which was a single engine with twin thrust chambers, providing a total of about
1,470 kN (150,000 kgp / 330,000 lbf) thrust, burning LOX and kerosene. The Titan upper stage
was powered by an Aerojet "LR-91-3" engine, similar to the LR-87-3 but with a single thrust
chamber and providing 356 kN (36,300 kgp / 80,000 lbf) thrust. Later versions of the Titan used
modified versions of the LR-87 and LR-91 that burned storable propellants.



In the late 1950s, the US wanted to go to still more powerful LOX-RP engines. This led to the
development of the Rocketdyne "H-1" engine, with eight used on the first stage of the early
"Saturn I" and "Saturn IB" boosters, providing 837 kN (85,300 kgp / 90,000 lbf) thrust each. A
improved version of the H-1 designated the "RS-27" was used for later variants of the Delta
launch vehicle. The H-1 also was the basis for the scaled-up Rocketdyne "F-1" engine, with
6,671 kN (680,000 kgp / 1.5 million lbf) thrust. Five such engines powered the first stage of the
"Saturn V" booster that sent Americans to the Moon.
In the meantime, the US had been pioneering LOX-LH2 propulsion, first developing the Pratt &
Whitney "RL10" engines with 66.7 kN (6,800 kgp / 15,000 lbf) thrust each, with two powering
the "Centaur" upper stage of the "Atlas Centaur" booster. The Centaur upper stage still retains
this engine in the 21st century, in the form of the "RL10A-4" variant, and it is also used on the
upper stages of the Boeing "Delta III" and "Delta IV" boosters, in the form of the more advanced
"RL10B-2" engine. A throttleable version, the "RL10A-5", was used on the McDonnell Douglas
DC-X/A demonstrator spacecraft in the 1990s.



Pratt & Whitney is now working on the "RL60" LOX-LH2 engine, which has a similar form
factor to the RL10 series but is much more powerful, with a thrust in the 267 kN (27,200 kgp /
60,000 lbf) range.


The next step from the RL10 was the much more powerful "J-2" LOX-LH2 engine, providing
105.95 kN (108,000 kgp / 238,000 lbf) thrust. NASA is now planning a simplified and uprated
version of the J-2, the "J-2S", with 1,179 kN (120,200 kgp / 265,000 lbf) thrust, for the new
manned Moon effort.
The J-2 led to the Rocketdyne "Space Shuttle Main Engine (SSME)", which as its name states is
the primary powerplant of the NASA space shuttle. The shuttle uses three SSMEs, with 2,090 kN
(213,000 kgp / 470,000 lbf) thrust each. The SSME's development was notoriously troublesome,
since it was pushing the state of the art and the program was underfunded. It has since become a
reliable and effective engine, and a simplified non-reusable version may be used on the new
manned Moon effort.

The latest American-designed engine is the Rocketdyne "RS-68" engine, used on the Delta 4
series of boosters. The RS-68 is currently the world's biggest LOX-LH2 engine, with a height of
5.18 meters (17 feet), a nozzle diameter of 2.44 meters (8 feet), and a launch thrust of 2,918 kN
(297,500 kgp / 656,000 lbf). The RS-68 is an entire),(s)-1.7465(9-1.7465(9-1.7465(9-0.5356(o(9-1.746.1578


The Soviets followed the SL-1 series of boosters with the much more powerful "Proton" booster,
which put the "Salyut" and "Mir" space stations into orbit. The first stage of the Proton is
powered by six "RD-253" engines using N2O4 / UDMH storable propellants and providing
3,090 kN (315,000 kgp / 695,000 lbf) thrust each.
Later, the Soviets developed a much more powerful LOX-RP four-chamber engine, the "RD170", with 8,182 kN (834,000 kgp / 1.84 million lbf) thrust. The first stage of the "Zenit" launch
vehicle is powered by a single RD-170 engine. The Soviets also developed a variant of the RD170 designated the "RD-180" with two thrust chambers instead of four and, unsurprisingly, half
the thrust.
In an interesting irony, the RD-180 is regarded as being competitive at the very least with
American rocket engine technology, development of which stagnated for a few decades. The
RD-180 has been adopted for the latest variants of the Atlas booster, the "Atlas III" and the
"Atlas V". Both these launch vehicles have abandoned the old half-stage scheme and now use a
single RD-180 engine. The RD-180 engines are provided for these boosters by a collaboration of
NPO Energomash of Russia and Pratt & Whitney in the US.
* As far as storable propellant engines used on spacecraft themselves go, one of the classic
examples was the "Service Propulsion System (SPS)" for the Apollo Command & Service
Module (CSM). The SPS generated 91.2 kN (9,300 kg / 20,500 lb) of thrust. It was a fully
restartable pressure-fed engine, with no turbopumps, featuring redundant subsystems where
possible; its design philosophy was to make it as simple and reliable as possible. Of course, the
Apollo Lunar Module (LM) also used storable propellant engines, with the descent stage engine
providing 44.5 kN (4,535 kg / 10,000 lb) thrust and the ascent stage engine providing 15.6 kN
(1,590 kg / 3,500 lb) thrust.
As mentioned, the space shuttle orbiter has a secondary set of storable propellant engines, known
as the "Orbital Maneuvering System (OMS)", for maneuvers after arrival in space. Each of the
two OMS engines on the orbiter provide 27 kN (2,750 kg / 6,070 lb) of thrust.
* While conventional chemical rocket engines continue to be refined, work has also been
performed on new configurations, such as the "linear aerospike" and "rocket-based combined
cycle" engines.
NASA was working with private industry on an aerospike engine for the cancelled X-33
experimental reusable launch vehicle. An aerospike engine is very different in appearance from a
conventional rocket engine. Instead of a bell-shaped nozzle, the aerospike looks like a wedge
rammed into the rear of a vehicle, with nozzle ports, or "thrust cell chambers", along each side of
the base of the wedge. Thrust cell chamber exhaust is confined on one side by the wedge, with
air pressure providing confinement on the other side. Propellant pumps and other hardware are
contained inside the wedge.
Other rocket companies have continued to experiment with the aerospike concept, launching
small rockets that feature a spike surrounded by exhaust holes. As with the cancelled X-33
engine, confinement is provided by the spike on the inside and air pressure on the outside. The


advantage of the aerospike nozzle is that it automatically adjusts for air pressure, while a
conventional bell nozzle is designed basically around one value of air pressure. Aerospike
advocates believe they can achieve efficiencies a quarter to a third better than those of a
conventional rocket nozzle.
The RBCC engine, as its name more or less hints, is a combination of jet engine and rocket
engine. An RBCC engine consists of a "supersonic combustion ramjet (scramjet)" -- basically
just a "stovepipe" with an air intake in front, fuel injectors and igniters in the middle, and an
exhaust at the back -- but with non-airbreathing rocket nozzles placed inside, within the flow
path. Early RBCC engines will use LOX-hydrocarbon propulsion, but LOX-LH2 propulsion is
expected over the long run.

An RBCC-powered spacecraft would take off using rocket propulsion, with the airflow through
the ramjet duct helping boost thrust through simple momentum transfer. At about Mach 2.5,
ramjet propulsion would take over, moving to scramjet mode at about Mach 6. At Mach 8 to 12,
the spacecraft would be above the atmosphere, and the R(c)-6.8
2 0 Td [(h)-0.953971-10.97553971(e)3.157


time. Asphault was a poor binder, however, tending to crack at cold ambient temperatures, with
the cracks interfering with the burning process; and to flow at high ambient temperatures,
requiring the rockets to be stored nose-down. It also produced a great deal of black smoke, which
caused particularly difficulties for use as "rocket assisted take-off (RATO)" boosters for aircraft.
If one aircraft took off with RATO, the next following it would have to take off through a black
haze that blocked the pilot's field of view.
After the war the Americans moved on to more sophisticated solid propellants, using synthetic
polymers, particularly synthetic rubbers such as butadiene tire rubbers, mixed with ammonium
perchlorate (NH4ClO4) oxidizer (which provides higher performance than potassium perchlorate
and burns cleaner) and large proportions of powdered aluminum. The powdered aluminum
burned at a high temperature, helping improve thrust. Use of high proportions of aluminum had
been held up for some time because the conventional wisdom said that proportions greater than
5% wouldn't burn, but this turned out to be superstition when researchers ignorant of this "rule"
tried higher proportions and found they got unprecedented levels of thrust. Later on, small
proportions of iron oxide were included to provide a high-temperature "thermite reaction" with
the aluminum powder. Modern solid fuels provide a specific impulse only a few percentage
points below that of LOX-RP.
The fact that the propellant mix was based on rubberlike polymers allowed the "grain", or solidrocket fuel element excluding the nozzle), to be cast in large blocks that resisted shrinkage or
cracking, which would have affected the continuity of their burn at the very least and caused
catastrophic failure at worst.



Electrical resistance heating wires could be inserted in the bottom of the grain as igniters. Since a
safe solid fuel had a high ignition temperature, the wires sometimes ignited a primer element that
had a lower ignition temperature, with this primer then igniting the grain. The primer might even
have two "stages", with one element with a low ignition temperature igniting one with an
intermediate ignition temperature, with the second element then igniting the grain.
The central mandrel that defined the hole configuration for the desired flight thrust profile was
coated with Teflon polymer to allow it to be removed from the cured grain. In the early days of
solid fuel rockets, grease was used instead of Teflon, but the grease contaminated the solid fuel
and that approach was abandoned.
Modern solid-fuel rocket engines are ideal for military applications. They can be stored almost
indefinitely and aren't overly fussy about how they are handled, and they can be used and
launched at any time with little preparation. Solid fuels are also denser than liquid fuels, allowing
missiles to be more compact, if not that much lighter. This compactness was a particular plus for
the development of solid-fuel long-range strategic nuclear missiles, since it allowed them to be
stored in a smaller and cheaper missile silo or be carried on a submarine.
Considerable effort was invested in the late 1950s to develop processes to manufacture the large
grains for the "Minuteman" ICBM and the "Polaris" submarine-launched ballistic missile
(SLBM). These processes were not trivial: the ammonium perchlorate oxidizer had to be very
finely and uniformly milled; all the materials in the solid fuel recipe had to very uniformly
mixed; and the grains had to be poured and then cured for several days in a vacuum environment
to prevent bubbles from forming.
Work was also done to synthesize high-performance solid fuels, which included proportions of
nitroglycerine and a particulate form of nitrocellulose, and in some cases a high explosive known
as HMX as well. These high-performance mixes were unsurprisingly less stable and more
troublesome in every respect than conventional mixes, and so they were only used for small final
stages that were more easily handled.
The work on developing long-range solid-fuel missiles also led to technology for solid-rocket
flight control, and for "thrust termination", or shutting down the engine of the upper stage so the
warhead could separate and proceed on its proper trajectory to its target.
Small solid-fuel missiles can use fins for flight control, but that isn't practical for long-range
missiles since they boost out of the atmosphere, making fins so much dead weight. A steerable
nozzle can be used as with a liquid fuel engine, but a simpler scheme was adopted for the
Minuteman and Polaris, using a pivoting ring around the lip of a fixed nozzle to redirect the
thrust. The ring was known as a "jetavator". Later, inert freon gas was selectively injected into
the throat of a fixed nozzle to deflect thrust. As far as thrust termination went, the problem was
that once a solid rocket motor is lit, it burns to termination and there's no way to shut it off.
There is a way to cheat, however, by venting the thrust from the stage to the sides or forward so
the warhead could continue on its way by itself.


These missile projects also led to the use fiberglass for motor casings, reducing the weight of the
rocket motor and so increasing payload. Building large "filament wound" casings was
troublesome, however, and so most casings were made of metal, usually steel, though
lightweight titanium could be used when weight was an issue and cost not too great an issue.
The size of solid-fuel grains grew by bounds through the 1950s, and by the early 1960s they
were so big that they were becoming too bulky and heavy to handle and transport in any sensible
way. To get around this problem of scale, a new technology, "segmentation", was developed in
which the grains were fabricated as cylindrical segments, with the segments locked together in a
single solid rocket motor using "lock rings". By the mid-1960s, segmented solid-rocket boosters
(SRBs) were being manufactured that could provide heavy thrust to help put increasingly large
payloads into orbit.

[1.5] SOLID PROPELLANT ENGINES: A SURVEY /
HYBRID ENGINES / GELS
* As with liquid-fuel rocket engines, trying to write a detailed history of solid-fuel rocket engines
here would be impractical, and a short survey will have to do. The first modern solid-fuel rockets
were developed in the late 1940s, for use as RATO boosters and to power relatively small
missiles, such as air-to-air missiles (AAMs). One particularly important example of this period
was the "T-41" and "T-42" solid rocket motors for t


The first large solid-fuel grain to be developed was the Thiokol "RV-A-10", with a diameter of
79 centimeters (31 inches) and a length of 4.37 meters (14 feet 4 inches). A refined variant was
used for the Sergeant battlefield missile. There had been doubts up to that time that it was
practical to built large solid-fuel rocket grains, but the RV-A-10 proved beyond doubt that it was
possible.
The RV-A-10 led the way to the much larger grains for the three-stage Minuteman ICBM and
the Polaris SLBM. The solid-rocket motor for the first stage of the Minuteman was an order of
magnitude bigger than the RV-A-10, being 1.67 meters (5 feet 5.7 inches) in diameter and 7.42
meters (24 feet 4 inches) long. Both the Minuteman and Polaris had filament-wound final stages,
though the first large-scale filament-wound stage had been flown on a Vanguard satellite launch
vehicle in 1959. High-performance solid fuels were also introduced for the Minuteman and
Polaris in later versions, and a later version of the Minuteman would also have a second stage
with a titanium casing. Ironically, the US imported most of its titanium from the Soviet Union.
Since there were very few civilian uses for titanium at the time, the Soviets had to be aware that
it was mostly being used in American weapon systems.
Work on large solid-fuel grains for the Minuteman and Polaris programs also led to the
development of the first all-solid-fuel space launch vehicle, the LTV "Scout", which would have
a long career putting small payloads into space. In addition, the Minuteman development effort
had a direct connection to the development of segmented solid rocket motors, with Aerojet
testing the concept in 1961 by the simple measures of cutting a Minuteman first stage in half and
then splicing it back together with a lock ring joint.
Both Aerojet and United Research, which would later become a component of the modern
United Technology Center (UTC), performed further work and static test firings of segmented
rocket boosters. In 1962, UTC won a contract from the USAF to build a five-segment SRB for
the Titan III space launch vehicle. The resulting SRBs went into service in 1965, with two SRBs
straddling the liquid-fuel Titan core. The initial Titan III SRB motor was 3.05 meters (10 feet) in
diameter and 25.8 meters (84 feet 8 inches) long. It led in the 1980s to the 5.5 segment motor for
the Titan 34D and the subsequent 7 segment motor for the Titan IV, which produces about 7,565
kN (771,000 kgp / 1.7 million lbf) thrust per SRB.
The biggest solid-rocket motor ever to be put into operation is the SRB for the US space shuttle.
Each SRB is 45.5 meters (149 feet 2 inches) long. The precise composition of the shuttle SRB
grain by weight is:
69.6%
16.0%
12.4%
2.0%
0.4%

ammonium perchlorate oxidizer
aluminum booster
polymer binder
epoxy curing agent
iron oxide combustion catalyst (thermite reaction with aluminum)

The shuttle SRBs are made up of four segments stacked on top of each other. The hole up the
center of the SRBs is cone-shaped at the bottom, leading to an 11-point star that runs to the top.
This scheme gives maximum thrust of 11,770 kN (1.2 million kgp / 2.65 million lbf) at liftoff,
falling off to a sustained level of thrust after that. The nozzle is steerable.


* As mentio

028(t)-2.53 -50.5 0 0 rg q 8

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028(t)-2.5 028o

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further combustion. This makes gels much safer to handle than their liquid forms. To get them to
burn in a combustion chamber, they are fed under pressure through an orifice that turns them into
an aerosol, allowing them to mix properly.
The potential advantages of this approach are high energy density, throttleable operation, and
relative safety in handling. Experiments have been performed in determining the suitability of
gelled propellants for military missiles. The status of research into gelled fuels remains unclear.

Additional Reading
1. Sutton, G.P., and Oscar Biblarz., “Rocket Propulsio

Unit-5
ADVANTAGES OF PROPULSION TECHNIQUES
Electric rocket propulsion – Ion propulsion techniques – Nuclear rocket – Types – Solar sail- Preliminary Concepts
in nozzleless propulsion.

Electric Rocket Propulsion

•

Electric propulsion is a technology aimed at achieving thrust with high exhaust velocities,
which results in a reduction in the amount of propellant required for a given space
mission or application compared to other conventional propulsion methods.

•

Reduced propellant mass can significantly decrease the launch mass of a spacecraft or
satellite, leading to lower costs from the use of smaller launch vehicles to deliver a
desired mass into a given orbit or to a deep-space target.

•

In general, electric propulsion (EP) encompasses any propulsion technology in which
electricity is used to increase the propellant exhaust velocity.

•

There are many figures of merit for electric thrusters, but mission and application
planners are primarily interested in thrust, specific impulse, and total efficiency in
relating the performance of the thruster to the delivered mass and change in the spacecraft
velocity during thrust periods.

•

While thrust is self-explanatory, specific impulse (Isp) is defined as the propellant
exhaust velocity divided by the gravitational acceleration constant g, which results in the
unusual units of seconds. The total efficiency is the jet power produced by the thrust
beam divided by the electrical power into the syste


•

Other propellant materials, such as cesium and mercury, have been investigated in the
past, but xenon is generally preferable because it is not hazardous to handle and process,
it does not condense on spacecraft components that are above cryogenic temperatures, its
large mass compared to other inert gases generates higher thrust for a given input power,
and it is easily stored at high densities and low tank mass fractions. Therefore, the main
focus will be on xenon as the propellant in ion and Hall thrusters, although performance
with other propellants can be examined using the basic information provided here.

•

In all electric propulsion the source of the electric power (nuclear, solar radiation
receivers, or batteries) is physically separate from the mechanism that produces thrust.

•

This type of propulsion has been handicapped by heavy and inefficient power sources.

•

The thrust usually is low, typically 0.005 to 1 N. In order to allow a significant increase
in the vehicle velocity, it is necessary to apply the low thrust and thus a small
acceleration for a long time (week or months).

Electric Rocket Propulsion

Simplified schematic diagram of arc-heating electric rocket propulsion system. The arc plasma
temperature is very high (~ 15,000 K) and the anode, cathode, and chamber will get hot (1000 K)
due to heat transfer.



•

Propellant is heated electrically (by heated resistors or electric arcs) and hot gas is then
thermodynamically expanded and accelerated to supersonic velocity through an exhaust
nozzle (see Fig.) .

•

These electrothermal units typically have thrust ranges of 0.01 to 0.5 N, with exhaust
velocities of 1000 to 5000 m/sec, and ammonium, hydrogen, nitrogen, or hydrazine
decomposition product gases have been used as propellants.

A Typical Ion Rocket

Simplified schematic diagram of a typical ion rocket, showing the approximate distribution of
the electric power

Electric Thruster Types
Electric thrusters are generally described in terms of the acceleration method used to
produce the thrust. These methods can be easily separated into three categories: electro-thermal,
electrostatic and electromagnetic. Common EP thruster types are described in the following.
Resistojet
Resistojets are electrothermal devices in which the propellant is heated by passing through
a resistively heated chamber or over a resistively heated element before entering a downstream


nozzle. The increase in exhaust velocity is due to the thermal heating of the propellant, which
limits the Isp to low levels (<500 s).
Arcjet
An arcjet is also an electrothermal thruster that heats the propellant by passing it though a
high current arc in line with the nozzle feed system. While there is an electric discharge involved
in the propellant path, plasma effects are insignificant in the exhaust velocity because the
propellant is weakly ionized. The Isp is limited by the thermal heating to less than about 700 s
for easily stored propellants.


•

The thruster was tested in a large space simulation chamber in the ESA Technology
centre in the Netherlands at a remarkable 30,000 V and produced an ion exhaust plume
that travelled at 210 km/s – over four times faster than state-of-the-art ion engine designs
achieve.

History of ion propulsion
A NASA engineer prepares an early ion engine for a vacuum chamber test in 1959.
Lined up at right are the major electrical parts.
• Among the most difficult challenges in the early development of ion engines was proving
that injecting electrons could neutralize an ion beam.
• Continually spewing positively charged ions will leave a spacecraft with a negative
charge so great that the ions are attracted back to the spacecraft.
• The solution is an electron gun that dumps the electrons into the ion stream, thus
neutralizing both spacecraft and exhaust. But the beam's interaction with the walls of
even a large vacuum chamber makes it very difficult to conduct meaningful beam
neutralization experiments on Earth.
• These uncertainties led to considerations for flight testing electric engines.
• Another challenge of electronic propulsion involved developing an efficient technique to
produce ions.
• Working at NASA's Lewis, Harold Kaufman invented an electron-bombardment
technique to ionize mercury atoms.
• At NASA/Marshall, a process was under development whereby cesium atoms would
become ionized upon contact with a hot tungsten or rhenium surface.
• Marshall's major development in electrical propulsion centered, however, on a 30kilowatt ion engine development contract, initiated in September 1960 with Hughes
Research Laboratory in Malibu, California.
At first, Marshall directed Hughes to design a laboratory model of an ion engine. The 0.01 lb.thrust model would be followed by the development of a 0.1 lb.-thrust engine. Marshall later
modified the Hughes contract to include a flight test model ion engine, primarily to determine
whether a beam neutralization problem existed in space.
• On Aug. 1, 1961, NASA awarded a contract to the Astro-Electronics Division of RCA to
design and build a payload capsule for flight-testing electric propulsion engines.
• The program called for seven capsules, three for ground tests and four for actual flight
tests. Each capsule was expected to carry two electric engines.
• The first was expected to carry one cesium-fueled ion-engine representing Stuhlinger's
design with the Hughes engine.
• The second was expected to carry one mercury-fueled ion engine representing Kaufman's
design with the Lewis engine. Plans called for the engines to operate from 1 to 2 kW of
power.
•



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Hughes demonstrated an ion engine on Sep. 27, 1961, at its research laboratories in
Malibu. Stuhlinger was among those on hand to greet the scientific and technical writers
who attended the event.

What happens to the ions once they leave the spacecraft?
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Positive ions shoot out of the back of DS1, making it move forward. At the same time, a
beam of electrons with negative charges is shot out of a cathode neutralizer. Things with
positive and negative charges are attracted to each other so the negative electrons fly
towards the positive ions.
Since a positive ion is an atom that is missing one or more electrons, when the electrons
get to the positive ions, they fill in the missing electron's position and make the ion back
into a neutral atom.
Once the ions have been neutralized, the atoms thus formed float off into the vast
emptiness of space.



Nuclear Propulsion

Introduction
For those who are interested in the exploration and development of space by humans,
nuclear propulsion technology is a very attractive option.
Why?
Compared with the best chemical rockets, nuclear propulsion systems (NPS's) are more
reliable and flexible for long-distance missions, and can achieve a desired space mission at a
lower cost.
• The reason for these advantages in a nutshell is that NPS's can get "more miles per
gallon" than a chemical rockets.
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Nuclear propulsion includes a wide variety of propulsion methods that use some form of
nuclear reaction as their primary power source. Many military submarines, and, owing to
crude prices and emissions, a growing number of large civilian surface ships, especially
icebreakers, use nuclear reactors as their power plants (nuclear marine propulsion for
civil use and nuclear navy for military use). In addition, various types of nuclear
propulsion have been proposed, and some of them tested, for spacecraft applications:



Antimatter catalyzed nuclear pulse propulsion
Bussard ramjet
Fission-fragment rocket
Fission sail
Fusion rocket
Gas core reactor rocket
Nuclear electric rocket
Nuclear photonic rocket
Nuclear pulse propulsion
Nuclear salt-water rocket
Nuclear thermal rocket
Radioisotope rocket
In a nuclear thermal rocket a working fluid, usually hydrogen, is heated to a high
temperature in a nuclear reactor, and then expands through a rocket nozzle to create
thrust.
• The nuclear reactor's energy replaces the chemical energy of the reactive chemicals in a
traditional rocket engine.
• Due to the higher energy density of the nuclear fuel compared to chemical ones, about
107 times, the resulting efficiency of the engine is at least twice as good as chemical
engines even considering the weight of the reactor, and even higher for advanced designs.
The most traditional type uses a conventional (albeit light-weight) nuclear reactor running at
high temperatures to heat the working fluid that is moving through the reactor core. This is
known as the solid-core design, and is the simplest design to construct.
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A solid-core design
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The solid-core has the downside that it can only be run at temperatures below the melting
point of the materials used in the reactor core.


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Since the efficiency of a rocket engine is strongly related to the temperature of the
working fluid, the solid-core design needs to be constructed of materials that remain
strong at as high a temperature as possible.
Even the most advanced materials melt at temperatures below that which the fuel can
actually create, meaning that much of the potential energy of the reactions is lost.
Usually, with hydrogen propellant the solid-core design is expected to deliver specific
impulses (Isp) on the order of 800 to 900 seconds, about twice that of liquid hydrogenoxygen designs such as the Space Shuttle main engine.
Other propellants are sometimes proposed such as water or LOX; although they would
provide reduced performance, their greater availability can reduce payload costs where
the mission delta-v is not too high, for example within its lunar space or between Earth
orbit and Martian orbit.
The weight of a complete nuclear reactor is so great that solid-core engines would be
hard-pressed to achieve a thrust-to-weight ratio of 1:1, which would be needed to
overcome the gravity of the Earth on launch.
Nevertheless the overall weight of the engine and fuel for a given amount of total
impulse is lower.
This means that solid-core engines are only really useful for upper-stage uses where the
vehicle is already in orbit, or close to it, or launching from a lower gravity planet, moon
or minor planet where the required thrust is lower.
To be a useful Earth launch engine, the system would have to be either much lighter, or
provide even higher specific impulse. Both would, of course, be even better.

Sketch of nuclear thermal rocket


The Advantage of Nuclear Propulsion Systems
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Nuclear propulsion systems have the ability to overcome the Isp limitations of
chemical rockets because the source of energy and the propellant are independent of each
other.
The energy comes from a critical nuclear reactor in which neutrons split fissile isotopes,
such as 92-U-235 (Uranium) or 94-Pu-239 (Plutonium), and release energetic fission
products, gamma rays, and enough extra neutrons to keep the reactor operating.
The energy density of nuclear fuel is enormous.
For example, 1 gram of fissile uranium has enough energy to provide approximately
one megawatt (MW) of thermal power for a day.
The heat energy released from the reactor can then be used to heat up a low-molecular
weight propellant (such as hydrogen) and then accelerate it through a thermodynamic
nozzle in same way that chemical rockets do. This is how nuclear thermal rockets
(NTR's) work.
There are two main types of NTR's: solid core and gas core.
Solid-core NTR's (See Figure) have a solid reactor core with cooling channels through
which the propellant is heated up to high temperatures (2500-3000 K).
Although solid NTR's don't operate at temperatures as high as some chemical engines
(due to material limitations), they can use pure hydrogen propellant which allows higher
Isp's to be achieved (up to 1000 s), since Isp is approximately 1/Mpropellant0.5, where
Mpropellant is the molecular weight of the propellant.



Schematic Diagram of a Solid Nuclear Thermal Rocket (NTR) Engine
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In gas-core NTR's, the nuclear fuel is in gaseous form and is inter-mixed with the
hydrogen propellant.
Gas core nuclear rockets (GCNR) can operate at much higher temperatures (5000 - 20000
K), and thus achieve much higher Isp's (up to 6000 s).
Of course, there is a problem in that some radioactive fission products will end up in the
exhaust, but other concepts such as the nuclear light bulb (NLB) can contain the uranium
plasma within a fused silica vessel that easily transfers heat to a surrounding blanket of
propellant.
At such high temperatures, whether an open-cycle GCNR, or a closed-cycle NLB, the
propellants will dissociate and become partially ionized.
In this situation, a standard thermodynamic nozzle must be replaced by a magnetic nozzle
which uses magnetic fields to insulate the solid wall from the partially-ionized gaseous
exhaust.
NTR's give a significant performance improvement over chemical engines, and are
desirable for interplanetary missions.



It may also be possible that solid core NTR's could be used in a future launch vehicle to
supplement or replace chemical engines altogether.
• Advances in metallurgy and material science would be required to improve the durability
and T/W ratio of NTR's for launch vehicle applications.
• An alternative approach to NTR's is to use the heat from nuclear reactor to generate
electrical power through a converter, and then use the electrical power to operate various
types of electrical thrusters (ion, hall-type, or magneto-plasma-dynamic (MPD)) that
operate on a wide variety of propellants (hydrogen, hydrazine, ammonia, argon, xenon,
fullerenes).
• This is how nuclear-electric propulsion (NEP) systems work.
To convert the reactor heat into electricity, thermoelectric or thermionic devices could be
used, but these have low efficiencies and low power to weight ratios.
• The alternative is to use a thermodynamic cycle with either a liquid metal (sodium,
potassium), or a gaseous (helium) working fluid.
• These thermodynamic cycles can achieve higher efficiencies and power to weight ratios.
• No matter what type of power converter is used, a heat rejection system is needed,
meaning that simple radiators, heat pipes, or liquid-droplet radiators would be required to
get rid of the waste heat.
• Unlike ground-based reactors, space reactors cannot dump the waste heat into a lake or
into the air with cooling towers.
• The electricity from the space nuclear reactor can be used to operate a variety of
thrusters.
• Ion thrusters use electric fields to accelerate ions to high velocities.
• In principle, the only limit on the Isp that can be achieved with ion thrusters is the
operating voltage and the power supply.
• Hall thrusters use a combination of magnetic fields to ionize the propellant gas and create
a net axial electric field which accelerates ions in the thrust direction.
• MPD thrusters use either steady-state or pulsed electromagnetic fields to accelerate
plasma (a mixture of ions and electrons) in the thrust direction.
• To get a high thrust density, ion thrusters typically use xenon, while Hall thrusters and
MPD thrusters can operate quite well with argon or hydrogen.
• Compared with NTR's, NEP systems can achieve much higher Isp's. Their main problem
is that they have a low power to weight ratio, a low thrust density, and hence a very low
T/W ratio.
• This is due to the mass of the reactor, the heat rejection system, and the low-pressure
operating regime of electrical thrusters.
• This makes NEP systems unfeasible for launch vehicle applications and mission
scenarios where high accelerations are required; however, they can operate successfully
in low-gravity environments such as LEO and interplanetary space.
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In contrast to a chemical rocket or an NTR which may operate only for several minutes to
less than an hour at a time, an NEP system might operate continuously for days, weeks,
perhaps even months, as the space vehicle slowly accelerates to meet its mission delta-V.
• An NEP system is well suited for unmanned cargo missions between the Earth, Moon
and other planets. For manned missions to the outer planets, there would be a close
competition between gas-core NTR's and high-thrust NEP systems.
Conclusions
• The performance gain of nuclear propulsion systems over chemical propulsion systems is
overwhelming.
• Nuclear systems can achieve space missions at a significantly lower cost due to the
reduction in propellant requirements.
• When humanity gains the will to explore and develop space more ambitiously, nuclear
propulsion will be an attractive choice.
• Robert H. Goddard, an American pioneer in astronautics and rocketry, made the
following prophecy on October 3, 1907:
"In conclusion then, the navigation of interplanetary space depends for its solution on the
problem of atomic disintegration... Thus, something impossible will probably be accomplished
through something else which has always been held equally impossible, but which remains so no
longer".
•

Space Mission Analysis
• For any space mission, there are a few basic questions that must be answered:
• What is the destination?
• What is the trip time?
• Do we want to return?
• What is the mass of the payload we want to send there (and bring back)?
Upon answering these questions, one can proceed to determine approximately what the
propellant requirements are using the rocket equation:


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A higher exhaust velocity is desired, because less propellant will be required for a given
space mission.
A performance parameter that rocket engineers like to use is the specific impulse (Isp)
which is simply the ratio of the thrust to the weight consumption rate of propellant
(Isp = F / ( dm/dt * g) = vexhaust / g , g=9.81 m/s2)
for example, if you have an engine with a specific impulse of 500 seconds, that means
you have an exhaust velocity of 4905 m/s and your engine will produce 500 pounds of
force for every pound of propellant it consumes per second.

Figure 1 shows a plot of the mass ratio (Minitial / Mfinal) for various mission ∆V's and
specific impulses. It is pretty clear from this diagram that a high specific impulse is
desired to minimize the propellant requirements. The specific impulse, Isp, is a rocket
engine's equivalent of an automobile's "miles per gallon" rating.
Limitations of Chemical Rocket Engines
In chemical rocket engines, such as the Space Shuttle Main Engine (SSME), the chemical
reaction between the hydrogen and oxygen releases heat which raises the combustion gases
(steam and excess hydrogen gas) up to high temperatures (3000-4000 K).
• These hot gases are then accelerated through a thermodynamic nozzle, which converts
thermal energy into kinetic energy, and hence provides thrust.
• The propellant and the heat source are one in the same. Because there is a limited energy
release in chemical reactions and because a thermodynamic nozzle is being used to
accelerate the combustion gases that do not have the minimum possible molecular
weight, there is a limit on the exhaust velocity that can be achieved.



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The maximum Isp that can be achieved with chemical engines is in the range of 400 to
500 s. So, for example, if we have an Isp of 450 s, and a mission delta-V of 10 km/s
(typical for launching into low earth orbit (LEO)), then the mass ratio will be 9.63.
The problem here is that most of the vehicle mass is propellant, and due to limitations of
the strength of materials, it may be impossible to build such a vehicle to just to ascend
into orbit.
Early rocket scientists got around this problem by building a rocket in stages, throwing
away the structural mass of the lower stages once the propellant was consumed.
This effectively allowed higher mass ratios to be achieved, and hence a space mission
could be achieved with low-Isp engines. This is what all rockets do today, even the Space
Shuttle.
In spite of the relatively low Isp, chemical engines do have a relatively high thrust-toweight ratio (T/W)2.
A high T/W (50-75) is necessary for a rocket vehicle to overcome the force of gravity on
Earth and accelerate into space.
The thrust of the rocket engines must compensate for the weight of the rocket engines,
the propellant, the structural mass, and the payload.
Although it is not always necessary, a high T/W engine will allow orbital and
interplanetary space vehicles to accelerate quickly and reach there destinations in shorter
time periods.

Fission and fusion
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Fission and fusion are different types of nuclear reactions in which energy is released
from the high-powered bonds between particles in the atomic nucleus.
The atomic nucleus is most stable when binding energies between particles are strongest.
This occurs with iron and nickel. For lighter atomic nuclei, energy can be extracted by
combining these nuclei together, a process known as nuclear fusion.
For nuclei heavier than those of iron or nickel, energy can be extracted by splitting them
apart in a process called nuclear fission.
Because the binding force in the atomic nucleus contains enormous energy, fission and
fusion can both provide tons of power, in principle. However, practical considerations
make the exploitation of nuclear power more difficult than something as simple as
starting a fire.
For fission, highly purified feedstock, usually uranium or plutonium isotopes, must be
used. Isotopes are favored because their instability makes them easier to break apart. The
purification of these isotopes is extremely expensive and requires multimillion-dollar
centrifuges.
In fusion, an extremely high threshold energy must be reached to combine atomic
nuclei. In nature, the only place where this occurs is in the core of a star. The
temperature required is in the millions of degrees. Superheated plasma and the
focusing of laser power are two methods to achieve this threshold energy.


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Because the matter that serves as the medium of fusion must be so hot, it must be isolated
from surrounding matter using powerful magnetic fields or inertial containment. This is
the principle behind the Tokamak reactor. Still, fusion requires so much energy that no
one has yet built a reactor that produces more than it consumes.
The downsides to fission power include both radioactive byproducts and its association
with nuclear weapons and meltdowns. In the last dec


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The fission reactions which we use to generate energy in nuclear power plants usually
require an input of energy to start. The most common reaction is the splitting of the
nucleus of specific types uranium atoms.
To start nuclear fusion large amounts of energy are needed to force two atomic nuclei
together. When the nuclei come together energy is released. Depending on the reaction
that energy might be more or less than the energy required to initiate the reaction.
Nuclear fusion is the reaction that ultimately drives the universe. Stars combine atomic
nuclei, which releases the energy that we experience as heat and light. The most common
reaction in stars is the combination of hydrogen nuclei to form helium. The energy input
to cause this reaction to occur comes from the massive gravity in the star that overcomes
all other forces to push atomic nuclei together.
The attempts to generate energy on Earth from nuclear fusion are attempts to hold
hydrogen in such high-energy environments to force this reaction to take place in a
controlled manner. Thus far scientists have been unable to create such a controlled
environment that is sustainable.
There are many more fusion reactions in stars beyond the hydrogen to helium reaction,
however. Deep within stars the pressures due to the gravity of the star push all kinds of
nuclei together to form more and more complex atoms. It is believed that the source of all
of the elements in the universe beyond hydrogen is due to such reactions deep within
stars.
Sometimes the elements that are created in the centers of the stars are unstable outside of
that high-energy environment. When released from the center of stars through numerous
types of cosmological incidents, these unstable atoms will start to break down or undergo
fission. Some of these elements are so unstable that they will break down so fast we will
never observe them in nature. Others are only slightly unstable and will last for millions
or billions of years, on average. These are the radioactive elements that we are familiar
with for fission reactions.
One example of such an unstable atom is uranium-235. So named because of the number
of neutrons and protons in its nucleus, U-235 survives, on average, about a billion years.
This is known as its half-life. If you have one pound of U-235 it will naturally decay over
about a billion years so that there is only a half of a pound of U-235 after that time and
the rest is changed to something else.
If we add energy to U-235, however, in the form of forcing another neutron into the
nucleus of the atom, we create uranium 236 which is highly unstable and will break down
very quickly, releasing energy in the process. This is the basis of the reaction in nuclear
power plants. When a neutron of a specific energy is forced into the nucleus the atom will
become unstable and it will split into two atoms with smaller nuclei. When that occurs,
neutrons are released that are just the right energy to split additional atoms, causing what
is known as a "chain reaction". This chain reaction will continue until many, many more
atoms are split, releasing large amounts of energy.



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Controlled nuclear fusion is the "Holy Grail" of energy production. Fusion reactions
combine relatively common isotopes of hydrogen into helium. The results of these
reactions are stable atoms that don't undergo further reactions. Fission power plants, the
ones that we are using now, however, use rare isotopes of unstable elements. The
resulting atoms that are left over are also unstable. Those unstable atoms release radiation
and must be carefully handled.
As you can see, while both are nuclear reactions, there are enormous differences between
fusion and fission. The study of both reactions is in the realm of nuclear physics and both
can tell us a lot about the nature of the universe.

Solar Sail
Introduction

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Solar Sails are Spacecraft which utilize the momentum transfer of solar photons onto
large, highly reflecting sails for passive propulsion. The idea of sailing is not new:
Ziolkovsky (1921) and Zander (1924) introduced this 'exotic' idea for propulsion in
space. The advantage is obvious: Solar Sails do not need to carry an active main
propulsion system nor any propellant for it. Therefore, extended missions in our solar
system and beyond seem possible. Through the continuous low thrust, trajectories could
be realized which would allow planetary missions with high science priority to be
performed. High energetic missions in particular, such as a Mercury orbiter mission,
main belt asteroid and comet rendezvous as well as sample return missions could be
realized within reasonable flight times.
Some of these missions can not be reasonably performed with conventional propulsion.
Against common impression, the low thrust level, moreover, does not necessarily
increase flight time when compared to a conventional, chemically propelled spacecraft.
For missions with high energy requirement very often multiple planetary flybys have to
be introduced for chemical propulsion in order to allow the mission to be feasible, which
in most cases increases flight time. Solar sail spiral trajectories do not necessarily require
these gravity assists and can cut down trip times.



Solar sails



The goals of the study were: to evaluate the benefits of solar sails for planetary missions; to
develop a solar sail technology roadmap; and,
to study the feasibility of a joint DLR/NASA solar sail demonstration mission that could be
performed at low-cost.



Artist's Impression; Solar Sail scenario in Mars Orbit

Feasibility Study Results
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The joint study concluded that a number of mid and far-term missions could be enhanced
or enabled using solar sails. The study also concluded that a low-cost technology
demonstration mission in Earth orbit is feasible. A demonstration mission is the
recommended approach for the development of this advanced propulsion concept. This
would demonstrate and validate the basic principles of sail fabrication, packaging,
storage, deployment, and control.
The mission scenario comprises a “piggyback” launch of a small spacecraft plus solar sail
with a total mass of less than 100kg on an ARIANE 5 into a geosynchronous transfer
orbit, where a 40m x 40m sail would be deployed. The aluminized sail film is to be
supported by deployable light-weight composite structure booms which are currently
being developed at the Institute of Structural Mechanics in Braunschweig. By proper
orientation of the sail towards the Sun during each orbit, the orbital energy would
increase, such that after roughly 500 days the orbital radius of the Moon would be
achieved. On-board cameras are foreseen to observe the sail deployment. An additional



science payload could provide remote sensing data of the Earth and also of previously not
very well explored lunar areas.
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Solar sails (also called light sails or photon sails, especially when they use light sources
other than the Sun) are a proposed form of spacecraft propulsion using large membrane
mirrors.
Radiation pressure is about 10-5 Pa at Earth's distance from the Sun and decreases by the
square of the distance from the light source (e.g. sun), but unlike rockets, solar sails
require no reaction mass.
Although the thrust is small, it continues as long as the light source shines and the sail is
deployed.
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic
radiation. If absorbed, the pressure is the power flux density divided by the speed of light.
If the radiation is totally reflected, the radiation pressure is doubled. For example, the
radiation of the Sun at the Earth has a power flux density of 1,370 W/m2, so the radiation
pressure is 4.6 µPa (absorbed)
In theory a lightsail (actually a system of lightsails) powered by an Earth-based laser
could even be used to decelerate the spacecraft as it approaches its destination
Solar collectors, temperature-control panels and sun shades are occasionally used as
expedient solar sails, to help ordinary spacecraft and satellites make minor attitude
control corrections and orbit modifications without using fuel.
This conserves fuel that would otherwise be used for maneuvering and altitude control. A
few have even had small purpose-built solar sails for this use.
For example, EADS Astrium's Eurostar E3000 geostationary communications satellites
use solar sail panels attached to their solar cell arrays to off-load transverse angular
momentum, thereby saving fuel (angular momentum is accumulated over time as the
gyroscopic momentum wheels control the spacecraft's attitude - this excess momentum
must be offloaded to protect the wheels from over spin).
The science of solar sails is well-proven, but the technology to manage large solar sails is
still undeveloped.
Mission planners are not yet willing to risk multimillion dollar missions on unproven
solar sail unfolding and steering mechanisms.
This neglect has inspired some enthusiasts to attempt private development of the
technology, such as the Cosmos 1.
The concept was first proposed by German astronomer Johannes Kepler in the
seventeenth century.
It was again proposed by Friedrich Zander in the late 1920s and gradually refined over
the decades.
Serious interest in lightsails began with an article by engineer and science fiction author
Robert L. Forward in 1984.



How Solar Sail works
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The spacecraft arranges a large membrane mirror which reflects light from the Sun or
some other source.
The radiation pressure on the mirror provides a small amount of thrust by reflecting
photons.
Tilting the reflective sail at an angle from the Sun produces thrust at an angle normal to
the sail.
In most designs, steering would be done with auxiliary vanes, acting as small solar sails
to change the attitude of the large solar sail (see the vanes on the illustration labeled
Cosmos 1, below).
The vanes would be adjusted by electric motors.
In theory a lightsail driven by a laser or other beam from Earth can be used to decelerate
a spacecraft approaching a distant star or planet, by detaching part of the sail and using it
to focus the beam on the forward-facing surface of the rest of the sail.
In practice, however, most of the deceleration would happen while the two parts are at a
great distance from each other, and that means that, to do that focusing, it would be
necessary to give the detached part an accurate optical shape and orientation.
Sails orbit, and therefore do not need to hover or move directly toward or away from the
sun. Almost all missions would use the sail to change orbit, rather than thrusting directly
away from a planet or the sun. The sail is rotated slowly as the sail orbits around a planet
so the thrust is in the direction of the orbital movement to move to a higher orbit or
against it to move to a lower orbit. When an orbit is far enough away from a planet, the
sail then begins similar maneuvers in orbit around the sun.
The best sort of missions for a solar sail involves a dive near the sun, where the light is
intense, and sail efficiencies are high. Going close to the Sun may be done for different
mission aims: for exploring the solar poles from a short distance, for observing the Sun
and its near environment from a non-Keplerian circular orbit the plane of which may be
shifted some solar radii, for flying by the Sun such that the sail gets a very high speed.
An unsuspected feature, until the first half of the 1990s, of the solar sail propulsion is to
allow a sailcraft to escape the solar system with a cruise speed higher or even much
higher than a spacecraft powered by a nuclear electric rocket system. The spacecraft
mass-to-sail area ratio does not need to achieve ultra-low values, even though the sail
should be an advanced all-metal sail. This flight mode is also known as fast solar sailing.
Proven mathematically (like many other astronautical items well in advance of their
actual launches), such sailing mode has been considered by NASA/Marshall as one of the
options for a future precursor interstellar probe exploring the near interstellar space
beyond the heliosphere. [5]
Most theoretical studies of interstellar missions with a solar sail plan to push the sail with
a very large laser Beam-powered propulsion Direct Impulse beam. The thrust vector
(spatial vector) would therefore be away from the Sun and toward the target.


Applications
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Robert L. Forward pointed out that a solar sail could be used to modify the orbit of a
satellite around the Earth.
In the limit, a sail could be used to "hover" a satellite above one pole of the Earth.
Spacecraft fitted with solar sails could also be placed in close orbits about the Sun that
are stationary with respect to either the Sun or the Earth, a type of satellite named by
Forward a statite.
This is possible because the propulsion provided by the sail offsets the gravitational
potential of the Sun. Such an orbit could be useful for studying the properties of the Sun
over long durations.
Such a spacecraft could conceivably be placed directly over a pole of the Sun, and remain
at that station for lengthy durations.
Likewise a solar sail-equipped spacecraft could also remain on station nearly above the
polar terminator of a planet such as the Earth by tilting the sail at the appropriate angle
needed to just counteract the planet pnc678(e)3.16033.Td 67424( )-80.6325(E)at671( )-210.881(b)-10.97


Nozzleless Propulsion
Introduction
The concept of nozzleless rocket motors stems from the possibility of obtaining the required
booster configuration in an integrated rocket ramjet type of vehicle. Despite the fact that
expansion of the chamber gases cannot be effected in nozzleless system as efficiently as in
nozzled rockets, an overall gain is still possible because of higher propellant loading in the
given volume. Typically a performance gain of upto 15% has been projected by ISRO. In
addition the system becomes much simpler leading to higher reliability.
The most critical aspects of a nozzleless system are the choice of propellant and
geometric configuration supplemented with a detailed understanding of erosive burning at
lateral velocities extending into supersonic flow regime. The theoretical modeling of such
systems has not yet come to a proven state.
Earlier studies about the properties of a propellant suitable for nozzleless configuration
have shown stringent demands on the burning rate characteristics, mechanical strength and
strain capacity.
Nozzleless propulsion system, the most advanced concept was successfully demonstrated
by AFRPL, USA in 1979. It was expected that such a system will reduce the cost of
production in view of the elimination of the nozzle assembly, the reduction of the case
insulation requirements etc., and also will improve the reliability on account of the system
simplicity.
The properties required for an ideal propellant for a nozzleless configuration shows that:1. The burning rate of the propellant must be higher in order to prevent a long and
inefficient tail off.
2. A superior strain capacity at low temperature in order to allow optimum web fraction,
propellant loading and total performance is required and,
3. A higher stress capacity at high temperature so that the grain structure can survive the
shear loads produced by the large axial pressure differential between the head end and
aft-end of a burning nozzleless grain is also required.
The above requirements reported by the ISRO shows that the cost of development and
propellant ingredient are typically higher for nozzleless motor. However, it is reported that
inspite of these factors, a straight forward nozzleless booster can be designed to yield
comparable performance at a price reduction of about 10% and a performance gain of upto
15% if the propellant strength and burning-rate/pressure exponent can be optimized.



Nozzleless Propulsion System
In the conventional solid rocket motor, the propellant is burnt inside a rocket chamber
and the hot gases thus generated are accelerated to supersonic condition through a
convergent-divergent type nozzle. The heat energy of the gases is converted into kinetic
energy inside the nozzle.
Nozzleless propulsion system attempts to perform the main task of the nozzle inside the
grain port itself, thereby saving the weight of the nozzle which can be replaced by
additional propellant. The basic configuration of such system is shown below.

On ignition of the grain, high volume of gas will be generated in the star portion of the
grain (section AA) because of large surface area available. This gas will converge at the
section CC and will flow through the tubular portion of the grain at section BB.
The gas is expected to reach sonic condition at the interface of the conical and cylindrical
section and accelerate to supersonic condition inside the tubular portion.
Simultaneously, small amount of mass addition will take place inside the tubular portion
due to the burning, which will progressively increase as a function of time.
Due to the existence of long tubular portion, erosive burning of the grain in the tubular
portion is expected. This will be further accelerated due to attainment of supersonic
condition of the gas.



Figures 2 shows the different phases of grain burning and the formation of nozzle shape
due to the erosive burning inside the grain as described above.
After the completion of the burning of the star portion, the gas will continue to be
generated (much lesser quantity) by the conical portion of the grain, more or less as an end
burning system. However, mass addition at the tubular portion will continue.
This is expected to function till the propellant burns completely at the aft end section due to
erosive burning.
Beyond this time, a nozzle hardware system will be necessary. This will be provided with a
silica phenolic throat insert embedded inside the grain as shown in the figure.

Additional Reading:
•

Sutton, G.P., “Rocket Propulsion Elements”, John Wiley & Sons Inc., New York, 7th Edn., 2001.


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