Axial and radial flow turbines - Vidyarthiplus

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

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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,

+=

u

c

u

cuW tt 322

The first term

u

ct 2 in the bracket depends on the nozzle or fixed angle (α2) and the ratio

2c

u=σ . The contribution of the second term

u

ct3 to the work is generally small. It is also

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.



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,

u

c

u

W

a=

=Ψ

φ

2

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

( ) ( ) ( )2

2

3

3

2

3

2

2

2

3

2

22

1

2

1

2

1wwuucc −+−+−=

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.



( ) ( )2

3

3

2

2

2

2

3

2

22

1

2

1

2

1uuwwcErb −+−+=

For axial machines, u = u2 = u3

( ) ( )( )2

2

2

3

2

2

2

2

2

3

2

3

2

2

wwc

wwccb

−+

−+−== ηε

Maximum utilization factor for a single impulse stage.

2

2

32

2

1

)(

c

ccu tt +=ε

After rearranging the terms, we have

)sin(4 2

2 σασεη −==b

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 mid-

span 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 10

6

= 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

• 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

• 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



• 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



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.



• 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



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.



• 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 real-

gas 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.

•

Advantages and disadvantages of scramjets

Special cooling and materials

• 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.



• 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

• 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

• 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

• 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.

• 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. High temperature can be employed

2. In the absence of rotating machinery its construction is very simple and cheap

3. It can operate effectively at high supersonic Mach numbers

4. It is not very sensitive to the quality of fuel

5. It provides high thrust per unit weight and frontal area



Ramjet engine’s Main disadvantages are;

1. It requires a launching device at supersonic speed

2. It is unsuitable for subsonic flight

3. It has low thermal efficiency and high TSFC

4. 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 4-

1 outside the engine. However, the ideal efficiency of the ramjet engine is still given by

Equation,

( ) γγη

/1

11

11

−−=−=

rti

Here, the temperature ratio, with the above assumption is given by

2

1

01

1

02

1

2

2

11 iM

T

T

T

T

T

Tt

−+====

γ



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

2

1

2

1

2

12

11

2

1

2

11

11

M

M

Mi −

+

−

=−

+

−=γ

γ

γη

)(1

1

21

11

2

1

Mf

M

i =

−+

=

γ

η

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,

γγγγ

γγ

/)1(

4

3

/)1(

1

2/)1(

4

3

1

2

−−

−

=

====

P

P

P

Pr

T

T

T

Tt

s

s

( ) γγη

/1

11

11

−−=−=

rtAS

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

1

1

21

1

2

1M

i

−+

=

γ

η

= 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 0.5

2/4 = 0.1963 m

2



11uAma ρ=

= 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

2

1

/)1(

1

2

2

1

1

M

P

P

D −

−

=

−

γη

γγ

ηD = 0.9, M1 = 1.5

P2/P1 = 3.2875 Ans.

P2 = 3.2875 x 0.44 = 1.446

(e) 45.1

2

11 2

1

1

01 =−

+= MT

T γ

= 1.45 x 245.9 = 356.55 K

ffBpa QmTTCm••

=− η)( 0203

fBp

a

fQTTC

m

mf η/)( 0203 −==

•

•

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,

AnsP

P22.3

440.0

417.1

4

03 ==

(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.

3976.141.12.012

11 22

4

4

04 =+=−

+= xMT

Ts

s

γ

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 + C2

4/2Cp

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)

umCmF

skgmmm

skgxm

a

fa

f

••

•••

•

−=

=+=+=

==

4

/593.59841.1752.57

/841.103188.0752.57

= (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 fuel-

rich 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. 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.

3. Gorden, C.V., “Aero thermodynamics of Gas Turbine and Rocket Propulsion”, AIAA Education

Series, New York, 1989.

4. 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

1

Solar sail

(not a rocket in

fact)

10-5

10-4

Years ∞ Satellite Altitude

control

2

Electric Prop.

(Electro thermal,

Electro Static,

Electro

Magnetic)

10-6

- 10-2

10-5

-10-3

Years 150 - 6000

Satellite control,

stabilization, orbit

maneuver

3 Stored cold gas

(N2, NH3 etc.) 10

-2 - 10

-1 ~ 10

-3 Years 50 - 100 -do-

4 Nuclear Rocket upto 105 20-30

Minute to

hours 800

Interplanetary and

space travel

5

Chemical Rocket

(Solid, Liquid

and Hybrid)

upto 107 upto 80

Seconds to

minutes@

150-450

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) Type of propellant: Solid, Liquid (mono propellant / bipropellant and hybrid rockets)

(b) Application: Launch vehicle, ABM’s, JATO’s, ICBM, IRBM, SAM etc.

(c) Size of Unit (and thrust level sometimes): 10 ton, 100 kg etc.

(d) 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 C for F in Equation (2.23), thus obtaining

• 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.



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. Combustion chamber pressure

2. Initial temperature of the solid propellant prior to start

3. Combustion gas temperature

4. Velocity of the gas flow parallel to the burning surface

5. 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,



dtrAdtmm bb ∫∫ ==•

ρ

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

KK

K

pp

p

T

P

PT

p

T

r

rT

r

∂

∂=

∂

∂=

∂

∂=

∂

∂=

1ln

1ln

π

σ

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



pKn

σπ−

=1

1

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

dT

da

aT

aP

p

n

p

1)(ln=

∂

∂=σ



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 (>__

cP ) 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__

cP . 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 ( n

caP ) + 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.

)1/()1(

1

1111

2)(

−+

++=

kk

tbbkRT

kPAV

dt

drA ρρ



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,

2

1

/)1(

1

212 1

1

2v

P

PRT

k

kv

kk

+

−

−=

−



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 2

1v 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.

−

−=

− kk

P

PRT

k

kv

/)1(

1

212 1

1

2

−

−=

− kk

o

P

P

M

TR

k

k/)1(

1

2

'

11

2

Thrust and Thrust Coefficient

2322 )( AppvmF −+=•

1PACF tF=



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.

t

kkkk

FA

A

p

pp

p

p

kk

kC 2

1

32

/)1(

1

2

)1/()1(2

11

2

1

2 −+

−

+−=

−−+

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 one-

dimensional 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

•

==

m

FgIc osp

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’

o

p

m

m=ζ

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,

•

∗ =

m

ApC t1

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 = osp gmI•

= 240 x 23.3 x 9.81 = 54.857 N

(v) Thrust-to-weight ratio of the vehicle is

Initial value = 54,857 / (200 x 9.81) = 28

Final value = 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 spIandccvm ,,, 2

∗•

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 0.0855

2 /4 = 0.00574 m

2

A2 = π D2/4 = π x 0.2703

2 /4 = 0.0574 m

2

The actual exhaust velocity

•

−−=

m

AppFv

))(( 232

2

= (62,250 – (0.070-0.1013) 106

x 0.0574) / 24.9

= 2572 m/sec

•

∗ =

m

ApC t1

= 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.



•

−+=

m

Appvc 232

2

)(

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

2). The propellant is pumped into a combustion chamber at some rate (mdot) where the fuel

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 half-

angles 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 rockets-

Numerical 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:

1) Take mass stored in a vehicle and throw it backwards (rocket propulsion). Use the

reaction force to propel the vehicle.

Propellant ---> burn ---> 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 energy

& momentum (turbojet).

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: 103-10

7 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

Specific Impulse: 100-300 sec

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

Specific Impulse: 100-400 sec

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. What is the

change

in velocity if the spacecraft burns its engine for one minute?

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.




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






Specific Heat Ratio



Liquid Oxygen & Kerosene*

* n-Dodecane, C12H26






Specific Heat Ratio



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.



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 (1.28),

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:



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,

Pt = Pc x [1 + (k - 1) / 2]-k/(k-1)

Pt = 5 x [1 + (1.20 - 1) / 2]

-1.20/(1.20-1)

Pt = 2.82 MPa = 2.82x106 N/m

2

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) ] At = (100 / 2.82x10

6) x SQRT[ (8,314 x 3,273) / (24 x 1.20) ]

At = 0.0345 m2

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

Nm2 = (2 / (k - 1)) x [(Pc / Pa)

(k-1)/k - 1]

Nm2 = (2 / (1.20 - 1)) x [(5 / 0.05)

(1.20-1)/1.20 - 1]

Nm2 = 11.54

Nm = (11.54)1/2 = 3.40

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

Ae = (At / Nm) x [(1 + (k - 1) / 2 x Nm2)/((k + 1) / 2)]

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

Ae = (0.0345 / 3.40) x [(1 + (1.20 - 1) / 2 x 11.54)/((1.20 + 1) / 2)]

(1.20+1)/(2(1.20-1))

Ae = 0.409 m2

The velocity of the exhaust gases at the nozzle exit is given by

Ve = SQRT[ (2 x k / (k - 1)) x (R' x Tc / M) x (1 - (Pe / Pc)(k-1)/k

) ] Ve = SQRT[ (2 x 1.20 / (1.20 - 1)) x (8,314 x 3,600 / 24) x (1 - (0.05 / 5)

(1.20-1)/1.20) ]

Ve = 2,832 m/s

Finally, we calculate the thrust,

F = q x Ve + (Pe - Pa) x Ae F = 100 x 2,832 + (0.05x10

6 - 0.05x10

6) 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

Nm

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

(1.20-1)/1.20 - 1]



Nm 2 = 9.19 Nm = (9.19) 1/2 = 3.03 Ae = (0.0345 / 3.03) x [(1 + (1.20 - 1) / 2 x 9. 19)/((1.20 + 1) / 2)] (1.20+1)/(2(1.20-1)) Ae = 0.243 m 2 Ve = SQRT[ (2 x 1.20 / (1.20 - 1)) x (8,314 x 3, 600 / 24) x (1 - (0.10 / 5) (1.20-1)/1.20 ) ] Ve = 2,677 m/s F = 100 x 2,677 + (0.10x10 6 - 0.05x10 6) x 0.243 F = 279,850 N

�� ,�"�� .�� D�@ � ��

Pe = 0.05 / 2 = 0.025 MPa At = 0.0345 m 2 Nm 2 = (2 / (1.20 - 1)) x [(5 / 0.025) (1.20-1)/1.20 - 1] Nm 2 = 14.18 Nm = (14.18) 1/2 = 3.77 Ae = (0.0345 / 3.77) x [(1 + (1.20 - 1) / 2 x 14 .18)/((1.20 + 1) / 2)] (1.20+1)/(2(1.20-1)) Ae = 0.696 m 2 Ve = SQRT[ (2 x 1.20 / (1.20 - 1)) x (8,314 x 3, 600 / 24) x (1 - (0.025 / 5) (1.20-1)/1.20 ) ] Ve = 2,963 m/s F = 100 x 2,963 + (0.025x10 6 - 0.05x10 6) x 0.696 F = 278,900 N )��,�"��,�"�� )�� H��



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.





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

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 single-

stage 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

all stages are sized. Results reveal that to maximize payload fraction for a given V requirement:

1. Stages with higher Isp should be above stages with lower Isp.

2. More V should be provided by the stages with the higher Isp.

3. Each succeeding stage should be smaller than its predecessor. 4. Similar stages should provide the same V.



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 Type of Load/Stress Internal pressure Tension biaxial, vibration

Axial thrust Axial, vibration

Motor nozzle Axial, bending, shear

Thrust vector control actuators Axial, bending, shear

Thrust termination equipment Biaxial, bending

Aerodynamic control surface or wings

mounted to case

Tension, compression, bending, shear, torsion

Staging Bending, shear

Flight maneuvering Axial, bending, shear, torsion

Vehicle mass and wind forces on launch pad Axial, bending, shear

Dynamic loads from vehicle oscillations Axial, bending, shear

Ground transport, Ground handling, including

lifting

Tension, compression, bending, shear, torsion,

vibration

Earthquakes (large motors) Axial, bending, shear



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-to-

housing 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( )-2156(o)-0.9564(a)3.15789(.4973(a)3.15789(( )-80.6325(m)-3.4916033( )-100.671(o)-0. )-80.6325(r)2.3678(o)-0.956418(y)-000.67143.15544( )-80.6325(l)-2(5.957028(f)2.36842( )-0.478208(t)-2.53536(h)-56417(a13(s)-1.746s)-1.7465(t)-2.535789(d(c)3.15789( )-)9.06272( )-0.479(d)-10.9756( )-80.6313(t)-2.5353s)389]TJ/R11 12 T)-0.956417(r)2.3.0831(p)-10.9756 o



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 hydroxy-

terminator 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,

ROCKET PROPELLANT PERFORMANCE

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

Oxidizer Fuel



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 stage-

to-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 stop-

valves, 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

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,

2

2

1ccpc gttuZ −=

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 Description Advantages Disadvantages

water

rocket

Partially filled pressurised

carbonated drinks container with

tail and nose weighting

Very simple to

build

Altitude typically limited to a

few hundred feet or so (world

record is 623 meters/2044 feet)

cold gas

thruster

A non combusting form, used for

attitude jets

Non

contaminating

exhaust

Extremely low performance

hot water

rocket

Hot water is stored in a tank at

high temperature/pressure and

turns to steam in exhaust

Simple, fairly

safe

Low performance due to heavy

tank

Chemically powered


Solid rocket

Ignitable, self

sustaining solid

fuel/oxidiser mixture

("grain") with central

hole and nozzle

Simple, often no moving

parts, reasonably good

mass fraction, reasonable

Isp. A thrust schedule can

be designed into the

grain.

Once lit, extinguishing it is

difficult although often

possible, cannot be

throttled in real time;

handling issues from

ignitable mixture, lower

performance than liquid

rockets, if grain cracks it

can block nozzle with

disastrous results, cracks

burn and widen during

burn. Refuelling grain

harder than simply filling

tanks, Lower specific

Impulse than Liquid

Rockets.

Hybrid rocket

Separate oxidiser/fuel,

typically oxidiser is

liquid and kept in a

tank, the other solid

with central hole

Quite simple, solid fuel

is essentially inert

without oxidiser, safer;

cracks do not escalate,

throttleable and easy to

switch off.

Some oxidisers are

monopropellants, can

explode in own right;

mechanical failure of solid

propellant can block

nozzle, central hole widens

over burn and negatively

affects mixture ratio.

Monopropellant

rocket

Propellant such as

Hydrazine, Hydrogen

Simple in concept,

throttleable, low

catalysts can be easily

contaminated,



Peroxide or Nitrous

Oxide, flows over

catalyst and

exothermically

decomposes and hot

gases are emitted

through nozzle

temperatures in

combustion chamber

monopropellants can

detonate if contaminated or

provoked, Isp is perhaps 1/3

of best liquids

Liquid

Bipropellant

rocket

Two fluid (typically

liquid) propellants are

introduced through

injectors into

combustion chamber

and burnt

Up to ~99% efficient

combustion with

excellent mixture

control, throttleable, can

be used with turbopumps

which permits incredibly

lightweight tanks, can be

safe with extreme care

Pumps needed for high

performance are expensive

to design, huge thermal

fluxes across combustion

chamber wall can impact

reuse, failure modes

include major explosions, a

lot of plumbing is needed.

Dual mode

propulsion

rocket

Rocket takes off as a

bipropellant rocket,

then turns to using just

one propellant as a

monopropellant

Simplicity and ease of

control

Lower performance than

bipropellants

Tripropellant

rocket

Three different

propellants (usually

hydrogen, hydrocarbon

and liquid oxygen) are

added to the airstream

to increase maximum

altitude

dangerous. Much heavier

than simple rockets.

Precooled jet

engine / LACE

(combined cycle

with rocket)

Intake air is chilled to

very low temperatures

at inlet before passing

through a ramjet or

turbojet engine. Can be

combined with a

rocket engine for

orbital insertion.

Easily tested on ground.

High thrust/weight ratios

are possible (~14)

together with good fuel

efficiency over a wide

range of airspeeds, mach

0-5.5+; this combination

of efficiencies may

permit launching to

orbit, single stage, or

very rapid

intercontinental travel.

Exists only at the lab

prototyping stage.

Examples include RB545,

SABRE, ATREX

Electrically powered


Resistojet rocket

(electric heating)

A monopropellant is

electrically heated by

a filament for extra

performance

Higher Isp than

monopropellant

alone, about 40%

higher.

Uses a lot of power and hence

gives typically low thrust

Arcjet rocket

(chemical burning

aided by electrical

discharge)

Similar to resistojet in

concept but with inert

propellant, except an

arc is used which

allows higher

temperatures

1600 seconds Isp

Very low thrust and high power,

performance is similar to Ion

drive.

Pulsed plasma

thruster (electric

arc heating; emits

plasma)

Plasma is used to

erode a solid

propellant

High Isp , can be

pulsed on and off

for attitude control

Low energetic efficiency

Variable specific

impulse

magnetoplasma

rocket

Microwave heated

plasma with magnetic

throat/nozzle

Variable Isp from

1000 seconds to

10,000 seconds

similar thrust/weight ratio with

ion drives (worse), thermal

issues, as with ion drives very

high power requirements for

significant thrust, really needs

advanced nuclear reactors, never

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.


Solar

thermal

rocket

Propellant is

heated by

solar collector

Simple design. Using hydrogen

propellant, 900 seconds of Isp is

comparable to Nuclear Thermal rocket,

without the problems and complexity

of controlling a fission reaction. Using

higher–molecular-weight propellants,

for example water water, lowers

performance.

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


light beam

powered

rocket

Propellant is heated

by light beam (often

laser) aimed at

vehicle from a

distance, either

directly or indirectly

via heat exchanger

simple in

principle, in

principle very high

exhaust speeds can

be achieved

~1 MW of power per kg of payload is

needed to achieve orbit, relatively high

accelerations, lasers are blocked by

clouds, fog, reflected laser light may be

dangerous, pretty much needs hydrogen

monopropellant for good performance

which needs heavy tankage, some

designs are limited to ~600 seconds due

to reemission of light since

propellant/heat exchanger gets white hot

microwave

beam

powered

rocket

Propellant is heated

by microwave beam

aimed at vehicle

from a distance

microwaves avoid

reemission of

energy, so ~900

seconds exhaust

speeds might be

achieveable

~1 MW of power per kg of payload is

needed to achieve orbit, relatively high

accelerations, microwaves are absorbed

to a degree by rain, reflected

microwaves may be dangerous, pretty

much needs hydrogen monopropellant

for good performance which needs

heavy tankage, transmitter diameter is

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:


Radioisotope

rocket/"Poodle

thruster"

(radioactive decay

energy)

Heat from

radioactive decay

is used to heat

hydrogen

about 700-800

seconds, almost no

moving parts

low thrust/weight ratio.

Nuclear thermal

rocket (nuclear

fission energy)

propellant (typ.

hydrogen) is

passed through a

nuclear reactor to

heat to high

temperature

Isp can be high,

perhaps 900 seconds

or more, above unity

thrust/weight ratio

with some designs

Maximum temperature is limited

by materials technology, some

radioactive particles can be

present in exhaust in some

designs, nuclear reactor shielding

is heavy, unlikely to be permitted

from surface of the Earth,

thrust/weight ratio is not high.

Gas core reactor

rocket (nuclear

fission energy)

Nuclear reaction

using a gaseous

state fission

reactor in intimate

contact with

propellant

Very hot propellant,

not limited by

keeping reactor solid,

Isp between 1500 and

3000 seconds but

with very high thrust

difficulties in heating propellant

without losing fissionables in

exhaust, exhaust inherently

highly radioactive, massive

thermal issues particularly for

below Earth's magnetosphere.

Antimatter

catalyzed nuclear

pulse propulsion

(fission and/or

fusion energy)

Nuclear pulse

propulsion with

antimatter assist

for smaller bombs

Smaller sized vehicle

might be possible

Containment of antimatter,

production of antimatter in

macroscopic quantities isn't

currently feasible. Theoretical

only at this point.

Fusion rocket

(nuclear fusion

energy)

Fusion is used to

heat propellant

Very high exhaust

velocity

Largely beyond current state of

the art.

Antimatter rocket

(annihilation

energy)

Antimatter

annihilation heats

propellant

Extremely energetic,

very high theoretical

exhaust velocity

Problems with antimatter

production and handling; energy

losses in neutrinos, gamma rays,

muons; thermal issues.

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 some solid

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

Usually, higher overall density; this allows a

more compact package, a small vehicle (less

drag)

Requires an ignition system

Can provide TVC, but at increased complexity Once ignited, cannot change predetermined

thrust or duration

Some propellants have nontoxic, clean exhaust

gases, but at a performance penalty

Integrity of grain (cracks, unbounded areas) is

difficult to determine in the field

Some grain and case design can be used with

several nozzles

Large boosters take a few seconds to start

Thrust termination devices permit control over

total impulse

Cannot be tested prior to use

Can be designed for recovery and reuse Thermal insulation is required in almost all

rocket motors

Some tactical missile motors have been

produced in large quantities

Needs a safety provision to prevent inadvertent

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 parts or

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, low-

total-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



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

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 ("convergent-

divergent" 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 solid-

state "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 submarine-

launched 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

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.

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

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 "RD-

170", 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 RD-

170 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,

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 solid-

rocket 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% ammonium perchlorate oxidizer

16.0% aluminum booster

12.4% polymer binder

2.0% epoxy curing agent

0.4% 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.



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 30-

kilowatt 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.



• 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?

• 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.

• 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.

A solid-core design • 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.



• 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 hydrogen-

oxygen 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

• 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

• 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.



• 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:

• 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.



• 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-to-

weight 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

• 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.



• 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

• 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.



• 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

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 • 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.

• 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

• 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

• 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

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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