Rocket and Missiles

SRI RAMAKRISHNA ENGINEERING COLLEGE , CBE-22

(AN AUTONOMOUS INSTITUTION AFFLIATED TO ANNA UNIVERSITY OF TECHNOLOGY, CHENNAI) COIMBATORE-22

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FOREWORD

The course material, “Rocket and Missiles” come to your hand with numerous people contributions. The material is intended for students studying Aeronautical Engineering, prepared based on Anna University syllabus. I am very thankful thankf ul to our dynamic Principal Dr.N.R.Alamelu and our eminent Director (Academics) Dr.A.Ebenezer Jeyakumar who helps me in learning things and inspire to do this activity.

I also render my sincere gratitude to my HOD, Prof.B.Suresh Kumar and our Department Academic coordinator Prof.V.Selvan, P rof.V.Selvan, Prof.C.J.Thomas Renald and my colleagues for helping and encouraging me to do this activity.

In any event I must acknowledge my final year undergraduate Aeronautical Engineering students, batch (2009-2013) of Sri Ramakrishna Engineering College. I hope that, this material will help in enriching your knowledge in the subject and as well as helpful in preparing for your semester exam.

SABARIMANIKANDAN.M AP/AERO

2


FOREWORD

The course material, “Rocket and Missiles” come to your hand with numerous people contributions. The material is intended for students studying Aeronautical Engineering, prepared based on Anna University syllabus. I am very thankful thankf ul to our dynamic Principal Dr.N.R.Alamelu and our eminent Director (Academics) Dr.A.Ebenezer Jeyakumar who helps me in learning things and inspire to do this activity.

I also render my sincere gratitude to my HOD, Prof.B.Suresh Kumar and our Department Academic coordinator Prof.V.Selvan, P rof.V.Selvan, Prof.C.J.Thomas Renald and my colleagues for helping and encouraging me to do this activity.

In any event I must acknowledge my final year undergraduate Aeronautical Engineering students, batch (2009-2013) of Sri Ramakrishna Engineering College. I hope that, this material will help in enriching your knowledge in the subject and as well as helpful in preparing for your semester exam.

SABARIMANIKANDAN.M AP/AERO

2


SEMESTER VII

08AH701

ROCKETS AND MISSILES

UNIT – UNIT – I I

ROCKETS SYSTEM

3 0 0 100

10

Ignition System in rockets – rockets – types types of Igniters – Igniters – Igniter Igniter Design Considerations – Considerations – Design Design Consideration of liquid Rocket Combustion Chamber, Injector Propellant Feed Lines, Valves, Propellant Tanks Outlet and Helium Pressurized and Turbine feed Systems – Systems – Propellant Propellant Slash and Propellant Hammer – Elimination Elimination of Geysering Effect in Missiles – Missiles – Combustion Combustion System of Solid Rockets.

UNIT – UNIT – II II

AERODYNAMICS OF ROCKETS AND MISSILES

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Airframe Components of Rockets and Missiles – Forces Forces Acting on a Missile While Passing Through Atmosphere – Atmosphere – Classification Classification of Missiles – Missiles – methods methods of Describing Aerodynamic Forces and Moments – Lateral Lateral Aerodynamic Moment Moment – – Lateral Lateral Damping Moment and Longitudinal Moment of a Rocket – lift lift and Drag Forces – Forces – Drag Drag Estimation – Estimation – Body Body Upwash and Downwash in Missiles – Rocket Rocket Dispersion – Dispersion – Numerical Numerical Problems.

UNIT – UNIT – III III

ROCKET MOTION IN FREE SPACE AND GRAVITATIONAL FIELD

10

One Dimensional and Two Dimensional rocket Motions in Free Space and Homogeneous Gravitational Fields – description of Vertical, Inclined and Gravity Turn Trajectories – Determination Determination of range and Altitude Simple Approximations to Burnout Velocity.

UNIT – UNIT – IV IV

STAGING AND CONTROL OF ROCKETS AND MISSILES

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Rocket Vector Control Control – – Methods – Methods – Thrust Thrust determination – determination – SITVC – SITVC – Multistaging Multistaging of rockets – rockets – Vehicle Vehicle Optimization – Optimization – Stage Stage Separation Dynamics – Dynamics – Separation Separation Techniques.

UNIT – UNIT – V V

MATERIALS FOR ROCKETS AND MISSILES

5

Selection of Materials – Materials – Special Special Requirements of Materials to Perform under Adverse Conditions.

TOTAL : 45

Text Books

1. 2.

Sutton, G.P., et al., “Rocket Propulsion Elements”, John Wiley & Sons Inc., New York, 1 993. Mathur, M., and Sharma, R.P., “ Gas Turbines and Jet and Rocket Propulsion”, Standard Publishers, New Delhi 1998 Reference Books

1. 2.

Cornelisse, Cornelisse, J.W., “ Rocket Propulsion and Space Dynamics”, J.W., Freeman & Co. Ltd., London, 1982. Parket, E.R., “ Materials for Missiles and Spacecraft”, McGraw -Hill Book Co. Inc., 1982.

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UNIT-1 ROCKET SYSTEMS TYPES OF IGNITER:

The types of igniters which are commonly used are, 

Gaseous Igniter  Liquid igniter  Solid igniter GASEOUS IGNITER:

It is the old and primitive type of igniter which is not used now. In this type of igniter the reactive gaseous mixtures are held in a very t hin tube with high pressure. It is hazardous in nature and reliable. Directional control can be done by using burst dampers. Example for gaseous igniters is shock tube.

LIQUID IGNITER:

Liquid igniter is of two types. Theyare, 

Liquid- Liquid type , which is known as hypergolic igniter  Liquid – Solid type, which is known as hybrid igniter CHARACTERISTICS OF HYPERGOLIC LIQUIDS:       

Hypergolic liquids have a very high bulk density. Ignition delay for these types of liquids should be less than 50 milliseconds. These liquids are chemically instable. They must be work well together with some of selected polymers and resins. Their viscosity should be less than 10 centistokes. They should have a very low vapour pressure. They should have a very good heat transfer characteristics.

SOME COMBINATIONS OF HYPERGOLIC LIQUIDS: FUEL

OXIDIZER

KEROSINE

RFNA

HYDRAZINE

CHLOROFLUORINE

AMMONIA

OXYGEN

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HYDROGEN

ClO3F

FACTORS AFFECTING IGNITION DELAY:

The factors which affect the ignition delay are, 

Purity of materials



Initial temperature and pressure.

t = A/

where , t = Time A= Minimum possible ignition delay E = Temperature coefficient R = Universal Gas constant T =Temperature

SOLID ROCKET IGNITER:

Solid rocket igniters are broadly classified as follows,

dvedgeldv

SOLID IGNITER

UNCONFINED IGNITER NOZZLE IGNITER

TOTALLY CONFINED IGNITER FILM IGNITER

BAG IGNITER

PYROCORE

JELLY ROLL POWDER CAN IGNITER

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CONDUCTING

BASKET

FILM IGNITER

IGNITER

PYROGEN ALCO JET


TOTALLY CONFINED IGNITERS:

BAG IGNITER: 

It is the old and primitive type of igniter.  We don’t have enough control over ignition in this type of igniter  After the ignition of fully charged bag igniter, the heat and pressure generation occurs.  The rate of heat and pressure release is very high and there is a possibility of bursting. ADVANTAGES:  

It is very easy to fabricate The cost of production is very low.

DISADVANTAGE:

This particular system is very far from meeting the requirements of modern high performance rocket motors. POWDER CANIGNITER:

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In this type of igniter pallets are used .Pallets are made up of black powder or metal oxidants and aluminium powder. Here directional control is done but not sufficient. It is only suitable for small rocket motors and not suitable for large rocket motors because of its erratic transient ignition characteristics and it is rapturous. ADVANTEGES: 

Ease of fabrication and production cost is low.

DISADVANTAGES:  

As the igniter is made of steel casing the weight is much heavier. Only suitable for short range missions.

JELLY ROLL:

It consists of a film coated pyrotechnic and a binder. Then the film is rolled over a rod with a squib support at the front and back. Addition to that a rubber support is given externally. Ignition is generally started at the squib. In jelly roll the ignition transfers layer by layer. Productive cover is used to tight the main charge. ADVANTAGES: 

These igniters are nozzle insertables.  They make efficient use of motor fuel volume.  The hardware weight is low. DISADVANTAGES: 

They are very fragile and not suitable for large rocket motor  They are difficult to manufacture and the principle of operation is complex.  They produce high shocks. UNCONFINED IGNITERS:

Actually they are confined. They are unconfined only relative to others.

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FILM IGNITER:

The film igniteris produced by painting an ignitable fuel oxidizer binder mixture directly ontothe propellant surface. The film normally contains, Fine metal powder – aluminium powder Per chlorate oxidizer - ammoniumper chlorate Polymeric binder. The film can be activated by the conventional pyrotechnic igniter. It permits the use of low conventional ignition system and has often be used an aid to ignite the systems which handle materials difficult to ignite. CONDUCTING FILM IGNITER:

It contains the strips of pyrotechnic material applied directly to the propellant, which can overlay of circuit leads. It consists of the application of thin strips within the perpendicular overlay of actuation circuitry. A typical pyrotechnic mixture consists of metal powder,per chlorateoxidizer , silver conductor and the polymeric binder. Aluminium foils are used as protective layer of conducting film igniter. ADVANTAGES:   

These igniters produce low pressure peaks They make efficient use of space They are intensive to electromagnetic radiation

DISADVANTAGES: 

They are very difficult to apply  Quality control is difficult  They cannot be removed from the motor easily  They are very sensitive to friction and resistance NOZZLE IGNITERS (or) BASICALLY CONTROLLED IGNITERS: BASKET IGNITER:

This type of igniter contains pallet charges. Basket igniter are fabricated from heavy wire mesh , perforated sheet metal or perforated glass fibre reinforced resins. The perforated container 8


retain the high surface area palette charge when it burns. The exhaust products ejected in a pattern determined by the geometry of the design contains reactive products as well as reactive materials.

This system makes available in the wide choice of configuration allowing for some flame pattern control. ADVANTAGES:  

This igniter is made efficiently strong to withstand environmental conditions. Proper control of length and port area can furnish a controlled flame pattern and give medium to fast ignition with low ignition charge.

DISADVANTAGES: 

The hardware weight is high.  Forward attachment is often difficult  The burning area of the pallets can’t be readily determined  Internal igniter pressure and mass delivery rate are difficult to determine.

PYROGEN:

A pyrogenigniter consists of small nozzle pressure chamber containing high energy fast burning rocket propellant usually having a complex geometry. Essentially it is a rocket motor within a rocket motor. The design is especially used in very large motor.

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ADVANTAGES: 

The igniters have little or no shocks.  They eliminate the handling of large amounts of relatively hazardous metal oxide charges.  They are adoptable to either head end or l auncher mount applications. DISADVANTAGES: 

The pyrogen must itself have an igniter and it’s therefore depends upon the principle used to ignite.

ALCOJET:

There are two tubes in this igniter .In the annular space between the two tubes, we have main charge. Booster charge present inside the tube. The booster charge is first i gnited. The ignition passes through the perforations in the inner wall to the main charge. There are perforations in the outer tube through which flame comes out. Since there is a control, it is a ballistically controlled igniter.

LIVE IGNITERCOMPONENTS:

The important components of a live igniterare ,      

Firing console Squib Transfer charge Booster charge Main charge Motor grain

SQUIB :

The squib is the primary element for ignition that affects the conversion of electrical impulse from the control console to chemical reaction in the rocket motor. The squib consists of the following parts, 1. INERT COMPONENTS :  Circuit element  Base or body 10

SRI RAMAKRISHNA ENGINEERING COLLEGE , CBE-22 

Insulation  Metal case 2. ACTIVE COMPONENTS :  Prime charge  Booster charge  Main charge CHARACTERISTICS OF A SQUIB:

1. 2. 3. 4. 5. 6.

A functioning time curve Pressure output characteristics Thermal output characteristics Auto ignition characteristics Static sensitivity characteristics Shock and mechanical sensitivity characteristics

IGNITER DESIGNCONSIDERATION :

The data to be considered while designing an i gniterare, 

The pyrotechnic material data  Propellant ignitability data  Rocket motor data  Back up data (previous test firing data). IGNITABILITY BOMB:

The ignitability bomb is a device used to determine the relative ignitability of the propellants at various pressures under the direct fire of ignition materials. INJECTORS :

An injector or ejector is a system of admitting the fuel into the combustion engine. Its function is similar to a carburettor. PRIMARY DIFFERENCE BETWEEN A CARBURATOR AND AN INJECTOR:

In an injector the fuel injection atomizes the fuel by forcibly pumping it through a small nozzle under high pressure while a carburettor relies on suction created by intake air rushing through a venturi to draw the fuel into the airstream. FUNCTION OF AN INJECTOR:

The injectors are mainly used to meter the flow of the liquid propellant to the combustion chamber which causes the liquids to be broken i nto small droplets. This process is known as atomization. It also helps to distribute and mix the propellant in a correctly proportionate mixture of fuel and oxidizer, which results in uniform propellant mass flow. INJECTION HOLE PATTERNS:

The injectionhole pattern on the face of t he injector is closely related to the internal manifolds or feed passages. These hole patterns provides the distribution of propellant from the injector inlet to all the injection holes. 11


A large complex manifold volume allows low passage velocities and good distribution of flow over the chamber.A small manifold volume allows for a light weight injector and reduces the amount of “dribble” after the main walls are shut. TYPES OF INJECTORS:

INJECTORS

IMPINGING STREAM TYPE

COAXIAL HOLLOW NON IMPINGING

POST INJECTOR

(or) SHOWER HEAD

SHEET (or) DOUBLETIMPIN

TRIPLET

IMPINGING

IMPINGIN

STREAMPATTERN

GSTREAM

SPRAY TYPE

SELF IMPINGING STREAM PATTERN

PATTERN

IMPINGING STREAM PATTERN :

The types of impinging stream pattern are , 

Doublet impinging stream pattern  Triplet impinging stream pattern  Self impinging stream pattern

These impinging stream type multiholes injectors are commonly used with oxygen hydrocarbon and storable propellants. In this type of injectors, the propellants are injected through a number of separate holes in impingement forms thin liquid fans that aids the atomization of liquids into droplets. Impinging hole injectors are also used like a cell impinging patterns. The two liquid stream forms like a fan which breaks into droplets. For uneven volume flow the triplet pattern seems to be more effective.

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NON- IMPINGING (or) SHOWER HEAD TYPE:

Nonimpinging (or) shower head injector employs non-impinging stream of propellants usually emerge in normal to the face of the injector. It releases the fuel and oxidizer on turbulence and diffusion to achieve good mixing. 13


This type of injectors is not used now, because it requires a large chamber volume for good combustion.

SHEET (or) SPRAY TYPE INJECTORS:

Sheet (or) spray type injectors give cylindrical, conical or other types of spray sheets , these sprays generally intersect and thereby promote mixing and atomization . By varying the width of the sheet (through an axially movable sleeve) it is possible to throttle the flow over a wide range without excessive reduction in the pressure drop. This type of variable area concentric tube injector was used on the descent engine of the lunar excursion module. THE COAXIAL HOLLOW POST INJECTOR:

The coaxial hollow post injector has been used for liquid oxygen and gaseous hydrogen injectors. It works well when the liquid hydrogen has absorbed heat from cooling jackets and has been gasified.This gasified hydrogen flows at a high speed of 330m/s. The liquid oxygen flows far slowly at a speed of 33m/s ,and the differential velocity cause a shear action which helps to break up the oxygen stream into small droplets .

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The injector has a multiplicity of these coaxial posts on its face . The coaxial hollow post injector is not used with liquid storable bipropellants in part because the pressure drop to achieve high velocity would become too high. DESIGN CONSIDERATION OF A LIQUID ROCKET COMBUSTION CHAMBER:

Combustion chamber which is also known as thrust chamber, where the combustion or burning of propellants take place. The combustion temperature is much higher than the melting points of most chamber wall materials. Therefore it is necessary to cool these walls or to stop rocket operation before the critical wall areas become too hot. If the heat transfer is too high and thus the wall temperatures become locally too high, then the thrust chamber will fail. VOLUME AND SHAPE CONSIDERATIONS:

Spherical volume gives the least internal surface area and mass per unit chamber volume. It is very expensive to build the spherical chambers. Today most of all prefer cylindrical or slightly tapered cone frustum with a flat i njector and a converging diverging nozzle. Neglecting the effect of the corner radii, the chamber volume is given by,

Here L is the length of the cylinder AL/At is the chamber contraction ratio, and Lc is the length of the conical frustum. CHAMBER VOLUME - DEFINITION:

The chamber volume is defined as the volume up to the nozzle throat section and it includes the cylindrical chamber and converging cone frustum o f the nozzle. The volume and shape of a combustion chamber are selected after evaluating various parameters. Some of them are as follows, 1. The volume has to be large enough for adequate mixing, evaporation and complete combustion of propellants. 2. Chamber volume varies for different propellants with the time delay necessary to vaporize and activate the propellants and with the speed of the propellant combination. 3. When the chamber volume is too small, combustion is incomplete and the performance is poor. 4. With higher chamber pressure or with highly reactive propellants and with injectors that give improved mixing, a smaller chamber volume is usually permissible. 5. The chamber volume and diameter can influence the cooling requirements. If the chamber volume and diameter are large, the heat transfer rates to the wall will be reduced, the area exposed to heat will be large, and the walls are somewhat thicker. 6. All inert components should have a minimum mass. The thrust chamber mass is a function of the chamber dimensions, chamber pressure, and nozzle area ratio, and the method of cooling. 7. Manufacturing consideration favour simple chamber geometry, such as a cylinder with a double cone bow tie shaped nozzle, low cost materials and simple fabrication process.

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8. In some applications the length of the chamber and the nozzle relate directly to the overall length of the vehicle.A large diameter but short chamber can allow a somewhat shorter vehicle with a lower structural inert vehicle mass. 9. The gas pressure drop for accelerating the combustion products within the chamber should be a minimum; any pressure reduction at the nozzle inlet reduces the exhaust velocity and t he performance of the vehicle. These losses become appreciable when the chamber volume less than three times the throat area. 10. For the same thrust the combustion volume and the nozzle throat area become smaller as the operating chamber pressure is increased. This means that the chamber length and the nozzle length also decrease with increasing chamber pressure, the performance will go up with chamber pressure. PROPELLANT HAMMER:

Propellant hammer is nothing but a pressure surging present in the liquid propellant feed line. Basically the feed lines are very thin. On sudden closure of valve, a pressure pulse is generated at the neighbourhood of the valve. It travels back to the tank at some velocity and keeps the liquid static pressureincreasing.

a

=

 /  1 + /

′

Where, a = velocity of propagation of pressure pulse E = Modulus of elasticity of pipeline material K = Bulk modulus of elasticity of propellant D =Diameter of propellant feed line t’ = wall thickness of feedline

Fig: Propellant hammer in the pipe line due to sudden closure of valve

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changes in the momentum of the fluid in the feed line is caused by the opening or closing of valves in the line result in pressure peaks analogous to the propellant hammer ,such situation occurs during the rocket engine start , during the initial bleed of the rocket engine or rocket engine set down . This situation fall under two categories.

1. Valve opening 2. Valve closure

In case of valve closure ,i.e , tc=valve closure time a = velocity of propagation of pressure pulse 2L/a ≥tc ; 2L/a
for fast valve closure for slow valve closure

TANK OUTLET DESIGN CONSIDERATION:

Before designing the tank outlet the designer have to solve three main problems. They are, 1. Cavitation 2. Dropout 3. Vortexing 1. CAVITATION:

Cavitation is the phenomenon which occurs when the static pressure drops below the vapour pressure of the propellant. This may be due to the increased flow velocity in the tank outlet. It can be also defined as the boiling of liquid at low pressures and the release of dissolved gas from the liquid. Small gas bubbles grow in the liquid and then collapse within a few milliseconds. This is accompanied by high temperature rises up to 10,000K and the pressure rises up to 400MPa. Cavitation is an undesirable phenomenon because there will be increased losses in the outlet. Cavitation occurs in the converging duct of the outlet where the fluid velocity increases and there is a corresponding decrease in static pressure. Fig: cavitation phenomenon due to sudden static pressure drop

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SOLUTION FOR CAVITATION:

Cavitation problem can be avoided by contouring the outlet, so that the static pressure is constant throughout the outlet. Cavitation can also suppress by avoiding high flow velocities or by using high fluid pressures or by combination of both. The high fluid pressures in the turbo pumps are achieved by high tank pressures, possibly in combination with booster pumps.

2. LIQUID DROP OUT:

Liquid drop out is an undesirable phenomenon in case of liquid rocket engines. Liquid dropout is basically a depression in the liquid surface at centre of the flow lines, which occurs in higher vertical velocity along the centre line of the outlet than along the wall exit.

Fig:Dropout inside a liquid fuel tank

Liquid dropout will not occur when the liquid surface remains stationary. This problem can be avoided by contouring the outlet so that the axial component of velocity along a stream line adjacent to the wall of outlet is equal to the average velocity which is obtained by dividing the flow rate by the cross sectional area.

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3. VORTEXING: Fig: Formation of vortex inside the fuel tank

Vortexing is a phenomenon which is similar t o the coriolisforce effects in bath tubs being emptied and can be augmented if the vehicle spins or rotates during flight. Typically a series of internal baffles is often used to reduce the magnitude of vortexing in propellant tanks with modest side acceleration. vortexing can greatly increase the unavailable or residual propellant , and thus cause a reduction in vehicle performance . OUTAGE:

The amount of liquid oxidizer or propellant present in the tank at the time of completing the operation of vehicle is called as an outage.

GEYSERING EFFECT :

The term geysering is applied to the phenomenon which occurs in a liquid propellant system, a column of liquid in long vertical lines is expelled by the release of bubbles. If the bubbles will swarm causing the creation of slow moving mass or a single large bubbles travels at faster velocity causing more and more bubble formation and decrease the column static pressure rapidly.

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Fig: Bubble formation inside the fuel tank due to Geysering effect

The pressure surging produced due to geysering can be large and damage the fluid lines, wall supports and the line supports. Geysering can be also results from the action of the release of super heat and reduced pressure boiling in a saturated or superheated liquid column. PROPELLANT SLOSH: SLOSH-DEFINITION:

Slosh refers to the movement of liquid inside an object, which is typically undergoing motion.

Fig: Sloshing of a liquid inside a glass

EXPLANATION:

Sometimes the liquid contains in the propellant tank may oscillate back and forth and this liquid motion is generally referred as propellant slosh.Propellants slosh generally occurs in space craft tanks, rockets (especially in upper stages), then cargo slosh in ships and t rucks transporting liquids (for example oil and gasoline) 20


The resulting oscillatory forces and moments on the tank walls are not negligible and must be considered in the dynamic analysis of the missiles. When the tank is partly empty, sloshing can uncover the tank outlet and allow gas bubbles to enter into the propellant discharge line. These bubbles can cause combustion problem in the t hrust chamber, the aspirating of bubbles or the uncovering of the tank outlets by liquids therefore needs to be avoided. Sloshing can also shifts in vehicles centre of gravity and makes the flight control difficult. Fig: Sloshing of liquid inside a rectangular fuel tank

In the missiles the dynamic excitation during the powered flight is strongly offered by the sloshing motion of the liquids in the tanks. The associated frequencies during sloshing can be accurately determined for the design of autopilot because they may be within the autopilot effective control frequency. The effect of propellant slosh in the structural dynamics of the missile is generally idealized mathematically based knowledge. The fundamental mode of propellant motion plays a very significant role inthe study of structural dynamics. METHOD TO AVIOD PROPELLANT SLOSH:

The propellant is replaced for analytical purposes by a mass mounted within the tank, a frictional guide which is perpendicular to the tank axis. The motion of the equivalent mass along the guide is restrained by a mass less spring. There are several types of slosh suppression devices has been employed successfully to i ncrease the damping of liquid sloshing induced by vehicle motions. The devices include rigid ring baffles (Of various geometries and orientation), cruciform baffles, deflectors, flexible flat ring baffle, floating can, positive expulsion bags and diaphragms. Gel, packed fibres, and foams have been employed in non space applications, but are not now being used for space vehicles.

21


Various ring baffle configuration used for suppression of sloshing in cylindrical & spherical tanks

PROPELLANT FEED SYSTEM:

Liquid propellants are required to be injected at a pressure slightly above the combustor pressure. There are two types of feed systems can be employed for this function. They are, 1. Gas pressure feed system 2. Turbo pump feed system The pressure feed system is much simpler and widely used for low thrust and short range operations. The latter is used in large engines. GAS PRESSURE FEED SYSTEM:

The gas pressure feed system is quite simple. An inert gas is separately carried at a pressure much higher than the injection pressure; this is used to exert the required pressure in the propellant tanks.

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The pressurizing gas is chosen on the basis of its chemical properties, density, pressure and the total weight of the gas and the tank. A gas which is ideal for one propellant unsuitable for another. Nitrogen, Helium and air have been used for pressurization. The propellants under high pressure are forced to flow into the thrust chamber through valves, feed lines and injectors. Several regulating and check valves are used for filling draining, starting and checking the flow of propellants. In this type of systems there are no moving parts such as turbines and pumps are used. Therefore this system is considerably simpler. However, the pressurization of the propellant tanks requires them to be comparatively much heavier and introduces a weight penalty besides other problems. Therefore this system is unsuitable for large rocket and long range missions.

Pressure for injection can also be generated within the propellant tank by introducing a small quantity of a gas, which reacts exothermally with the propellant, this produces high pressure gas required to force the propellant into t he combustor.

23


TURBO PUMP FEED SYSTEM:

In the turbo pump feed system, the propellants are pumped into the combustor by gas turbine driven by centrifugal pumps.

The turbines derive the power from the expansion of hot gases .The gases are generated separately by the gas generator. Figure above depicts a general arrangement of a turbo pump system. In order to achieve flexibility in choosing the design and operating parameters the fuel and oxidizer pumps can be separately by their turbines. The turbine operates on a separate gas stream generated from the propellants in an i ndependent gas generator. A pressurizing gas can be used to increase the pressure of the propellants at the pump suctions to avoid cavitation and the resulting instability in pump operation. Generally turbine speeds are high , therefore propellant pumps can be driven at optimum speeds through reduction gear with an additional weight penalty. The working gas for the turbine can also be generated at optimum temperature and pressure. The generator also has its own injection and ignition systems. The flow of propellants to the gas generator occurs due to the action of pressurizing gases. If the gas pressurization is not employed to t he propellants can be bled from the delivery lines of the pumps. The propellant flow required for driving the turbines is of the order of 1.5 to 5% of the main flow. The turbine exhaust is also expanded through an exhaust nozzle to provide an additional thrust.

24


An auxiliary power unit is also needed in a rocket engine. A single turbine can develop sufficient power to drive the propellant pumps as well as the electric generator. Besides working on high energy gases bled from the main thrust chamber or combustor it can also employ its own combustor with a gas pressure feed system. An alternative method which is comparatively simpler is to generate the working gases by burning solid propellants in a manner similar to the solid propellant rocket. The turbines and pumps for rocket applications are designed to meet some special requirements. There are enormous temperature differences with a turbine inlet at a high temperature of the propellants are highly reactive. Therefore the sealing arrangement in propellant pumps should be perfect and resistant to corrosion. Both positive displacement and turbo pumps can be used for delivering propellants from the tank to the combustion chamber. However centrifugal pumps are widely used. VALVES AND PIPE LINES: VALVES:

Valves control the flows of liquids and gases and pipes conduct these fluids to the intended components. There are no rocket engines without them. There are many different types of valves. All have to be reliable, light weight, leak proof, and must withstand intensive vibrations and very loud noises. With many of these valves, any leakage or valve failure can cause a failure of the rocket unit itself. Allvalves are tested for two qualities prior to installation; they are tested for leaks - through the seat and alsothrough the glands--and for functional soundness or performance. The propellant valves in high thrust units handle relatively large flows at high service pressures. Therefore, the forces necessary to actuate the valves are large. Hydraulic or pneumatic pressure, controlled bypilot valves, operates the larger valves. These Classification of Valves Used in Liquid Propellant Rocket Engines 1. Fluid valve: For carrying fuel, oxidizer,cold pressurized gas, and hot turbine gas this type of valve is used. 2. Application or Use: The valves which are mainly used for propellant control are Thrust chamber valve (dual or single),bleed valve, drain valve, filling valves, by-pass valve, preliminary stage flow valve, pilot valve, safety valve; overboard dump valve, regulator valve, gas generator control valve, sequence control valve. 3. Mode of Actuation: The valves are operated by different means of actuation. The different modes are, 

Automatically operated (by solenoid, pilot valve, trip mechanism, pyrotechnic, etc.)



Manually operated



Pressure-operated by air, gas, propellant, or hydraulic fluid (e.g., check valve, tank vent valve, pressure regulator, relief valve)

4. The flow magnitude determines the size of the valve.

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5. Valve Types: Normally open, normally closed, normally partly open, two-way, three-way, with/without valve position feedback, ball valve, gate valve, butterfly type,spring loaded valve. PIPES (or) LINES:

The various fluids in a rocket engine are conveyed by pipes or lines, usually made of metal and are joined byfittings or welds. Their design must provide thermal expansion and provide support to minimize vibrationeffects. For gimballed thrust chambers it is necessary to provide flexibility in the piping to allow the thrust axis tobe rotated through a small angle, typically +3 to 10 °. This flexibility is provided by flexible pipe joints and or byallowing pipes to deflect when using two or more rightangle turns in the lines. Sudden closing of valves can cause propellant hammer in the pipelines, leading to unexpected pressure rises which can be destructive to propellant system components. The friction of the pipe and the branching ofpipelines reduce this maximum pressure. Propellant hammer can also occur when admitting the initial flow of high-pressure propellant intoevacuated pipes. The pipes are under vacuum to remove air and prevent the forming of gas bubbles in the propellant flow, which can cause combustion problems. COOLING OF THRUST CHAMBER: NEED FOR COOLING:

The primary objective of cooling is to prevent the chamber and nozzle walls from becoming too hot, so they will no longer able to withstand the imposed loads and stresses, thus causing the chamber or nozzle to fail. Most materials lose strength and become weaker as temperature is increased. Cooling thus reduces the wall temperatures to an acceptable limit.

METHODS OF COOLING THETHRUST CHAMBER:

The cooling methods of a thrust chamber are briefly classified as below,

Now a days there are two most cooling methods are commonly used. They are, Active cooling system and Passive cooling system.

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ACTIVE COOLING SYSTEM:

In liquid rocket motor, the nozzle and chamber walls are exposed to hot combustion products. Usually these walls are provided with ducts The four most important active cooling methods are, 1. 2. 3. 4.

Regenerative cooling Film cooling Transpiration cooling Dump cooling

REGENERATIVE COOLING:

It is one of the most efficient and sophisticated means of cooling. This method is used in many of the large rocket engines. The thrust chamber and nozzle wall contains passages through which one of the propellants, usually the fuel flows. The passages may either formed by a si mple, double wall construction, by composing the thrust chamber and nozzle of a bundle of coolant tubes, or by milling out the coolant ducts in the wall of the chamber and nozzle. The coolant passing at high pressures through the ducts then it is injected into the combustion chamber. In some cases, if the coolant is at a super critical pressure, it is possible to use the absorbed energy to drive a turbo pump unit before the coolant is injected into the combustion chamber. The size of the coolant ducts and coolant flow rate are determined by the following considerations: the total amount of heat absorbed should not raise the bulk temperature to the boiling point, or to such a level that propellant decomposition takes place, the local heat transfer rate should not exceed the maximum nucleate boiling heat transfer rate, the pressure in the cooling jacket should not become too low. Coolant boiling is accomplished with the formation of large vapor bubbles and a strong decrease in density and cooling capacity. Moreover, a blockage of the flow may occur. Propellant decomposition may form deposits on the hot walls of the cooling jacket, thus effectively reducing the conductivity of the wall, and hence the heat transfer rate. Local nucleate boiling strongly increases the heat transfer rate, however if film boiling t akes place, an insulating vapor film at the wall reduces the possible heat flexures strongly. If the fl uids are at super critical pressures, neither boiling nor nucleate or film boiling will occur and high heat transfer rates are possible.

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Regenerative cooling is very effective as nearly all heat energy that has transferred to the wall is fed back into the thrust chamber and hence is available for propulsion. This requires a complicated construction and there is a large pressure drop along the coolant jacket, hence needed very high pump pressure. Moreover, some propellants only allow low wall temperatures otherwise decomposition may take place. FILM COOLING:

Film cooling method is suited when it is used with the combination of other methods such as regenerative cooling or insulation cooling. Pure film cooling permits a relatively simple chamber and nozzle design. The coolant is injected along the gas side wall surface by means of tangential slots. The coolant forms a cool boundary layer between the gas side wall surface and hot gases. As this boundary layer gradually mixes with the main flow, its temperature rises and downstream of the slot new coolant has to be injected. DUMP COOLING:

Dump cooling resembles regenerative cooling, but after having performed its cooling function, the coolant is dumped overboard at t he nozzle exit. Many o the restrictions for Regenerativecooling also hold for dump cooling. The heated, gasified coolant can be accelerated to supersonic speeds thus providing a small extra thrust. The method is especially suited for low pressure engines, using low molecular weight propellants, but yields a performance loss as compared to regenerative cooling. On the other hand, the construction is simpler as compared to regeneratively cooled engines.

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PASSIVE COOLING SYSTEMS:

Among these systems, the most important ones are: insulation cooling, heat sink cooling, ablative cooling and radiation cooling. INSULATION COOLING:

This method is not a real method of cooling by itself; it is mostly used in combination with other cooling techniques such as, heat sink, radiation and regenerative cooling. A very special material is pyrolytic graphite. This material has high and l ow conductivity directions. While the conductivity parallel to the layer planes is in the order of 2x103 w/m.k, the conductivity perpendicular to the layer plane is only 5.75w/m.k. this make it is possible to conduct the heat in preferred directions, and so to avoid the heating of critical parts. HEAT SINK COOLING:

Heat sink cooling is mostly used in solid rockets. The method consists of applying a piece of solid material with good conductivity and a high specific heat capacity to certain hot spots. The heat sink absorbs the heat from the hot gases, thereby raising its own temperature but keeping the wall relatively cool. This method is only suitable for short duration applications, but is sometimes used in combination with insulation cooling for small liquid rocket engines. ABLATIVE COOLING:

Ablative cooling consists of covering hot gas side of the engine wall with a material that decomposes endo thermally at high temperatures, while forming a insulating char layer. It is often used in combination with radiation and insulation cooling and chosen for upper stage motors and reaction control engines for the sake of simplicity. It is also an effective means to keep the temperature of variable thrust motors within an acceptable range. Regenerative cooling often poses a problem for variable thrust motors, because of the variable chamber pressure and flow r ate. Therefore, ablative cooling offers a simple and efficient way to keep the engine wall relatively cool. RADIATION COOLING:

Radiation cooling is often used in upper stage engines and reaction control engines in combination with insulation and ablative cooling. The hot walls radiate the heat to the surroundings. 29


As the radiative heat flux is proportional to T4, the material temperature must be high to obtain a large radiative heat flux. Refractory metals, such as molybdenum, niobium can withstand hi gh temperature without losing their strength. Some refractory metals easily react with the combustion products. As the melting point of their oxides or compounds often is much lower than that of the metals, coatings have to be applied on many cases. The refractory alloys based on titanium, niobium and molybdenum have found successful applications as nozzle construction materials. Wolfram (tungsten) alloys have found applications for nozzle inserts. COMBUSTION SYSTEM OF SOLID ROCKETS: PHYSICAL AND CHEMICAL PROCESS:

The combustion in the solid propellant motor involves exceedingly complex reaction taking place in the solid, liquid & gas phase of a heterogeneous mixture. Visual observations and measurements of flames in simple experiments such as strand burner test give an insight into the combustion processes. For double base propellants, the combustion flame structure appears to be homogeneous and one-dimensional along the burning direction. When the heat from the combustion melts, decomposes and vaporizes the propellant at the burning surface, the resulting gases seems to be already premixed. Burn rate catalysts seem to affect the primary combustion zone rather than the processes in the condensed phase. They catalyze the reaction at or near the surface, increase or decrease the heat input to the surface, the change the amount of propellant that is burned. Solid Fuel Geometry

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Solid Fuel Geometry Dependent Thrust-Time Curve

(Typical solid propellant grain configurations and the corresponding thrust-time curves) BASIC CONCEPTS:

A simple solid rocket motor consists of a casing, nozzle, grain (propellant charge), and igniter. The grain behaves like a solid mass, burning in a predictable fashion and producing exhaust gases. The nozzle dimensions are calculated to maintain a design chamber pressure, while producing thrust from the

exhaust gases.

IGNITION PROCESS:

Solid propellant ignition consist of a series of complex rapid events, which starts on receipt of a signal and include heat generation, transfer of the heat from the igniter to the motor grain surface, spreading the flame over the entire burning surface area, filling the chamber free volume with gas and elevating the chamber pressure without series abnormalities such as over pressure, combustion oscillation, damaging shock waves, hang fire extinguishment and chuffing.

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Satisfactory attainment of equilibrium chamber pressure with full gas flow depends on:                     

Characteristics of the igniter and the gas temperature. Motor propellant composition and surface ignitability. Heat transfer by radiation and convection between gas and grain surface. Grain flame spreading rate. The dynamics of filling the motor free volume with the hot gas. Ignitibility of a propellant is affected by, The propellant formulation. The initial temperature of the propellant. The surrounding pressure. The mode of heat transfer. Grain surface toughness. Age of the propellant. The velocity of the hot igniter gas. The cavity volume and configuration The variables determining grain-relative performance are core surface area and specific impulse. Surface area is the amount of propellant exposed to interior combustion flames, existing in a direct relationship with thrust. An increase in surface area will increase thrust but will r educe burn-time since the propellant is being consumed at an accelerated rate. The optimal thrust is typically a constant one, which can be achieved by maintaining a constant surface area throughout the burn. Examples of constant surface area grain designs include: end burning, internal-core and outer-core burning, and internal star core burning. Solid propellants are either "composites" composed mostly of large, distinct macroscopic particles or which are a homogeneous mixture of one or more primary ingredients Often, the ingredients of a double base propellant have multiple roles such as RDX which is both a fuel and oxidizer or nitrocellulose which is a fuel, oxidizer and plasticizer.

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Grain:

Solid fuel grains are usually molded from a thermoset elastomer (which doubles as fuel), additional fuel, oxidizer, and catalyst. HTPB is commonly used for thi s purpose. Ammonium perchlorate is the most common oxidizer used today. The fuel is cast in different forms for different purposes. Slow, long burning rockets have a cylinder shaped grain, burning from one end to the other. Most grains, however, are cast with a hollow cross section, burning from the inside out (and outside in, if not case bonded), as well as from the ends. The thrust profile over time can be controlled by grain geometry. For example, a star shaped hole down the center of

the grain will have greater initial thrust because of the

additional surface area. As the star points are burned up, the area and thrust are reduced.

surface

Casing:

The casing may be constructed from a range of materials. Cardboard is used for model engines. Steel is used for the space shuttle boosters. Filament wound graphite epoxy casings are used for high performancemotors. Nozzle:

A Convergent Divergent design accelerates the exhaust gas out of the nozzle to produce thrust. Sophisticated solid rocket motors use steerable nozzles for rocket control.

COMBUSTION MECHANISM OF SOLID PROPELLANTS:

Some solid rocket propellants are mixed at the molecular level. A double base propellant made from nitrocellulose and nitro-glycerin. The dominant difference is the break in temperature slope at the solid gas interface. The solid usually requires some heat input to gasify and this heat is the heat of pyrolysis. Consequently, the gas phase heat transfer at the interface goes towards providing both the latent heat and continued heat transfer into the solid.

Advantages: 

Solid propellant rockets are much easier to store and handle than liquid propellant rockets.  High propellant density makes for compact size as well.  These features plus simplicity and low cost make solid propellant rockets ideal for military applications.  These features plus simplicity and low cost make solid propellant rockets ideal for military applications whenever large amounts of thrust are needed and cost is an issue. 33


Disadvantages: 

Relative to liquid fuel rockets, solid fuel rockets have lower specific impulse.  The propellant mass ratios of solid propellant upper stages is usually in the .91 to .93 range which is as good or better than that of most liquid propellant upper stages but overall performance is less than for liquid stages because of the solids' lower exhaust velocities.  Solid rockets cannot be throttled in real time.  Solid fuel rockets are intolerant to cracks and voids. COMBUSTION INSTABILITY

Combustion instability occurs when normal velocity (Vn) is not equal to the combustion velocity or flame velocity(Vf). There are 2 types of combustion instability: 1) Set of acoustic resonance, which can occur with any rocket motor. 2) Vortex shedding phenomenon, which only with particular type of propellant grains. 

These two types of problems, mainly occurs only when the rocket combustion is not controlled. It causes excessive pressure vibration forces or excessive heat transfer.



The combustion in liquid rocket is never perfectly smooth, there are some fluctuations of pressure, temperature, and velocities are present.

ROUGH COMBUSTION:

Rough combustion is defined as the Combustion that gives greater pressure fluctuation at a chamber wall location whichoccurs at completely random intervals is called rough combustion. POGO OSCILLATION:

Periodic variations of thrust, caused by combustion instability or longitudinal vibrations of structures between the tanks and the engines which modulate the propellant flow, are known as "pogo oscillations" or "pogo", named after the Pogo stick. Three different types of combustion instabilities occur. Some of them are, CHUGGING:

Chugging, the first type of combustion instability occurs mostly from the elastic nature of the feed systems and due to low frequency in the feed system which ranges from 100-400 HZ. This can cause cyclic variation in thrust, and the effects can vary from merely annoying to actually damaging the payload or vehicle. Chugging can be minimized by using gas-filled damping tubes on feed lines of high density propellants. BUZZING:

This is the intermediate type of instability and its frequency ranges from 400-1000HZ. This can be caused due to insufficient pressure drop across the injectors. It generally is mostly annoying, rather 34


than being damaging. However, in extreme cases combustion can end up being forced backwards through the injectors. This can cause explosions with monopropellants. SCREECHING (OR) SCREAMING (OR) SQUEALING:

This is the third type of instability which has higher frequency of range 1000HZ and above. It is mostly perplexing which occurs both liquid and solid propellant rockets. This type is most destructing and has capability of destroying the engine much less than 1 sec. POPPING:

Popping is an undesirable random high amplitude pressure disturbance that occurs during steady state operation of a rocket engine with hypergolic propellant. It’s one of the pressure source triggering high frequency, instability in a rocket engine. ELIMINATION OF POPPING:

The elimination of popping is usually achieved by re-design of the injector rather than the application of baffles and absorbers.

ANSWER THE FOLLOWING IN SHORT 1. What is an igniter? 2. Name the types of igniters 3. What are the types of liquid igniter? 4. State any 5 characteristics of hypergolic liquids 5. State any 4 combinations of hypergolic ignition 6. Name the factors which affect the ignition delay and also give its equation with its terms 7. Classify solid rockets 8. Give the advantage and disadvantages of a bag igniter 9. Give the disadvantage of a basket igniters 10. What are the important components of a pyrotechnic igniter? 11. Give any 4 characteristics of squib 12. What are the factors to be considered while designing an igniter? 13. Distinguish between pressure feed system and pump feed system 14. What is geysering effect? 15. What is meant by outage? 16. Define combustion instability 17. Define cavitation and how cavitation will be avoided? 18. What are the problems to be avoided while designing a fuel t ank outlet? 19. What is meant by liquid drop out? 20. What is an injector? 21. What are the types of injectors? 22. Define atomization of fuel 23. What is meant chugging? 24. Define the term buzzing 25. Define the term screeching 26. Define the term popping 27. What is an ignitability bomb? 28. Name the components of live igniters 29. What are the methods used for cooling of thrust chambers? 30. Define the term rough combustion 31. Draw a neat sketch of solid rocket combustion chamber 32. Name the types of valves which are used in rockets. 33. What are the modes of actuations used for operating a valve in a rocket? 35


34. Give the applications of valves in a rocket.

DETAILED ANSWERS:

1. Classify the different types of igniters with neat sketches. 2. What is an injector? What is the main difference between an injector and a carburettor? Classify its various types with neat sketches. 3. Distinguish between Helium pressure feed system and centrifugal pump feed system. Pictorially represent Helium pressure feed system and explain in detail. 4. Elaborately explain the propellant pump feed system with an appropriate sketch. 5. What are the important design considerations in the section of l iquid rocket combustion chamber volume and shape? List and explain them briefly. 6. What is the need for cooling a thrust chamber? What are the different methods of cooling of thrust chambers? Explain them briefly and draw appropriate sketches wherever necessary. 7. What is propellant slosh? Discuss its effects on flight vehicles and explain how it is controlled? 8. What are problems generally faced by a designer while designing the liquid propellant tank outlet design? Explain them briefly 9. Explain the phenomenon, propellant hammer in a liquid propellant rocket engine with an appropriate sketch. 10. What is geysering effect? When and where does it occur? Explain your answer with a neat sketch. 11. Define combustion instability and explain briefly about the various types of combustion instability. 12. Elucidate the combustion mechanism of a solid propellant rocket.

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UNIT-2 AERODYNAMICS OF ROCKETS AND MISSILES

AIRFRAME COMPONENTS OF A MISSILE:

The components or parts which are experienced by the course of air are known as airframe components .The body of the missile can be divided into three major sections .They are 

Nose or Fore body  Midsection or Main body  The aft or Boat tail section  Fins

MAJOR COMPONENTS OF A MISSILE

NOSE (or) FORE BODY:

It is the first and foremost component of a missile which experiences air while travelling through the atmosphere. Several types of nose sections were used in various types of missiles. Some of the types are, 37


 Conical fore body  Ogival fore body  Hemispherical fore body

CONICAL FORE BODY:

These types of fore body are used in missiles, which are intended to fly at supersonic speeds. The missile, while travelling in the atmosphere oblique shock is formed at the tip of the wedge and apex of the cone. There are various aerodynamic and thermodynamic changes are noticeable in the flow characteristics of air, in the case of conical nose. CONICAL NOSE OF A SUPERSONIC MISSIE

OGIVAL FORE BODY:

Ogival nose configuration is used more frequently than the conical nose. An ogive is similar to a cone except that the plan form shaped is formed by an arc of a circle instead of a straight line as shown in figure. The ogival shape has several advantages over the conical section. ADVANTAGES: 1. Slightly greater volume for a given base and length(L/D ratio) 2. A blunter nose provides structural superiority. 3. Slightly lower drag.

HEMISPHERICAL FORE BODY:

This type of nose is used on some of the missiles, particularly those which use IR (infrared) seekers. 38


This type of nose imposes an extremely high drag penalty on the missile. The use of this type of nose on missiles indicates the extent to which an aerodynamicist must compromise to achieve an optimum and feasible missile system.

MID SECTION:

In most missile configurations, the mid section is in cylindrical shape. The shape is advantageous from the stand points of drag, ease of manufacturing, and the load carrying capability. The zero-lift drag of a cylindrical body is caused by skin friction force only. At low angle of attack, a very small amount of normal force is developed on t he body, this results from the “carryover “from the nose section. BOAT TAIL:

The tapered portion of the aft section of a body is called the boat tail. The purpose of boat tail is to decrease the drag of a body which has a squared off base. The mid section has relatively large base pressure and consequently high drag values because of large base area. By “boat tailing” the rear portion of the body, the base area is reduced and thus the base drag is reduced. However, the decrease in base drag may be partially nullified by the boat tail drag. FINS:

The purpose of putting fins on the rocket is to provide stability, provide lift and control the flight path of the missile. The plan form of fins of a rocket is of different types. They are of clipped tip delta, rectangular, triangular, trapezoidal etc.

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AERODYNAMIC SURFACES OF MISSILES: 1. SUPERSONIC WING CROSS SECTIONAL SHAPES :

The various supersonic wings cross sectional shapes are, 1. Double wedge 2. Modified double wedge and 3. Biconvex 1. Double wedge :

The double wedge offers a least drag but l acks strength. 2. Modified double wedge:

The modified double wedge has relatively low drag and comparatively stronger than the latter one. 3. Biconvex:

The biconvex causes considerable drag but it is the strongest of the three designs. The biconvex shape has a slight advantage in minimum drag for unit cross sectional strength in addition to the absence of sharp corner. The sharp corners affect the flow conditions over the surface. The biconvex section also provides larger wedge angles at the leading and trailing edges. SUPERSONIC WING PLAN FORMS:

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(a) CLIPPED TIP DELTA RECTANGULAR

(b) DELTA (or) TRIANGULAR

(c)

(d) RECTAGULAR WITH RAKE The main difference between the subsonic and supersonic types of wing plan forms is the symmetry about the chord and sharpness of the leading edge. For the supersonic case, the need for sharp leading edge is to encounter the type of flow and pressure distribution while travelling faster than speed of sound. AERODYNAMIC CONTROLS OF A MISSILE:

Aerodynamic control is the connecting link between the guidance system and the flight path of the missile. Effective control of flight path requires smooth and exact operation of the control surfaces of the missile. They must have the best possible design configuration for the intended speed of the missile. The control surface must move with enough force to produce the necessary change of direction. The adjustments they make must maintain the balance and centre of gravity of the missile. The control surface must also be positioned to meet variations in lift and drag at different flight speeds. All these conditions contribute to the flight stability of the missile. ARRAGEMENTS OF CONTROL SURFACES IN A MISSILE

(a) CONVENTIONAL

(b) “H” TYPE (or) DOUBLE RUDDER

The types of aerodynamic controls of a missile are, 1. 2. 3. 4.

Canard control Wing control Tail control Unconventional control

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(c) V-TAIL


1. CANARD CONTROL:

Canard control is also quite commonly used, especially on short-range air-to-air missiles. The primary advantage of canard control is better maneuverability at low angles of attack, but canards tend to become ineffective at high angles of attack because of flow separation that causes the surfaces to stall. Since canards are ahead of the centre of gravity, they cause a destabilizing effect and require large fixed tails to keep the missile stable. These two sets of fins usually provide sufficient lift to make wings unnecessary.

1. a.SPLIT CANARD:

A further subset of canard control missiles is t he split canard. Split canards are a relatively new development that has found application on the latest generation of short -range air-to-air missiles. The term split canard refers to the fact that the missile has two sets of canards in close proximity, usually one immediately behind the other. The first canard is fixed while the second set is movable. The advantage of this arrangement is that the first set of canards generates strong, energetic vortices that increase the speed of the airflow over the second set of canards making them more effective. In addition, the vortices delay flow separation and allow t he canards to reach higher angles of attack before stalling. This high angle of attack performance gives the missile much greater maneuverability compared to a missile with single canard control.

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AERODYNAMIC CHARACTERISTICS OF CANARD CONTROL:

1. The canard control missile has the advantage of small control surfaces for longitudinal control and it places the portion of the control equipment well forward in the body out of the way of the main propulsion and guidance unit. 2. This type tends to give low drag as much as the main lifting surfaces fixed and it can be made of large sweep back type where in the lift to drag ratio can be optimized. 3. The canard control surfaces are deflected in the positive manner that is the l eading edge upward to provide a positive angle of attack of the missile and this is in turn places the control surfaces at quite large angle of attack relative to the free stream especially when the missiles pitched to large angles. 4. This change tends to increase loads and hinge moments on the control surfaces. High control surface rates and hence high power will be required, to increase the angle of attack to acquire the required maneuver. WING CONTROL:

Wing control was one of the earliest forms of missile control developed, but it is becoming less commonly used on today's designs. Most missiles using wing control are longer-range missiles. The primary advantage of wing control is that the deflections of the wings produce a very fast response with little motion of the body. This feature results in small seeker tracking error and allows the missile to remain locked on target even during large maneuvers. The major disadvantage is that the wings must usually be quite large in order to generate both sufficient lift and control effectiveness, which makes the missiles rather large overall. In addition, the wings generate strong vortices that may adversely interact with the tails causing the missile to roll. This behaviour is known as induced roll, and if the effect is strong enough, the control system may not be able to compensate.

TAIL CONTROL:

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Tail control is probably the most commonly used form of missile control, particularly for longer range air-to-air missiles and surface-to-air missiles. The primary reason for this application is because tail control provides excellent maneuverability at the high angles of attack often needed to intercept a highly maneuverable aircraft. Missiles using tail control are also often fitted with a non-movable wing to provide additional lift and improve range. Some good examples of such missiles are air-to-ground weapons like Maverick and AS.30 as well as surface-to-surface missiles like Harpoon and Exocet. Tail control missiles rarely have canards. UNCONVENTIONAL CONTROL:

The surface of a missile that create a jet exhaust perpendicular to the vehicle surface and produce an effect similar to thrust Unconventional control systems is a broad category that includes a number of advanced technologies. Most techniques involve some kind of thrust vectoring. Thrust vectoring is defined as a method of deflecting the missile exhaust to generate a component of thrust in a vertical and/or horizontal direction. This additional force points the nose in a new direction causing the missile to turn. Another technique that is just starting to be introduced is called reaction jets. Reaction jets are usually small ports in vectoring. These techniques are most often applied to high off-boresight air-to-air missiles to provide exceptional maneuverability. The greatest advantage of such controls is that they can function at very low speeds or in a vacuum where there is little or no airflow to act on conventional fins. The primary drawback, however, is that they will not function once the fuel supply is exhausted. Note that most missiles equipped with unconventional controls do not rely on these controls alone for maneuverability, but only as a supplement to aerodynamic surfaces like canards and tail fins.

Classification of Missile

Missiles are generally classified on the basis of their Type, Launch Mode, Range, Propulsion, Warhead and Guidance Systems.

Type:

1. Cruise Missile 2. Ballistic Missile Launch Mode:

1. 2. 3. 4.

Surface-to-Surface Missile Surface-to-Air Missile Surface (Coast)-to-Sea Missile Air-to-Air Missile 44


5. 6. 7. 8.

Air-to-Surface Missile Sea-to-Sea Missile Sea-to-Surface (Coast) Missile Anti-Tank Missile

Range:

1. 2. 3. 4.

Short Range Missile Medium Range Missile Intermediate Range Ballistic Missile Intercontinental Ballistic Missile

Propulsion:

1. 2. 3. 4. 5. 6.

Solid Propulsion Liquid Propulsion Hybrid Propulsion Ramjet Scramjet Cryogenic

Warhead:

1. Conventional 2. Strategic Guidance Systems:

1. 2. 3. 4. 5. 6. 7. 8.

Wire Guidance Command Guidance Terrain Comparison Guidance Terrestrial Guidance Inertial Guidance Beam Rider Guidance Laser Guidance RF and GPS Reference

On the basis of Type:

(i) Cruise Missile: A cruise missile is an unmanned self-propelled (till the time of i mpact) guided vehicle that sustains flight through aerodynamic lift for most of its flight path and whose primary mission is to place an ordnance or special payload on a target. They fly within the earth’s atmosphere and use jet engine technology. These vehicles vary greatly in their speed and ability to penetrate defences.Cruise missiles can be categorised by size, speed (subsonic or supersonic), range and whether launched from land, air, surface ship or submarine.

Depending upon the speed such missiles are classified as: 1) Subsonic cruise missile

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2) Supersonic cruise missile 3) Hypersonic cruise missile

Subsoni c cr ui se missil e

Subsonic cruise missile flies at a speed lesser than that of sound. It travels at a speed of around 0.8 Mach. The well-known subsonic missile is the American Tomahawk cruise missile. Some other examples are Harpoon of USA and Exocet of France. Super soni c cru ise missil e

This missile travels at a speed of around 2-3 Mach i.e.; it travels a kilometre approximately in a second. The modular design of the missile and it s capability of being launched at different orientations enable it to be i ntegrated with a wide spectrum of platforms like warships, submarines, different types of aircraft, mobile autonomous launchers and silos. The combination of supersonic speed and warhead mass provides high kinetic energy ensuring tremendous lethal effect. BRAHMOS is the only known versatile supersonic cruise missile system which is in service. H yper soni c cru ise missil e

This missile travels at a speed of more than 5 Mach. Many countries are working to develop hypersonic cruise missiles. BrahMos Aerospace is also in the process of developing a hypersonic cruise missile, BRAHMOS-II, which would fly at a speed greater than 5 Mach. (ii) Ballistic Missile:

A ballistic missile is a missile that has a ballistic trajectory over most of its flight path, regardless of whether or not it is a weapon-delivery vehicle. Ballistic missiles are categorised according to their range, maximum distance measured along the surface of earth's ellipsoid from the point of launch to the point of impact of the last element of their payload. These missiles carry a huge payload. The carriage of a deadly warhead is justified by the distance the missile travels. Ballistic missiles can be launched from ships and land based facilities. For example, Prithvi I, Prithvi II, Agni I, Agni II and Dhanush ballistic missiles are currently operational in the Indian defence forces.

On the basis of Launch Mode: (i) Surface-to-Surface Missile: A surface-to-surface missile is a guided projectile launched from a hand-held, vehicle mounted, trailer mounted or fixed installation. It is often powered by a rocket motor or sometimes fired by an explosive charge since the launch platform is stationary. (ii) Surface-to-Air Missile: A surface-to-air missile is designed for launch from the ground to destroy aerial targets like aircrafts, helicopters and even ballistic missiles. These missiles are generally called air defence systems as they defend any aerial attacks by the enemy. (iii) Surface (Coast)-to-Sea Missile: A surface (coast)-to-sea missile is designed to be launched from land to ship in the sea as targets. (iv) Air-to-Air Missile: An air-to-air missile is launched from an aircraft to destroy the enemy 46


aircraft. The missile flies at a speed of 4 Mach. (v) Air-to-Surface Missile: An air-to-surface missile is designed for launch from military aircraft and strikes ground targets on land, at sea or both. The missiles are basically guided via laser guidance, infrared guidance and optical guidance or via GPS signals. The type of guidance depends on the type of target. (vi) Sea-to-Sea Missile: A sea-to-sea missile is designed for launch from one shi p to another ship. (vii) Sea-to-Surface (Coast) Missile: A sea-to-surface missile is designed for launch from ship to land based targets. (viii) Anti-Tank Missile: An anti-tank missile is a guided missile primarily designed to hit and destroy heavily-armoured tanks and other armoured fighting vehicles. Anti-tank missiles could be launched from aircraft, helicopters, tanks and also from shoulder mounted launcher.

On the basis of Range:

This type of classification is based on maximum range achieved by the missiles. The basic classification is as follows: (i) Short Range Missile (ii) Medium Range Missile (iii) Intermediate Range Ballistic Missile (iv) Intercontinental Ballistic Missile

On the basis of Propulsion: (i) Solid Propulsion: Solid fuel is used in solid propulsion. Generally, the fuel is aluminium powder. Solid propulsion has the advantage of being easily stored and can be handled in fuelled condition. It can reach very high speeds quickly. Its si mplicity also makes it a good choice whenever large amount of thrust is needed. (ii) Liquid Propulsion: The liquid propulsion technology uses liquid as fuel. The fuels are hydrocarbons. The storage of missile with liquid fuel is difficult and complex. In addition, preparation of missile takes considerable time. In liquid propulsion, propulsion can be controlled easily by restricting the fuel flow by using valves and it can also be controlled even under emergency conditions. Basically, liquid fuel gives high specific impulse as compared to solid fuel. (ii) Hybrid Propulsion: There are two stages in hybrid propulsion - solid propulsion and liquid propulsion. This kind of propulsion compensates the disadvantages of both propulsion systems and has the combined advantages of the two propulsion systems. (iii) Ramjet: A ramjet engine does not have any turbines unlike turbojet engines. It achieves compression of intake air just by the forward speed of the air vehicle. The fuel is injected and ignited. The expansion of hot gases after fuel i njection and combustion accelerates the exhaust air to a velocity higher than that at the inlet and creates positive push. However, the air entering the engine should be at supersonic speeds. So, the aerial vehicle must be moving in supersonic speeds. Ramjet engines cannot propel an aerial vehicle from zero to supersonic speeds. 47


(iv) Scramjet: Scramjet is an acronym for Supersonic Combustion Ramjet. The difference between scramjet and ramjet is that the 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. (v) Cryogenic: Cryogenic propellants are liquefied gases stored at very low temperatures, most frequently liquid hydrogen as the fuel and liquid oxygen as the oxidizer. Cryogenic propellants require special insulated containers and vents which allow gas to escape from the evaporating liquids. The liquid fuel and oxidizer are pumped from the storage tanks to an expansion chamber and injected into the combustion chamber where they are mixed and ignited by a flame or spark. The fuel expands as it burns and the hot exhaust gases are directed out of the nozzle to provide thrust.

On the basis of Warhead: (i) Conventional Warhead: A conventional warhead contains high energy explosives. It is filled with a chemi al explosive and relies on the detonation of the explosive and the resulting metal casing fragmentation as kill mechanisms. (ii) Strategic Warhead: In a strategic warhead, radio active materials are present and when triggered they exhibit huge radio activity that can wipe out even cities. They are generally designed for mass annihilation.

On the basis of Guidance Systems: (i) Wire Guidance: This system is broadly similar to radio command, but is less susceptible to electronic counter measures. The command signals are passed along a wire (or wires) dispensed from the missile after launch. (ii) Command Guidance: Command guidance involves tracking the projectile from the launch site or platform and transmitting commands by radio, radar, or laser impulses or along thin wires or optical fibres. Tracking might be accomplished by radar or optical instruments from the launch site or by radar or television imagery relayed from the missile. (iii) Terrain Comparison Guidance: Terrain Comparison (TERCOM) is used invariably by cruise missiles. The system uses sensitive altimeters to measure the profile of the ground directly below and checks the result against stored information. (iv) Terrestrial Guidance: This system constantly measures star angles and compares them with the pre- programmed angles expected on the missile’s intended trajectory. The guidance system directs the control system whenever an alteration to trajectory is required. (v) Inertial Guidance: This system is totally contained within the missile and is programmed prior to launch. Three accelerometers, mounted on a platform space-stabilised by gyros, measure accelerations along three mutually perpendicular axes; these accelerations are then integrated twice, the first integration giving velocity and the second giving position. The system then directs the control system to preserve the pre-programmed trajectory. These systems are used in the surface-to-surface missiles and in cruise missiles.

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(vi) Beam Rider Guidance: The beam rider concept relies on an external ground or ship-based radar station that transmits a beam of radar energy towards the target. The surface radar tracks the target and also transmits a guidance beam that adjusts its angle as the target moves across the sky. (vii) Laser Guidance: In laser guidance, a laser beam is focused on the target and the laser beam reflects off the target and gets scattered. The missile has a laser seeker that can detect even miniscule amount of radiation. The seeker provides the direction of the l aser scatters to the guidance system. The missile is launched towards the target, the seeker looks out for t he laser reflections and the guidance system steers the missile towards the source of laser reflections that is ultimately the target. (viii) RF and GPS Reference: RF (Radio Frequency) and GPS (Global Positioning System) are examples of technologies that are used in missile guidance systems. A missile uses GPS signal to determine the location of the target. Over the course of its flight, the weapon uses this information to send commands to control surfaces and adjusts its trajectory. In a RF reference, the missile uses RF waves to locate the target.

FORCES ACTING ON A MISSIE WHILE PASSING THROUGH ATMOSPHERE:

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DERIVATION:

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53


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For finned rockets, the coefficient cd is usually smaller than dcl/dα that is only 2-4% of dcl/dα and therefore can be neglected.

LATERAL AERODYNAMIC DAMPING MOMENT OF THE ROCKET:

The lateral angular velocity Ω gives rise to an additional aerodynamic moment which is proportional to the angular velocity MΩ and so directed that it tends to reduce the angular velocity and this moment is known as lateral aerodynamic damping moment

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.

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LONGITUDINAL AERODYNAMIC MOMENT:

In case of symmetric finned rockets the component Mx of the aerodynamic moment along a longitudinal axis is zero. However it is not for the rockets with slanted fins. In such a rocket each fin is mounted to make certain angle with longitudinal axis in such a way that on rotation of missile through 360/n degrees (n-number of fins). Each fin assumes the position occupied by the adjacent fin prior rotation when fins are slant mounted, a moment arises during the flight, which tends to rotate the rocket about its axis of symmetry. symmetry. For simplicity study the motion of such rocket at an angle of attack, α=0. Since each fin encounters the airflow at an angle, the fins are acted upon by a lift force L, perpendicular to the rocket axis. axis. The centre of pressure of this force i.e the point of intersection intersection of its line of action with the plane of the fin i s at a distance of r c.c. If there are n number of fins the total longitudinal moment is n.L1.r c . since the lift force is proportional to the air air density and the square of the velocity and further further to the fin angle angle ε.

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LONGITUDINAL AERODYNAMIC DAMPING MOMENT:

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LONGITUDINAL AERODYNAMIC DAMPING MOMENT

DRAG ESTIMATION:

The drag of the rocket vehicle can be split into following components, components, 

WAVE DRAG: Wave is mainly due to the presence of shock waves and dependent on the Mach number. The wave drag is connected with the shock wave, and hence occurring only at supersonic speeds.

1. The amount of wave drag for the t he conical body is estimated as,

Where, θ is the half cone angle in radians. 2. The wave drag of an isolated, rectangular rectangular wing span, b, with a double wedge profile is is estimated as,

Where, θ is the half wedge wedge angle. Both wave drag coefficients are strongly dependent on θ and decrease with increasing Mach numbers.

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VISCOUS DRAG: The viscous drag is formed due to friction. It is the main drag component at subsonic speeds. It can be estimated by considering the friction drag coefficient CDf, for a flat plate of equal length and equal wetted area as a rocket vehicle. For a laminar boundary layer we may estimate,

For a turbulent boundary layer we may estimate as,

These coefficients are based on the wetted area as a reference area. For most large rockets, one may assume the boundary layer to be t urbulent. Transition from laminar to turbulent takes place around R e=106 based on body length, so that for small vehicles, still a major portion of the boundary layer may be laminar. Surface roughness may cause a transition from laminar to turbulent at lower Reynolds number. 

INDUCED DRAG: Induced drag is a result of the development of lift. In a subsonic case, the induced drag, based on the projected wing area, Sw, is

At supersonic speed, it can be well approximated by,



BASE DRAG: Base drag is strongly affected by the shape of the vehicle, and the presence of a jet. The total drag is found by the addition of all components. It turns out that the total drag coefficient can be well approximated for preliminary calculations by,



INTERFERENCE DRAG: Interference drag is due to the interaction of various flow fields.

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ROUGHNESS DRAG: It is mainly due to the surface roughness such as rivets and welds.

ROCKET DISPERSION: DISPERSION-DEFINITION

Dispersion is defined as the measure of deviation of the rocket’s trajectory from the standard nominal trajectory. For a rocket, dispersion arises from three different sources. They are, 1. Events that occur at launching, 2. Events during burning after launching, and 3. Events after burning. For rockets, most of the dispersion arises during the burning period after launching. FACTORS CAUSING DISPERSION :

The factors that induce dispersion of rocket’s trajectory are,  The propellant mass and composition Inaccuracy  The rocket total mass, axial and lateral Moments of inertia and resultant centre of    

gravity Inaccuracies Launcher deflection The thrust force of the rocket engine: because of the tolerance in rocket engine design, propellant properties, and manufacturing Thrust and fin misalignments: It is an important source of dispersion in case of unguided rockets. Atmospheric disturbances such as wind profile, tail wind, cross wind, and gusts, variation in atmospheric density.

METHODS TO ESTIMATE DISPRSION:

There are some methods to estimate the dispersion of trajectory for a rocket. They are, 

Root Mean Square Method



Monte Carlo method



Method of covariance matrix

1. The Root Mean Square Method:

The Root Mean Square Method simulates the rocket trajectory perturbing one parameter at time and the results are compared with the nominal results. The sum of squares deviations for all parameters is square of total deviation. 2. Monte Carlo method:

Monte Carlo method of dispersion removes smaller dispersion parameters. Each input parameter is selected randomly in the defined ranges and used in the simulation of trajectory.

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3. The Method of covariance matrix:

In probability theory and statistics, covariance is a measure of how much two variables change together. A covariance matrix is a matrix whose element in the i, j position is the covariance between the i th and j th elements of a random vector (that is, of a vector of random variables). Each element of the vector is a scalar random variable, either with a finite number of observed empirical values or with a finite or infinite number of potential values specified by a theoretical joint probability distribution of all the random variables. TYPES OF ROCKET DISPERSION:

There are two types of rocket dispersion, such as I. II.

In plane dispersion (or) Range dispersion Lateral dispersion (or) Out of plane dispersion

IN-PLANE DISPERSION (or) RANGE DISPERSION:

In the absence of perturbing forces giving rise to rocket dispersion, the trajectory of the rocket would lie in the launch plane. But practically such factors are generally active and try to produce that cause. The dispersion of the rocket, which may be of any type sometimes the rocket, can suffer both types. LATERAL DISPERSION (or) OUT OF PLANE DISPERSION:

If the perturbing forces are active, the axis of the rocket will deviate from the target to the trajectory of the mass centre by an angle known as angle of attack. Since the t hrust is directed along the axis of the rocket, the deviation gives rise to a thrust component normal to the trajectory. The trajectory thus departs from the intended path and put the rocket away from the target.

MINIMIZATION OF ROCKET DISPERSION:

For trajectory vehicles, dispersion can be minimized by means of a special guidance system. The guided system is thought to be known as the brain of a rocket or a missile. The distinct tasks of a guidance system are as follows: 1. It maintains the missile in proper attitude. Using instruments like gyros, the control system correct the problems experienced through rotation and translation motion of a rocket. 2. The control guidance system also helps in tracking the positions, computing the tracking information, correcting the signals and then steering the rocket in a correct orbit and thus helps in minimizing the dispersion.

Short answers: 1. What are the airframe components of a missile? 2. Name the different types of nose cones in a missile 3. What are the advantages of ogival fore body? 62


4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

What are the aerodynamic controls present in a missile? What do you mean by canard control of guided missiles? What is the important of boat tail in missiles? Sketch the different shapes of supersonic wing cross section Sketch the various supersonic wing plan forms How do you classify the missiles based on navigation and mission? Mention the aerodynamic characteristics of air to surface missile What is meant by lateral aerodynamic damping moment? Distinguish between body up wash and body downwash in missile aerodynamics What are the forces which act on a trajectory vehicle while passing through the atmosphere? What are the different types of drag which acts on a missile in atmosphere? atmosphere? W hat is meant rocket by rocket dispersion? What are the types of rocket dispersion? What are the factors which causes rocket dispersion? How do you minimize rocket dispersion? What are the methods used to estimate rocket dispersion?

BRIEF ANSWERS: 1. Explain the various airframe components and various aerodynamic aerodynamic controls of a missile. Draw sketches wherever necessary. 2. Explain the forces acting on a missile while passing through the atmosphere. Elucidate your answer with a neat sketch. 3. What are the different types of drag which acts on a missile in atmosphere? Clearly Clearly explain what wave drag is. What is its relative importance in the total drag estimation of a supersonic missile? How is wave drag coefficient estimated estimated for double wedge, modified double wedge and biconvex profiles of supersonic airfoils? 4. With the help of a neat sketch clearly explain how fins impart stability to a rocket in flight which is in atmosphere. 5. What are the various wings cross sectional shapes that are generally used for supersonic missiles? Sketch such shapes and mention their advantages advantages and limitations. 6. With a neat sketch clearly explain the l ateral aerodynamic aerodynamic moment of a rocket and briefly elucidate the variation of lateral aerodynamic aerodynamic moment coefficient variation with angle of attack. How does thus variation affects the stability of the rocket flight? 7. With a neat sketch clearly explain the l ongitudinal aerodynamic aerodynamic moment of a rocket. 8. List any four basic aerodynamic design considerations for the development of air to air missiles. What factors limits the range of such missiles? 9. Classify the various types of missiles. 10. What is rocket dispersion? How it is i s classified? What are the important factors that cause dispersion? How it can be minimized?

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UNIT – UNIT – 3 3 ROCKET MOTION IN FREE SPACE AND IN GRAVITATIONAL FIELD NEWTON'S LAW OF UNIVERSAL GRAVITATION: Newton's law of universal gravitation states that every point every point mass in the universe attracts every other point mass with a force a force that is directly is directly proportional to the product of their masses and inversely proportional to the square of the distance between them them.. (Separately it was shown that large spherically symmetrical symmetrical masses attract and are attracted as if all their all their mass were concentrated concentrated at their centers.) This centers.) This is a general physical general physical law derived from empirical from empirical observations by what Newton what Newton called induction. called induction.

Every point Every point mass attracts every single other point mass by a force a force pointing pointing along the line the line intersecting both points. The force is proportional is proportional to the product the product of the two masses two masses and inversely proportional to the square the square of the distance between them

,

where:     

F is is the force between the masses, G is the gravitational the gravitational constant, m1 is the first mass, m2 is the second mass, and r is is the t he distance between the centres of the masses.

Assuming SI Assuming SI units, F units, F is is measured in newtons in newtons (N), m1 and m2 in kilograms in kilograms (kg), r in in −11 2 −2. meters (m), and the constant G is approximately equal to 6.674×10 N m kg Newton's law of gravitation gravitation resembles resembles Coulomb's Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies. Both are inverse-square are inverse-square laws, in laws, in which force is inversely proportional to the square of the distance between the bodies. Coulomb's Law has the product of two charges in place of the product of the masses, and the electrostatic the electrostatic constant in place of the gravitational constant.

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Newton's law has has since been been superseded superseded by Einstein's Einstein's theory of general general relativity, but relativity, but it continues to be used as an excellent approximation approximation of the effects of gravity. Relativity is required only when there is a need for extreme precision, or when dealing with gravitation for extremely massive extremely massive and dense objects. THE EQUATIONS OF MOTION

To describe the motion of the rocket r ocket vehicle we need the following reference frames: frames: Inertial frame: OXYZ

This frame is chosen such that the trajectory of the centre of mass of the vehicle lies in the XZ plane. So this plane is determined by the t he launch direction (initial velocity) and the direction of the gravitational field. The inertial frame will be specified further where necessary. The unit vectors along the axes of the inertial frame will be ex, ey and ez.

Vehicle reference frame oxyz:

The origin of this frame is the centre of mass of the rocket. The x-axis coincides with the longitudinal axis of the rocket and is positive forwards. The y- and z-axes are chosen such that they form an orthogonal right handed Cartesian frame, frame, the xz- plane coinciding with the XZ plane. The unit vectors along the axes of the vehicle reference frame are e x , ey and ez. The position of the rocket is determined by the X and Z coordinates of its centre of mass, while the orientation is determined by the angle between the x axis and X axis: the pitch angle θ The equation of two dimensional motion (along the axes of the vehicle reference frame) frame) can be obtained by substitution of v=p=r=0.However, in this simple case, we prefer to express the equations in components along the axes of the t he inertial frame. The equations for translation motion can be obtained from the vector equation,

As we will only consider nominal trajectory, the thrust is assumed to act along the x-axis, i.e,Fx=Fy=0, while its application point will be assumed assumed to lie on the x axis, ye=ze=0. The thrust F and aerodynamic force Fa are given by,

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Fig: coordinate systems to describe the two-dimensional rocket motion

The gravitational field strength g, and the position vector, R cm of the centre of mass are resolved into components along the inertial axes

By using the equation and the relation between the unit vectors in both reference frames,

We obtain the equations,

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The equation of rotational motion is obtained by substitution of p=r=Ze=Fz=0

Letting be the velocity components of the centre of mass along the X and Z axes respectively, and nothing that the pitch rate q, is related to the pitch angle θ, by

The equations of motion can be written as

This instantaneous mass of the rocket follows from the differential equation

The thrust can be written as 67


The above equations are the complete equations for two dimensional rocket motion. This system of equations is still rather complicated. The aerodynamic forces are dependent on velocity and position; the gravitational components are in general dependent on the position, while the thrust is dependent on the position owing to the atmospheric pressure term. In general, analytic solution of these equations is not possible. TSIOLKOVSKY ROCKET EQUATION (OR) IDEAL ROCKET EQUATION (OR) EQUATION OF OBERTH

The Tsiolkovsky rocket equation , or ideal rocket equation, describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself (a thrust) by expelling part of its mass with high speed and move due to the conservation of momentum. The equation relates the delta-v (the maximum change of speed of the rocket if no other external forces act) with the effective exhaust velocity and the initial and final mass of a rocket For any such maneuver (or journey involving a number of such maneuvers):

where: is the initial total mass, including propellant, is the final total mass, is the effective exhaust velocity( where is the specific impulse of a time period and is Standard Gravity), is delta-v - the maximum change of speed of the vehicle (with no external forces acting), refers to the natural logarithm function.

This equation was independently derived by Konstantin Tsiolkovsky towards the end of the 19th century and is widely known under his name or as the 'ideal rocket equation'. Derivation

Consider the following system: In the following derivation, "the rocket" is taken to mean "the rocket and all o f its unburned propellant". Newton's second law of motion relates external forces ( system as follows: 68

) to the change in linear momentum of the


where

and

is the momentum of the rocket at time t=0:

is the momentum of the rocket and exhausted mass at time

:

and where, with respect to the observer: is the velocity of the rocket at time t=0 is the velocity of the rocket at time is the velocity of the mass added to the exhaust (and lost by the rocket) during time is the mass of the rocket at time t=0 is the mass of the rocket at time The velocity of the exhaust in the observer frame is related to the velocity of the exhaust in the rocket frame by (since exhaust velocity is in the negative direction)

Solving yields:

and, using

, since ejecting a positive

If there are no external forces then

Assuming

results in a decrease in mass,

and

is constant, this may be integrated to yield:

or equivalently or

or

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where is the initial total mass including propellant, the final total mass, and the velocity of the rocket exhaust with respect to the rocket (the specific impulse, or, if measured in time, that multiplied by gravity-on-Earth acceleration). The value

where

is the total mass of propellant expended, and hence:

is the mass fraction (the part of the initial total mass that is spent as reaction mass).

Applicability

The rocket equation captures the essentials of rocket flight physics in a single short equation. It also holds true for rocket-like reaction vehicles whenever the effective exhaust velocity is constant; and can be summed or integrated when the effective exhaust velocity varies. It does not apply to non rocket systems, such as aero braking, gun launches, space elevators, launch loops, and in tether propulsion. ROCKET PARAMETERS:

The mass ratio is the very important parameter in determining the ideal velocity of the rocket. Mass ratio is defined as the ratio between the initial and final mass of the rocket. Mass ratio = M0/M1

Next to the mass ratio we can also define some of the other dimensionless quantities. We divide the initial mass (M 0) of the rocket into three parts. They are, 1. Payload mass(Mu) 2. Propellant mass(Mp) 3. Structural mass (M c)

Therefore we also define the initial mass and final mass as, Initial mass,M0 = Mu+Mp+Mc Final mass, M1 = Mu +Mc 1. PAYLOAD MASS (λ):

Payload ratio is defined as the ratio between payload mass to the initial mass of the rocket. It is defined by the symbol λ.

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2. PROPELLANT RATIO (Φ):

Propellant ratio is defined as the ratio between useful propellant mass to the initial mass of the rocket. 3. STRUCTURAL EFFICIENCY (ε):

Structural efficiency is defined as the ratio of structural mass to the summation of propellant mass and structural mass. It is denoted by the symbol ɛ. NOTE: 1. Mass ratio ˄, is always larger than 1.But in gravitation less field it is less than 1. 2. The payload ratio, structural efficiency and propellant ratio are always less than 1. 3. In general the range of these parameters for a single stage rocket is,

It can be checked easily that the various parameters are related by,

Apart from the mass parameters, the two other rocket parameters which relate the mass and thrust are, 1. The Specific thrust (β):

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2. The thrust-to-weight ratio(ψ0):

THE BURNOUT RANGE:

Burnout is defined as the termination of a rocket operation because of fuel exhaustion or shut off. The distance covered at a time t is given by,

In order to evaluate the above integral we have to know V as a function of time, m=m(t), has to be known.  For burnout range we have to derive expressions for two different propellant consumptions.  The first one yields a constant thrust and the second one yields the constant specific thrust. There are two cases in case of burn out range. They are, 1. Constant Thrust 2. Constant Specific Thrust

CASE1: CONSTANT THRUST:

In this case the propellant consumption is,

Consequently the instantaneous mass of the rocket during thrusting is given by,

The burning time t b follows from,

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Solve the above equation for getting t b using mass ratio and thrust to weight ratio, which yields

IMPULSIVE SHOT:  For a fixed ψ0 the burning time increases with increasing specific impulse, and increasing mass ratio˄.  The burning time decreases if ψ 0 increases, and t b→0 if ψ0→∞.  In that case all the propellant is consumed instantaneously. This is called an impulsive shot.

The velocity as a function of time is given by (for zero initial velocity)

Substitute the velocity equation in eqn no1, and evaluate the integral which leads to

Introduce the range function p(t), which is defined as,

Ad using thrust to weight ratio equation, the range can be written as,

The burnout range i.e, the distance covered at t=t b, then,

Where,

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Therefore the burnout range is given by,



We see that the burnout range is proportional to the square of the specific impulse and inversely proportional to the thrust to weight ratio.  For an impulsive shot ∆s b =0. If ˄→∞ the function p b approaches unity.

DIMENSIONLESS ACCELERATION:

It is defined as,

This equals the specific thrust and is increasing monotonically from ψ0 to ˄ψ0 at burnout. The dimensionless burnout range in free space

The figure gives the dimensionless burnout range, ∆s b/g0Isp2, as a function of ˄and also depicts the range as a function of instantaneous mass ratio M0/ (M0-m0t). CASE 2: CONSTANT SPECIFIC THRUST:

In this case,

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So

By differentiating the above equation, the propellant consumption as a function of time is found to be,

And the burning time follows from the eqn 2,

In this case, the specific impulse can be i nterpreted as a burning time, namely the burning time of the rocket with mass ratio˄=e and a constant specific thrust of unity. As the acceleration is constant and equal to g0β0, velocity and range are given by

And thus the burnout

It can be verified easily that, in the case of constant specific thrust, burning time and burnout range are larger than the corresponding quantities in the case of constant thrust with the same initial specific thrust.

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ROCKET MOTION IN A HOMOGENEOUS GRAVITATIONAL FIELD:

Homogeneous gravitational field is defined as the gravitational field at which the field strength g, is constant throughout. If we consider the earth locally as being flat, the local gravitational field may be considered homogeneous. Actually the earth is nearly spherical and its gravitational field can be approximated very well by a central inverse square field. However as long as the altitude and range are small relative to the mean earth’s radius, the earth may be considered flat and the field strength can be approximated very well by a constant. For small rockets, such as sounding rockets and tactical missiles this approximation yields good results. For launch vehicles and intercontinental ballistic missiles the powered flight trajectory of the first stages can also be calculated by good approximation with the flat earth assumption. For upper stages, however, the velocity will be so large that the flat earth approximation will lead to unacceptable deviations from the real trajectory. However, as most part of this trajectory is a coast phase, the trajectory can be approximated by a ballistic one and can be determined analytically in case of spherical earth.

If we choose the X-axis of the inertial system to coincide with the flat earth surface and the Z-axis vertical, then gx=0 and gz= -g0, where it is assumed that motion takes place near the surface of the earth. Then the equation of transitional motion become,

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Then the thrust is given by,

There are two cases in case of homogeneous gravitational field. They are, 1. Vertical Flight 2. Inclined Flight (or) Constant Pitch Angle CASE1: VERTICAL FLIGHT:

If during the whole flight θ=900, and if we have zero initial horizontal velocity, the trajectory will be straight line parallel to the z-axis. In that case Vz equals to the total velocity V, and the equation of motion simplifies to

As initial conditions we will choose a zero velocity and altitude at t=0. Equation 1 can be integrated independently of the mass flow program, leading to

We see that, in order to determine V as a function of time. Even the burn out velocity in t his case is dependent on the thrust program because the burning time depends on it. Again we will assume a constant thrust, in which case the mass flow is given by,

For this case the burning time is already derived in burn out range derivation. Then we find the velocity as a function of time

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CULMINATION TIME: Maximum altitude is reached at V=0. For ψ 0≥1 this will always occur for t>t b and we find for the culmination time.

The culmination time does not depend on ψ 0. Integration of V with respect to time yields the altitude as a function of time. Using the range function p, the altitude is given by

Fig: The dimensionless burnout velocity for vertical ascent in a homogeneous gravitational field

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Fig: The burnout and culmination altitudes for vertical ascent in a homogeneous gravitational field and in vacuum

From the figure above there is an optimal thrust to weight ratio, yielding a maximum value of the burnout altitude. The optimal value of ψ0 is found by differentiating the expression for h b with respect to ψ0 and setting the result equal to zero. Apart from the solution ψ0→∞, which yields a maximum burnout altitude, this leads to

The corresponding value of burnout altitude then is,

The maximum culmination altitude is given by,

CASE 2: CONSTANT PITCH ANGLE:

For constant pitch angle case we have to consider the equation of motion with θ=θ0. For simplicity , we assume t=0, in the origin of the inertial frame, with zero initial velocity. The equations for the velocity components can be integrated directly yielding,

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From burn out range derivation we derive burn out velocity. From that we use burn out velocity ,

We see that gravity losses increase with increasing pitch angle θ 0, and increasing burning time t b. The flight path angle between the velocity vector and the X-axis and positive if Vz is positive follows from,

The angle of attack, i.e. the angle between the longitudinal axis of the roc ket and the velocity vector is given by,

By using tanγ equation it can be derived that,

We see that, in general flight path angle and angle of attack will not be constant and the trajectory will be curved. Only in the case that ln M0/M1 is proportional to the flight path angle and the angle of attack is constant and the resulting trajectory will be a straight line. If we consider a constant thrust then t he velocity components, the flight path angle and the angle of attack follows a function of time by substitution of

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Sub the above in equations Vx, Vy and tanα equations. We then find that during powered flight γ increases and the trajectory is curved upwards. By taking the limit for t→0

Consequently, the angle of attack decreases during powered flight. Its initial value is given by,

After burnout, γ decreases and α increases. Then the trajectory is curved downwards. Culmination altitude is reached if γ=0, or equivalently if Vz=0, leading to,

The culmination time is independent of thrust. Fig: the angle of attack for flights with constant pitch angle and constant thrust in a homogeneous gravitational field and in vacuum.

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During powered flight, the coordinates are determined by,

The position at burn out is given by,

After burnout the position follows from

The coordinates for the culmination point are obtained by substitution of t=tc in the above equations.

GRAVITY TURN TRAJECTORY (OR) ZERO LIFT TRAJECTORY:

To reduce the aerodynamic forces on a rocket during its flight through the atmosphere, one will endeavour to keep the angle of attack as small as possible. For simple aerodynamically stabilized vehicles, this is accomplished by fixed fins. Vehicle that are mechanically stabilized or more or less complicated control systems to generate the moments necessary to keep the angle of attack as small as possible. This is of course not the case for aerodynamically controlled rockets during manoeuvring. 82


For launch vehicles, ICBMs and uncontrolled aerodynamically stabilized rockets we can say that the flight through the atmosphere takes place with zero angle of attack. In that case there is no lift and the curvature of trajectory is solely due to gravity, and hence the name gravity turn or zero lift trajectory . As the angle of attack is zero, the flight path angle equals the pitch angle,

Then the equation of motion become,

Where

It is convenient in this case to use the total velocity V and the flight path angle γas dependent variables instead of Vx and Vz and the summation yields,

The differential equation for γ is found by multiplication of eqn of motion eqn by Vz and by Vx and subtract the results we get,

The equations for the gravity turn, in general, cannot be solved analytically. However some special cases exist which allow for analytical solutions. These are constant specific thrust and constant pitch rate.

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CASE 1: CONSTANT SPECIFIC THRUST: β = β0. In this case the the equations of motion become

Elimination of t from the above equations leads to

Integration of the above equation leads to

We now define a velocity factor, Ӷ

If V0 and γ0 are initial velocity and initial flight path angle respectively, then the above two equations can be combined and can be written as,

KICK ANGLE:

In preliminary trajectory calculations the pitch over period is represented mathematically by an instantaneous rotation of both vehicle and velocity vector over an angle δ0, called the kick angle. The flight path angle then is,

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The relation between time and flight path angle can be written as,

The velocity factor and the time factor for the gravity turn with constant specific thrust in a homogeneous gravitational field

Substitution of V =V(γ,γ0,V0) from above two equation and changing to the variable q, defined as

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Simplifies and integrate which leads to

By introduction of a time factor Ӷ’, defined as,

t-t0 can be written as

The coordinates X and Z follows from

Again using the variable q is defined and we can derive as,

CASE2: CONSTANT PITCH RATE: q = q0. In that case

(1)

And the equations of motion become

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(2)

(3)

Differentiation of equation 2yields,

(4)

Equation (4) can be satisfied either if cos γ = 0, which means that we have a vertical ascent with zero pitch rate or if

(5) By combining the (2) and (4) eqn we see that the specific thrust is determined by,

(6)

As according to eqn (1)

(7)

Eqn (6) can be integrated, leads to

(8)

thus as burnout,

(9)

Which determines γ b . the burning time follows from

(10)

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Sub equation (7) into eqn (5) and the integration of resulting yields the velocity as the function of γ

(11)

By using the equations we find

(12) (or )

(13) So in this case gravity losses amount to 50% of the ideal velocity. This is the consequence of low thrust (β<2) and the resulting large burning time. The trajectory is obtained by integrating

(14)

(15)

These equations can be also integrated analytically.

SHORT ANSWERS

1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15.

Define Newtons Law Of Universal Gravitation Write the Equation of Translation motion of a rocket Write the Rotational Motion of a rocket State the equations of motion of a rocket What is Tsiolkovsky Rocket Equation? What are the Applications of Tsiolkovsky Rocket Equation? Define mass ratio What is pay load ratio? Define the following with their specific notations a) Propellant Ratio b) Structural efficiency c) Specific thrust d) Thrust to weight ratio What is mean by burnout? What is an impulsive shot? Define Dimensionless acceleration and also draw the dimensionless burnout range in free space What do you mean by homogeneous gravitational field? What is zero lift trajectory and state its significance? Define kick angle

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ANSWER IN DETAIL:

1. State the equations of motion of a rocket 2. Derive the equation of Oberth in terms of ideal velocity and mass ratio of a rocket (Or) Derive Tsiolkovsky Rocket equation (or) ideal rocket equation in terms of mass ratio 3. Derive an expression for burnout range in terms of specific impulse, mass ratio and thrust to weight ratio of a rocket. Assume the rocket develops a constant thrust 4. Derive an expression for the burnout range in case of constant specific thrust 5. Obtain an expression for burnout altitude and culmination altitude attained by a sounding rocket. Thrust developed by the rocket is constant. Aerodynamic effects can be neglected. Assume the rocket motion is in homogeneous gravitational field 6. Explain what is homogeneous gravitational field and also obtain an expression for a rocket in vertical flight 7. A rocket unit undergoes an inclined trajectory with constant pitch angle. The rocket develops constant thrust and its motion is in a homogeneous gravitational field. Derive expressions for burnout velocity and burnout altitude and culmination time. Show that the restical component of velocity is zero at culmination. Neglect the aerodynamic forces in the derivation

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UNIT-4 STAGING AND CONTROL OF ROCKETS AND MISSILES

BASIC PHASES OF A TRAJECTORY VEHICLE:

The three basic phases of a trajectory vehicle are, 1. BOOST PHASE 1.a. OPEN LOOP PHASE 1.b. CLOSED LOOP PHASE (OR) GUIDANCE PHASE 2. COASTING PHASE (OR) BALLISTIC PHASE 3. RETURN PHASE (OR) RECOVERY PHASE

BASIC MISSILE TRAJECTORY

1. BOOST PHASE:

The boost phase is the phase of the flight that is powered by a rocket motor. At this phase the rocket undergoes a constant acceleration to attain its maximum velocity. The boost phase can be sub divided into, 1. Open loop phase and 2. Closed loop phase (or) guidance phase. The open loop phase is pre programmed and consists of vertical takeoff, during which the rocket is rolled such that the thrust vector plane coincides with the desired plane of motion followed by the subsequent pitch over and gravity. The closed loop phase consists of computation of steering commands from the vehicles actual location, velocity and the coordinates of the desired point. 90


2. COASTING PHASE (OR) BALLISTIC PHASE:

In this stage the rocket undergoes negative acceleration due to gravity, coasting to its maximum altitude. During the coasting phase the rocket attains a maximum point. The maximum point or altitude at which the rocket attains is known as an apogee. The coasting phase is also known as the ballistic phase which always occurs outside the atmosphere. The ballistic phase covering the major part of the range and at the end of which the vehicle enters the atmosphere. 3. RETURN PHASE (OR) RECOVERY PHASE (OR) RE-ENTRY PHASE :

This is the final phase where the recovery system is deployed and the rocket falls back to the ground.

THRUST VECTOR CONTROL (or) THRUST VECTORING:

Thrust vector control (TVC) is the intentional change of the thrust vector with respect to the symmetry axis of the rocket. By changing the direction of the thrust vector, a control moment about a lateral axis of the rocket can be generated. REASONS FOR THRUST VECTOR CONTROL:

The reasons for thrust vector control are, 1. 2. 3. 4.

To willingly change the flight path or trajectory. To rotate the vehicle or change its attitude during powered flight. To correct for deviation from the intended flight. To correct for thrust misalignment of a fi xed nozzle in the main propulsion system during its operation.

METHODS OF THRUST VECTOR CONTROL:

Some of the methods of thrust vector control are, 1. 2. 3. 4. 5.

JET VANES JET AVATORS HINGE/GIMBAL SCHEME SWIVELLING NOZZLES/MOVABLE NOZZLES SECONDARY FLUID INJECTION THRUST VECTOR CONTROL(SITVC)

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1. JET VANES:

FOUR ROTATING HEAT RESISTANT AERODYNAMIC VANES IN A JET

Jet vanes are the pairs of heat resistant, aerodynamic wing shaped surfaces submerged in the exhaust jet of a fixed rocket nozzle. This method is used both in liquid and solid rocket motors. This was the first method used for controlling the thrust vector. When the vanes deflections are larger they cause extra drag. In German-V2 four graphite vanes are used. ADVANTAGES:

1. It is a proven technology 2. Low actuation power is needed for this method

DISADVANTAGES:

1. Erosion of jet vanes takes place 2. Thrust loss is of 0.5% to 3%

2. JET AVATORS:

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It is used in solid type of rocket motors. The most common method of thrust direction control is by the use of rings called jet avators. The jet avator consists of two rings one for yaw control and one for pitch control. Since the rings are external to the nozzle minimum thrust is lost compared to jet vanes. ADVANTAGES:

1. It is a proven technology on Polaris missile. 2. Low actuation power is needed. 3. Light weight. DISADVANTAGES:

1. Erosion and thrust loss taken place. 2. Limited durational operation only. 3. HINGE (OR) GIMBAL SCHEME:

It is used in liquid type of rocket motors. In hinge type, the whole engine is pivoted on a bearing and thus the thrust vector is rotated. For small angles this scheme has negligible losses in specific impulse and it is used in many vehicles. It requires a flexible set of propellant piping (bellows) to allow the propellant to flow from the tank of the vehicle to the movable engine. ADVANTAGES:

1. It is simple and proven technology. 2. Low torque and low power is needed. 3. Only very small thrust loss.

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DISADVANTAGES:

1. It requires flexible piping. 2. Large actuators are needed for high slew rate.

4.SWIVELLING NOZZLE (OR) MOVABLE NOZZLE:

It is used in solid type of rocket motors. Movable nozzles are one of the mechanical types and are most efficient. They do not significantly reduce thrust or specific impulse and are weight competitive with other mechanical types. The movable nozzle consists of a molded multilayer bearing (which acts as a seal), a load transfer bearing and a visco elastic flexure. ADVANTAGES:

1. It is a proven technology 2. No sliding (or) moving seals 3. Predictable actuation power DISADVANTAGES:

1. High torque at low temperature is needed 2. Needs continuous load to maintain seal.

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5.SECONDARY FLUID INJECTION THRUST VECTOR CONTROL:

SIDE INJECTION

The injection of secondary fluid through the wall of the nozzle into the main gas stream has the effect of forming oblique shocks in the nozzle diverging section. It causes an unsymmetrical distribution of the main gas flow which produces a side force. The secondary fluid can be stored in liquid or gas from a separate hot gas generator, a direct bleed from the chamber, or the injection of a catalyzed monopropellant. When the deflections are small, this is a low loss scheme, but for large moments (large side force), the amount of secondary fluid becomes excessive. This scheme has found application in few large solid propellant rockets such as Titan-III ADVANTAGES:

1. 2. 3. 4.

It is a proven technology Components are reusable Light weight and compact Low actuation power is needed

DISADVANTAGES:

1. Toxic liquids are needed for high performance 2. It requires excessive maintenance 3. Toxic fumes with some propellants may poll ute atmosphere.

THRUST TERMINATION:

The engine thrust must be cut off, the instant that proper velocity is achieved to conserve fuel and or the rocket obtained a desired orbit. The thrust termination in liquid propellant rocket engines is easily accomplished by closing the fuel valve. But in solid propellant motors the problem is more difficult. One method to terminate the thrust in solid motor is the rupture disks, which vent the combustion chamber, reducing the thrust to zero.

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Recent development has indicated that thrust termination can be affected by nozzle blow out or by blowing out the forward section of the combustion chamber. By this means the combustion chamber pressure can be reduced below that required for sustained burning and hence terminate the thrust. Careful design must be made in order that random re ignition does not occur once burning is stopped. The accomplishment of thrust termination on TVC paves the way for application of this type of motor to ballistic missiles, which require thrust cut off for different range missions. It has been an error in the burn out velocity that has a large detrimental effect of the accuracy of the ballistic missiles. Hence it is important that the thrust termination of the propellant unit can be accurately accomplished and with a good degree of repeatability for one motor to another. THRUST MAGNITUDE CONTROL:

Thrust Magnitude Control (TMC) allows for large thrust variations usually with small variations in chamber pressure.

TRANSLATING INLET NOZZLE

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PINTLE NOZZLE

In some solid propellant rocket motors, TMC has been used without varying the throat area by reducing the mass flow into the chamber. As a result of the reduced mass flow, the chamber pressure decreases too. This may cause irregular combustion, or even extinguishments. Apart from this, the exhaust velocity is also lowered. Two possible systems without these adverse effects are t he translating inlet nozzle and the pintle nozzle. Both systems vary the throat to modulate the thrust. The translating nozzle is primarily designed for two different thrust magnitudes. In the figure port A is either closed or fully opened. If the port A is closed, the sustain throat is the only way through which propulsive gases can leave the rocket engine. If port A is opened, an extra boost flow can leave the combustion chamber and the boost throat acts as a nozzle throat. The pintle nozzle employs a centre body that can move in an axial direction; thereby continuously vary in throat area. The central body, which holds the movable pintle, is mounted on the nozzle inlet. It is of course, possible to combine TVC and TMC to obtain real thrust vector control, i.e both magnitude and direction of the thrust can be varied. Another TMC device that should be mentioned in this section is the extendable exit cone. If during powered flight under expansion losses become unacceptably large, one can increase the t hrust by lengthening the exit cone. This may be done by moving aft an extension to the divergent part of the nozzle. This concept was planned for the space shuttle engine but has be abandoned to keep the mechanism simple. MULTISTAGING OF ROCKETS:

Most modern, high performance rockets particularly those used in space applications are multistage rockets. The Saturn-V, moon rocket is a perfect example of a multistage vehicle. This rocket uses three distinct stages in order to send its payload of astronauts and equipments towards the moon. REASONS FOR MULTISTAGING:

1. To improve performance by eliminating dead weight during powered flight. 2. To maintain acceleration within reasonable limits by reducing thrust in mid flight.

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NOMENCLATURE OF A MULTISTAGE ROCKET:

FIG: A THREE STAGE ROCKET

Before entering into the multi staging of rockets we have to distinguish a stage and a sub rocket. STAGE:

A stage (which is also known as a step), is a complete propulsion unit with motor, propellant feed system, tanks, propellant together with control equipment, which is discarded completely when all the propellant of that stage is consumed. SUB ROCKET:

A sub rocket is a complete rocket vehicle, consisting of one or more stages together with a payload and the guidance and control system. MUTISTAGING OF ROCKETS:

The figure above shows a three stage rocket. In this stage we have three stages and three sub rockets. The first sub-rocket is the complete rocket vehicle. The second sub-rocket is the first sub rocket minus the first stage. The third sub-rocket, finally, is the second sub rocket minus the second stage, or equivalently the payload plus the t hird stage. In general for a N-stage rocket, Sub rocket 1

= complete rocket

Sub rocket (i+1) = sub rocket i- stage i, where i = 1.........N-1 98


Payload sub rocket N = actual payload. TYPES OF MUTISTAGE ROCKETS:

There are two fundamental types of rocket staging. They are, 1. Series staging 2. Parallel staging 1.SERIES STAGING:

Series staging is also known as vertical staging. In a series staged rocket, the second stage fires after the first stage is finished. The series staging is also known as t andem staging. Some of the best examples of series rockets are, Explorer I and Saturn V. 2.PARALLEL STAGING:

Parallel staging is defined as staging a vehicle such that the upper stage engines are also used during lower stage operation. This is usually accomplished by arranging the stages alongside one another, hence the name parallel staging. The perfect example of parallel staging is Titan III C ADVANTAGES: 1. Reduction of gravitational losses. 2. In a gravitational field, the parallel staging is always advantageous to consume the propellant as fast as possible. DISADVANTAGES: 1. The disadvantage of parallel staging is that the rocket is likely to be bulky and for the flight through the atmosphere the drag penalty may be large. 2. The second disadvantage of parallel staging is the reduction in nozzle efficiency of the engine of the thrust stage.

STAGE SEPARATION DYNAMICS: STAGE SEPARATION TECHNIQUES:

In multistage launch vehicles the stage separation process is broadly classified into two categories. They are, 1. SEPARATION OCCURING WITHIN THE ATMOSPHERE. 2. SEPARATION OCCURING OUT OF ATMOSPHERE.

1. SEPARATION OCCURING WITHIN THE ATMOSPHERE:

Separation within the atmosphere is otherwise known as booster separation/lower stage separation/strapton separation.

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The burn out of the first stage generally occurs within the upper regions of the atmosphere (i.e) 45km to 60km, to minimize the energy lost due to the aerodynamic forces. The ignition of the second stage must be done as quickly as possible after the first stage burnout. There are two techniques of separation are avail within the atmosphere. They are, a. FIRING IN THE HOLE TECHNIQUE b. ULLAGE ROCKET TECHNIQUE a. FIRING IN THE HOLE TECHNIQUE:

Firing in the hole staging is also known as vented inter stage separation or hot separation. This technique involves the firing of t he upper stage motor before the thrust level of the lower stage motor has decayed to zero (i.e. before the actual separation takes place). DRAWBACKS: 1. Care must be taken 2. Adequate ventilation holes are provided in the structure of the lower stage separation bay to prevent an excessive build up of pressure from the jet efflux which might cause the rupture of lower stage tanks. 3. In practice even though burnout conditions have been reached, the tanks still usually consists of unusable propellant, which may cause hazard. 4. There is a risk of tank rupture by direct jet impingement. So the upper surfaces of the tank should be stronger and hence heavier which imposes additional weight penalty.

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b. ULLAGE ROCKET TECHNIQUE:

This technique involves the use of short duration solid propellant rockets which are called ullage rockets, to bridge the gap caused by the decay of lower stage thrust and subsequent build up of lower stage thrust. The nominal thrust level of the upper stage motor is not reached until there is an appreciable separation distance between the two stages. DRAWBACK: 1. Heavy weight.

2. SEPARATION OUT OF ATMOSPHERE (IN SPACE):

Separation occurring out of atmosphere is also known as vacuum/space/upper stage separation. The separation of subsequent stages takes place either at extreme high altitudes in space. 101


The problem of separation is relatively simplified when occurs in space because of absence of aerodynamic forces but it does not mean as soon as burn out of lower stage occurs the ignition of upper stage is initiated. This separation technique involves two methods. a. HELICAL COMPRESSION SPRING TECHNOLOGY b. SHORT DURATION SOLID PROPELLANT TECHNOLOGY

a. HELICAL COMPRESSION SPRING TECHNOLOGY:

In this technology, separation may be obtained by a single compression spring centrally located but in practice it was a large number of small springs located symmetrically around the periphery. This is done in case of accommodation and secondly to minimize the possibility of separation aborting through spring f ailure. ADVANTAGES: 1. No separate command is needed for actuation 2. Highly reliable

DRAW BACK:

1.

Much heavier when compared to other j ettisoning system.

STAGE SEPARATION SYSTEMS: Selection of stage separation system of launch vehicle is an extensive and exhaustive process. The critical criterions are, 1. Joint rotation 2. Simultaneity 3. Reliability 4. Confinement of debris 5. Low shock levels 6. Weight 7. Cost. The selected separation system should also meet all the functional requirements viz,  

  

To achieve collision free separation of spent stages, ie, to establish clearances, between the separating bodies to ensure safe separation. To provide the structural rigidity to attach the two bodies, the ability of the mechanism to withstand the flight loads encountered during flight that is structural integrity should be maintained. To provide the means to severe the structural connection To impart positive separation velocity to the separation bodies. To impart minimum tip off rate to ongoing stage. 102


Minimum shock transmission to the payload interfaces o r the continuing stages

ELEMENTS (OR) SYSTEM FOR SEPARATION PROCESS: Generally three basic elements are required for the functioning of separation process. They are, a) b) c)

An actuator -to trigger the event usually electric or pyro based Release / Severance system for physical separation Jettisoning systems – to impart sufficient relative separation velocity

1)

ACTUATOR: The actuator system as the word indicates actuates the triggering of the separation event. Thus, there is a delay between actuating the trigger and physical separation. Usually actuators are either a) b)

Electric or Pyro based.

2)

SEVERANCE/ RELEASE MACHANISMS: The severance/release systems impart physical separation to bodies; they are primarily 2

types; a) b)

Mechanical systems & Pyro –technique devices. The design requirements for these systems are,        

Load carrying capability & compatibility with vehicle structure. Minimum electrical power for separation system. Minimum system weight & minimum volume. Minimum impulse & minimum tip off rates. High reliability, maintainability & long storage life. Survival of extremely high or low temperatures No contamination, debris free & survival of nuclear environment Safe handling & easy transportation.

A) Mechanical systems: 1.

Ball & lock systems

Ball & lock system consists of upper & lower stages adopter rings held together by steel balls which in turn are held by a retainer ring. The retainer ring is provided with escape holes for balls. In the locked condition, the holes in the retainer ring are given an angular offset. During release, pyro-thrusters rotate the retainer ring which nullifies the offset. A stopper limits retainer ring rotation. Helical compression springs positioned between the flanges impart the required differential separation velocity. The lower stage outer ring is provided with through holes for the balls in the locked condition and the upper stages adapter ring is provided with conical ball seat, the radial component 103


of the spring forces pushes the balls outward & releases the inner ring which ensures a clean separation.

2.

Merman band /Clamp band:

Multistage launch vehicles use clamp band joint for separation of upper stages & payload fairing. The necessary preload on clamp is given by tensioning two steel band segments placed over the clamps & connected by two tension bolts & nuts. In this type of joint the tapered interfaces flanges are held together by a series of aluminum clamps made of m250 steel circumferentially positioned. These clamps are preloaded using two steel band segments through two connecting bolts & nuts under tension pyro-cutters severe the connecting bolts when separation of the joint is required. . 2. COLLET MECHANISM: The collect mechanism consists of a collect housing / cylinder with a piston holding the finger spread out in locked position. The mechanism can carry tensile loads when in locked position. When gas pressure is introduced in to the cylinder bore it acts on piston causing it t o move forward & allowing the collect fingers to collapse due to their strain energy. This action permits separation of the vehicle from the spent stages. The device is capable of resisting high tensile loads and it can withstand the flight dynamic loads. It withstand a maximum temperature Gradient from 80 K 353 K .This system has to be protected from excessive aerodynamic Heating using cowlings & it has to be made waterproof for reliable operation. This system provides a debris free clean separation.

B)

PYRO SEPARATION DEVICES:

These systems use pyro active element for imparting physical separation, two types are commonly employed they are,

1.

Explosive Bolt: In the explosive bolt, the pyro c harge is electrically initiated to severe the bolt at notches provided at separation planes. 2.

Frangible nut: In frangible nut pyro activation causes the nut to open out and to release the studs engaged in nut threads. JETTISONING DEVICES: These systems have been used to provide the required relative separation velocity to the separating bodies. Energy required for jettisoning the systems are provide by employing an yone of the following type of thrusters,   

Spring thrusters Pneumatic thrusters Rocket thrusters

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Some of the Jettisoning systems usually employed in launch vehicles are described below:

1.

SPRING THRUSTERS:

In spring thrusters, springs are packed and compressed to the required energy level. D isc springs depending or coil springs are employed depending on the jettisoning requirements; high energies are met with disc springs. The advantage of spring thrusters is that spring energy characteristics can be evalued prior to the assembly of the system and once assembled jettisoning spring force is always available for the function. Thus, separate command is not needed for the actuation and is highly reliable. To draw back with the spring thrusters is that they are heavier compared to the other types of jettisoning system. For smaller mass with lower energy requirements spring thrusters is an i deal choice whereas for large size boosters with higher jettisoning energy requirements their use i s not recommended.

2.

ROCKET THRUSTERS:

Rocket thrusters are used for jettisoning higher diameter massive boosters where the associated energy requirements are higher. The advantage of the rocket thrusters is that it can store much higher energy for a given weight of thrusters.

3.

PNEUMATIC THRUSTERS:

In this type, the working medium is pressurized nitrogen gas. These thrusters are light in weight as the working medium is gas. The energy stored depends on the initial pressure and stroke length and there for by changing the pressure stored energy also can be varied. The pressure holding characteristics of the rolling diaphragm and joints is the limiting factor for the stored energy. Pneumatic thrusters do not require separate command for actuation as the jettisoning force is always available. I In pneumatic thrusters design must be simple, relatively steady operation process, less disturbances no exhaust ports are required and heat insulation is required.

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107


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ANSWER IN A SHORT: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

What are the basic phases of a trajectory vehicle? What is coasting phase with reference to the motion of a multistage launch vehicle? What is meant by Thrust Vector Control? What is the need for TVC? What are the different types of Thrust Vector Controls? What do understand by the term Thrust Magnitude Control What is an apogee? What is meant by thrust termination? Is thrust termination easy in solid propellant engines or liquid engines? Justify. What is a multistage rocket? What is the need for staging? What are the types of multistage rockets? Give example. Distinguish a stage and a sub-rocket List out the various systems which are employed in stage separation List the important stage separation techniques which are used in space What are the important stage separation techniques which are used within the atmosphere?

ANSWER ELABORATELY:

What is a Thrust Vector Control? Explain the methods by which TVC can achieved. Briefly explain what is meant by Thrust Magnitude Control. Explain the various systems which are employed in stage separation. What is a multistage rocket? Briefly explain its nomenclature with a neat sketch also explain its types. 5. Elucidate the various stage separation techniques involved in stage separation dynamics. 6. Elucidate the various stage separation systems which are involved in stage separation dynamics 7. Explain the optimization of a multistage rocket. 1. 2. 3. 4.

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UNIT-5 MATERIALS FOR ROCKETS AND MISSILES

THE EFFECT OF SPACE ENVIRONMENT ON MATERTIALS:

The space environment presents in several materials problem, not ordinarily experienced by engineering principles. The energy spectrum of major constitutions of space radiations such that, any radiation induced changes in materials will be due ti ionisation and excitation processes. The coupling of these effects near the vacuum environment will produce effects, not necessarily experienced under separate exposures. Organic compounds are very susceptible to the ionisation excitation processes and the mutation is generally proportional to the total energy absorbed. On the other hand metals and most inorganic compounds are little affected by ionization mechanism. Thus ultra violet radiation in space will affect mainly unshielded organic compounds. Most of such compounds are black to ultra violet radiation and therefore damage will be confined to the exposed surfaces only. In operation within the geomagnetic radiation belt the concentration rates will be hi gh enough to affect organic compounds adversely. Structural metals however will not be affected to any appreciable extent by this radiation. Most organic structural materials require large dose of irradiation before macro changes occur. Therefore they may be protected for years by very light shielding. In general it can be assumed that a material will be stronger in a vacuum environment does not affect the structure of the material. The absence of atmosphere is most drastic in the effect of the fatigue characteristics of the material. Friction and wear of moving surfaces is both a mechanical and chemical process. Such barriers are usually reinforced by the physical assistance of a hydro dynamically established and maintained film of fluid lubricant. At the low pressures that exist in space liquid lubricants will evaporate. Use of low vapour pressure fluids can be made for moderate life systems. For high temperatures long life operation especially under radiation exposure, only solid lubricants become practical. The facing surfaces are separated by a solid film having a very low vacuum pressure. Sometimes even ball and roller bearings are subjected to sliding and the films sometimes may wear out. In the hard vacuum of space when the lubricant film fails the surfaces will become clean and this results in the bearings become rough and may become static. AERODYNAMIC HEATING: DEFINITION:

Aerodynamic heating is a phenomenon due to the result of friction between the rapidly moving vehicle and the surrounding air. It is a well known phenomenon for re-entry vehicles, but it may also important for launch vehicles.

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EXPLANATION:

In the ballistic missile the airframe components of the missile experiences high temperature due to aerodynamic heating. In the case of short range missiles, materials can withstand up to the temperature limit of 300C. But ballistic missile nose cone has war head, which has to protect. During re entry, the missile enters the atmosphere at a mach number of 8. At that stage there will be a boundary layer formation leading to a sharp velocity gradient. So there is a reduction in kinetic energy from the surface of boundary layer. This kinetic energy of flow has been connected into internal energy of the flow. This results in rise in temperature of fluid and at surface of nose cone. The temperature of the fluid is maximum and the heat is transferred from fluid to solid surface. So this temperature of solid surface depends on free stream Mach number. At very high mach, when temperature exceeds 800K, molecules start vibrating and separate into atoms at 2000K. At around 700K, even N2 dissociate into charged ions (plasma). So nose cone i s surrounded by hot plasma and there is no transmission. This makes the guidance and control system ineffective.

AERODYNAMIC HEATING OVER A HYPERSONIC VEHICLE

AVOIDANCE OF AERODYNAMIC HEATING:

1. In order to avoid the aerodynamic heating problem, we have to think of Thermal Protection System (TPS), which is used like a sheet over the primary structure. TPS will absorb most of heat and only less amount of heat is transmitted to primary structure. Example:  Carbon Epoxy Composite-------------- can withstand impact loads.  Carbon- Carbon Epoxy composite---can withstand high temperature.  Silica tiles -------------------------------- has high thermal diffusivities.

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2. Ablative materials are also used to avoid aerodynamic heating problem. The term ablative material generally refers to a polymer or a resin, which is applied on the surface of a rocket or a missile. These materials pyrolyses layer by layer when the surface is heated and thus protect the structure of the re entry vehicles.

CERAMIC MATERIALS: Ceramic materials are inorganic, non-metallic materials made from compounds of a metal and a non metal. Ceramic materials may be crystalline or partly crystalline. They are formed by the action of heat and subsequent cooling.

Clay was one of the earliest materials used to produce ceramics, but many different ceramic materials now used in domestic, industrial and building products. Ceramics materials tend to be strong, stiff, brittle, chemically inert, and non conductors of heat and electricity. TYPES OF CERAMIC MATERIALS:

The types of ceramic materials are, 1. Crystalline ceramics 2. Non crystalline ceramics.

1. CRYSTALLINE CERAMICS:

Crystalline ceramic materials are not amenable to a great range of processing. Methods for dealing with them tend to fall into one of two categories - either make the ceramic in the desired shape, by reaction in situ, or by "forming" powders into the desired shape, and then sintering to form a solid body. Ceramic forming techniques include shaping by hand (sometimes including a rotation process called "throwing"), slip casting, tape casting (used for making very thin ceramic capacitors, etc.), injection moulding, dry pressing, and other variations. 2. NON-CRYSTALLINE CERAMICS:

Non-crystalline ceramics, being glasses, tend to be formed from melts. The glass is shaped when either fully molten, by casting, or when in a state of toffee-like viscosity, by methods such as blowing to a mold. If later heat-treatments cause this glass to become partly crystalline, the resulting material is known as a glass-ceramic.

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CERAMIC BEARINGS USED IN ROCKETS .

APPLICATION OF CERAMICS IN ROCKETS AND MISSILES:

Ceramic are used in either sprayed or protective coatings or monolithic field bodies. Ceramic structures can be successfully designed and they are flown on missiles in such applications as radomes, wing leading edges, engine nozzle inserts and jet vanes. PROPERTIES OF CERAMIC MATERIALS:

Ceramics exhibit virtually no plastic deformation and are very much weaker in tension than in compression. The various properties of ceramic materials are, 1. Thermal conductivity 2. High modulus of elasticity 3. Tensile weakness. Physical properties of ceramic compounds which provide evidence of chemical composition include odour, colour, volume, density (mass / volume), melting point, boiling point, heat capacity, physical form at room temperature (solid, liquid or gas), hardness, porosity, and index of refraction. THERMAL SHOCK:

Thermal shock occurs when a thermal gradient causes different parts of an object to expand by different amounts. This differential expansion can be understood in terms of stress or of strain, equivalently. At some point, this stress can exceed the strength of the material, causing a crack to form. If nothing stops this crack from propagating through the material, it will cause the object's structure to fail. When a material is rapidly heated as in case of a re entry body or the throat of a rocket nozzle at ignition, then the temperature is uniform throughout the section. The temperature gradient will be dependent on thermal conductivity, density and the specific heat of the material. This temperature gradient, in turn will produce thermal stresses, which will be 113


dependent on the coefficient of thermal expansion of the material. Thermal shocks are not confined to ceramic materials alone, but these materials are more susceptible to the thermal shock when compared to most other materials. Many metals are thermal shock sensitive, particularly upon sudden chilling. At low temperature the cold side will be placed in tension and in these metals which have high ductile brittle transition temperatures. Due to thermal shock fracture can also occur. MATRIAL SELECTION CONSIDERATION FOR ROCKETS:

The selection criteria for materials for rockets are, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

High strength at elevated temperature Ease of fabrication High thermal conductivity Resistance to chemical action to vapours High specific heat Resistance to corrosion Resistance to mechanical and thermal shock High melting point Low thermal expansion Good vibration resistance.

SELECTION CRITERIA FOR MATERIALS FOR SPACE CRAFT STRUCTURES:    

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Extreme working temperature High value of strength to weight ratio Strength should not deteriorate at extreme temperature to lower acceptable limit The material can able to withstand, 1. Shock or pressure load 2. Thermal load 3. Impact loads Material should not lose its properties when exposed to cyclic loads.

MATERIALS THAT CAN BE USED IN DIFFERENT PARTS OF ROCKETS AND MISSILES SHORT RANGE TACTICAL MISSILE:

NOSE: Air – to-Air missiles:

For IR homing, quartz or arsenic trisulphide glass molded to shape or fabricated with stainless steel heat sink at tip of the nose. For active homing, fiberglass reinforced resin impregnated RADOME (clipped word: Radar + dome shape) molded. Surface-to-Air missile:

For IR homing, quartz or arsenic trisulphide glass molded to shape or fabricated with stainless steel heat sink at tip of the nose. For active homing, fiberglass reinforced resin impregnated RADOME (clipped word: Radar + dome shape) molded.

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Air-to-surface missile:

For IR homing, quartz or Arsenic trisulphide glass molded to shape or fabricated with stainless steel heat sink at the tip. For some active homing, fiberglass reinforced resin i mpregnated RADOME molded and the warhead would be encased in steel or aluminum alloys. Fore bodies:

In all cases the structure would be of aluminum alloys or steel.the most commonly used material is the aluminum alloy. Rear bodies:

Same as the fore body except that where the rear body consists of propulsion system or its components like combustion chamber, steel and steel alloys are used. If weight reduction is required in aft position, magnesium alloy may be used in boat tail section. Wings and fins:

Normally aluminum alloy plates at required geometric shapes were used. Reinforced fiber glass resin impregnated composite structures can also be used for this application. In this case metal inserts would be need for leading edges if the missile speed were high. Nozzles:

Mostly steel with graphite or molybdenum inserts with or without ceramic coatings were used. MEDIUM RANGE TACTICAL MISSILE:

Same as for short range tactical missiles except that the greater portion of the structure will be made of steel. Jettisioning devices, boosters are mainly made of fiberglass reinforced resin impregnated structures. Generally aluminum alloy, titanium alloy, stainless steel, inconel, hastalloys, ceramic coatings were used in medium range tactical missiles. LONG RANGE MISSILES: NOSE SECTION:

Inter Continental Ballistic Missile warheads are encased in austenitic stainless steel types of AISI 321 type with ablative coatings. For drag type re entry bodies with payload at electronic equipment are well insulated and encased in stainless steel or fiberglass reinforced impregnated composite structures with ablative coatings. In the case of fiberglass reinforced structures, they must be stiffened by a skin of stainless steel of austenitic type on the inside surface. For glide type re entry bodies like manned capsules, the construction would be of space structures with materials either stainless steel or composites with radiation or micro meteoroid shields. MAIN BODIES:

Generally of austenitic stainless steel of type AISI 347 or AISI 327 with critical parts made of chrome molybdenum vanadium ferritic steel are used. Sometimes titanium or boron fiber reinforced structures 115

Rocket and Missiles

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