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CHAPTER 1

ELECTRIC GUN TECHNOLOGIES

1.1 INTRODUCTION

Effective fire power has been considered as one of the prime

requirement of Future Main Battle Tank. This is mainly controlled by

projectile muzzle velocity and its impact energy on the target, rate of fire of

the gun towards the target, accuracy in firing and time of flight. This

requirement can be systematically tailored by introducing a suitable gun

propulsion concept which can be able to launch a projectile with hyper

velocities. It is now a globally accepted fact that, gun performance with

conventional propulsion techniques is limited to the velocities of 1.6 km/s to

1.7 km/s, with this, desired muzzle energies required for Future Armoured

fighting vehicle (AFV) cannot be achieved. Hence, introduction of new

concept of propulsion with the acceptable constraints of firing platforms are

therefore essential. It is therefore necessary to initiate work in this area at the

earliest to meet the requirements of FMBT, for which work is likely to be

launched shortly (Oberle et al 1989).

The total system would be benefited, if the Future Main Battle

Tank (FMBT) gun is designed, in such a way that, it could demonstrate

increased target effects, acceptable launch efficiency and gun lifetime, energy

storage and pulsed power supply system of acceptable size and weight, and a

reduced logistic burden through the elimination of conventional propellants.

Electric gun technology has not yet been invented; scientific and engineering

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developments are needed in several areas to assure future success. Balancing

the technology risks in these areas during the development is important to

achieve an acceptable solution. To determine whether the target is achieved or

not for a given mission, the total system is evaluated against a representative

mission profile. Each mission has different gun system requirements. In many

cases, the pulsed power system is the pacing component in terms of size and

its weight (Ian McNab 1997). Extensive work and research are being

conducted all over the world for the minimization of the volume occupied by

the power supply and its weight. The energy storage devices and switching

devices occupy most of the space in a pulsed power supply system. The

modern technology advancements in new solid state devices and high energy

density components have enabled pulsed power systems to stay powerful, yet

reduce in size and weight. Due to constraints on compact power source,

feasibility study is carried out by the Government of India to design a 500-kJ

pulsed power supply system, which can be used, to accelerate the projectile at

a velocity of 1000 m/s to 1500 m/s for surface fire and other missions. The

pulsed power supply will need to have fire rates of 8 rounds per minute. The

Anna University, Chennai has initiated a program to develop a 500-kJ pulsed

power supply system using computer simulation techniques.

1.2 OBJECTIVES OF THE THESIS

The rail gun over all efficiency depends on the rail gun design

and its pulsed power supply systems. The rail gun design

depends on the rail gun key parameters such as current

distribution over a rails, magnetic flux density between the

rails, temperature distribution inside the rails and armature

surface, and repulsive force acting on the rails. The rail gun

key parameters are affected by a number of parameters such

as velocity of the moving armature, armature and rail

geometry, rail dimensions, armature and rail materials. The

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first objective of this thesis is to determine the effect of rail

dimensions on rail gun design parameters.

For the past several years, the values of inductance gradient of

the rails were calculated using numerical and analytical

methods. The analytical method is suitable to solve the simple

problems but numerical problems need code and programs as

it is a time consuming process. Hence, a simple method is

needed to calculate inductance gradient of rails. As the

inductance gradient (L’) values depend on rail dimensions,

now researchers focused on obtaining a simple formula to

compute the L’ values with respect to rail dimensions. The

second aim of this thesis is to extract an empirical formula,

which can be used, to compute the inductance gradient of the

rail.

The pulsed power supply system (PPS) is the key part of the

electromagnetic rail gun. Generally, the PPS is made up of

modules called pulse forming network (PFNs). The pulse

forming network (PFN) is connected to choice of energy

sources. The energy is required to be stored properly and is to

be delivered to the load at appropriate time. Today, the energy

storage systems which feed the rail launcher are large and

extensive work and research is being conducted all over the

world for the minimization of the volume occupied by the

power supply and to reduce its weight. Due to constraints on

compact power source feasibility study is being carried out, by

the Government of India and Anna University, Chennai, to

design a 500kJ pulsed power supply system that can be used

to accelerate the projectile at a velocity of 1000 m/s to

1500m/s. The third aim of thesis is to design a 500-kJ pulsed

power supply system, using computer simulation techniques

such as PSPICE and MATLAB, to get the desired velocity of

the projectile.

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The requirement of pulsed power system given by the Government

of India as follows:

Energy rating = 500 kJ/shot and 8 rounds/minute (Total of 4MJ)

Muzzle velocity = 1 to 1.5km/s,

Pulse width = 4 - 5ms and

Volume occupied by pulsed power supply and its weight.

1.3 PROBLEM DEFINITION

The advancement of technology in the field of modern

weaponisation, utilizes the electrical energy as an important tool.

Electromagnetic rail gun systems are such that it accelerates the projectile to

greater velocities.

The Figure 1.1 shows the essential components of an

electromagnetic pulsed power system.

Figure 1.1 Essential components of an Electromagnetic pulsed power

system

The energy supply, in most cases the ordinary power network, is

connected to the energy storage system which, in turn, is connected to the

pulse forming equipment through a fast switching device. The energy storage

is usually either of capacitive or inductive type, i.e. the energy is stored

electrostatically or magnetically. The pulse forming equipment, which is

charged from the energy storage device, is used to give the right shape of the

pulse for the intended application.

Energy

supplyEnergy

storage

SwitchPulse

forming

equipment

Load

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The essential component for successful implementation of rail

gun system is power supply which can provide conditioned

power. Today, the space occupied by the power supply is still

large. There have been continual advances in power supply state

of the art, which have been quite dramatic over the past few

years for energy density. Power supply technology is

developing quickly and it appears that projected improvements

will provide adequately compact components for field portable

applications. The energy storage devices and switching devices

occupy most of the space in a pulsed power supply systems. The

recent technology advancements in new solid state devices and

high energy density components have enabled pulsed power

systems to remain powerful, yet reduce in size and weight.

Various forms of energy storage devices include battery,

capacitor, compulsator and inductor. Each type of topology has

its own advantages and disadvantages. Hence, in order to design

a pulsed power supply system in a compact space, comparative

studies have to be made between the existing energy storage

devices to select a suitable candidate to design a 500-kJ pulsed

power supply system.

As a very high value of current and short duration pulse is

applied to the rail gun, the current does not penetrate the rails

and armature completely and the current density is not uniform

over the rail cross section it is called skin effect. Moreover, the

current is distributed more near the surface of each conductor.

This makes the electromagnetic analysis of the rail gun

extremely complex. Hence, in order to gain a quantitative

understanding of the rail gun key parameters, it is desirable to

calculate them well in advance before real time system.

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To calculate the inductance gradient of the rails numerical

methods or analytical methods are used. These two methods are

time consuming, a simple method has to be developed to

compute the L’ value of the rails.

Implementation of the rail impedance in a simulation is

difficult. Because the impedance of the rails varies with respect

to projectile position. In order to implement variable impedance

of the rails using simulation, a suitable model has to be

developed.

In order get a high velocity of the projectile and to utilize the

barrel length effectively, the pulsed power supply has to deliver

a constant current to the load. Obtaining the constant load

current depends on the connection of capacitors and pulse

shaping inductance values. By choosing the proper value of

pulse shaping inductance and then firing the capacitor banks

sequentially the constant load current pulse can be obtained.

Hence, based on the above discussions, it is concluded that before

the rail gun system became synchronous, simulation has to be carried out well

in advance to predict the performance of rail gun.

1.4 METHODOLOGY ADOPTED

In order to select a suitable candidate, for the energy storage

system, to design a 500-kJ pulsed power supply in a given

space, for rail gun application in this thesis, different types of

pulsed power supplies which produce a pulsed output are

studied. A detailed feasibility study is done on different

available energy storage devices. Each type of topology has its

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own advantages and disadvantages. So a logical compromise

has been made taking account of the constraints which are

posted by the desired energy requirement. The most feasible one

is to be chosen by studying all the technicalities of the system.

The rail gun key parameters mainly depend on the rail geometry

and rail dimensions. In order to investigate the effect of rail

geometry and rail dimensions on rail gun key parameters

computer simulation codes are used. In this work, finite element

computer software package named Maxwell Electro Magnetic

Field Solver ANSOFT is employed to perform this task. Eddy

current field solver and thermal field solver were chosen to

carry out the investigation. Eddy current field solver is used to

perform the electromagnetic analysis and thermal field solver is

used to perform the thermal analysis of rail gun. Eddy current

field solver gives the electromagnetic losses that occur in rails

due to ohmic heat. These electromagnetic losses are coupled

with thermal field solver and then the temperature distribution

in the rails is calculated.

In order to compute the inductance gradient of the rails in a

simple manner, a new empirical formula is extracted using the

regression analysis technique.

The pulsed power supply for electromagnetic launcher with the

given specification is designed using PSPICE and MATLAB

software. PSPICE software is used to optimize the pulsed power

supply, in order to get the constant load current. In this work,

the capacitors are divided into different stages and they then

fired sequentially to obtain the constant current load current.

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The non linear impedance of rail gun is implemented using the

available model called ZX element in PSPICE.

MATLAB is used to optimize the pulsed power supply for the

specification given by the Government of India. The

implementation of load impedance of the rails is difficult in

MATLAB simulation. In this work, a new model, which can be

used to implement the load impedance of the rails, is developed

in MATLAB simulation. The mass of the projectile and firing

time of capacitor bank are being considered to optimize the

pulsed power supply.

1.5 BRIEF LITERATURE REVIEW RELATED TO THIS

THESIS

The literature forms the backbone of all the work. Surveying the

literature is gaining the experience about the work done previously and steps

taken in particular field of interest.

The literature survey were made in the following areas

1. Electric gun technology.

2. High Energy storage devices and switching devices.

3. Modeling of rail gun.

4. Capacitor based pulsed power supply design.

(a) Electric gun technology

Henry Kolm et al (1980) have explained the importance of rail gun

and its limitation. They have mentioned that the fundamental limitation of the

rail gun is inefficiency due loss of inductively stored energy in the form of a

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muzzle arc at the instant of launch. Other problems are containment of the

percussive forces which tend to blow the rails apart and the destructive effect

of high brush current density. They have mentioned that the length of rail

guns is limited by increasing resistive and inductive loss. They also have

suggested that the rail guns can be connected in series to overcome this

limitation.

Hammon et al (1992) have discussed the fundamental concept of

Electromagnetic rail gun and ET gun system. They also have discussed the

fundamental issues and the primary design philosophy as well as advances in

the critical pulsed power components. They also have given the space

occupied by each component in a pulsed power supply system. They have

suggested that, the volume reductions of components can be effected in one

(or more) of two ways: reducing the size of the component at fixed ratings or

increasing the rating while maintaining the size.

Fred Charles Beach (1996) has given the theory behind the rail gun.

He has made the comparison between the conventional gun and rail gun. He

has suggested that the rail gun is a good choice due to its high projectile

velocity, low system vulnerability, low firing signature, extended projectile

shelf life, selectable lethality, ease of projectile storage, handling and

resupply, and minimal environmental impact.

Ian McNab (1997) has focused on the pulsed power system needed

to drive the gun. He has suggested that rotating machines offer attractive high

energy storage capability and high output voltages. He also has mentioned

that, the multiplicity of auxiliaries required to support a rotating machine,

may be a significant obstacle to their introduction in situations such as the

FMBT, where weight and volume system constraints are difficult and where

operation on the battlefield will be stressing.

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Young- Hyun et al (2002) have discussed the method of

obtaining the load resistance of ETC gun by conducting an experiment. This

study has indicated that, the load resistance can be estimated with an

empirical method. The measured current and voltage histories, give the

system information that makes it, possible to express the resistance as a

function of the discharging voltage and current. The local characteristics of

the power, the transferred energy and the time derivative of the current which

can be obtained from the measured current and voltage are considered along

with the system equation to analyze the resistance of ETC gun. This empirical

approach can be utilized to identify the time-varying system parameters that

are difficult to obtain with generalized system identification methods.

Bryan Mcdaniel (2006) has discussed different types of rail gun

which can be used to accelerate the projectile with hyper velocity. He has

indicated that to improve the magnetic field between the rails one more rail is

connected parallel to the first rail called augmented rails. Due to this, the

force acting on the projectile can be increased. He also has made a

comparison between the different types of energy fed rail gun. He has

suggested that the distributed energy fed rail gun has more advantage than

breech fed rail gun as it has low inductive loss. He also has developed DES

rail gun using PSPICE simulation and compared the results by conducting an

experiment.

(b) High Energy storage devices and switching devices

Donald et al (1986) have developed MHD Generator pulsed power

supply which can be used to energies the electromagnetic launcher to

accelerate projectile to the velocity of 1.5km/s. They also have developed

a first order performance model for the integrated EML and the generator,

and implemented on a personal computer system. They have made trade of

study on numerous parameters of interest, and required propellant and

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other characteristics were specified. Result of model development and

trade studies were presented and they indicate significant technology

advances are required to realize this concept in EML application. They

also have suggested that to get higher power, high conductivity plasma

and magnetic flux density are required.

Karthaus et al (1989) have developed battery based pulsed power

supply based on SCR switching technology, energy storage, and pulse

transformer. They have presented the description and expected performance

of system. They also have tested the pulsed power supply with dummy load

and the test results have shown that using one battery, the PPS delivered

152kA current with decay time of 3.5ms for the load resistance of 0.5milli

ohm.

Spann et al (1991) have explained the working principle of

compulsator briefly. They also have discussed about different types of

compensation technique used compulsator design. They have given procedure

to design the compulsator and designed the compulsator for 18 different

missions. The machines have been sized to account for all magnetic energy

requirements and the compulsator is unique in its ability to efficiently recover

magnetic energy from the launcher. Finally they have presented a simple

method of estimated compulsator mass and size.

Akiyama et al (1992) have studied a repetitive pulsed power

generator using inductive energy storage. They have suggested that, an

opening switch, to interrupt a large current rapidly, is essential to realize the

inductive pulsed power generator, which has the advantage of extreme

compactness and light weightiness in comparison with a capacitive energy

storage system. They also have studied two kinds of repetitively operated

opening switches where developed in Kumamoto University. One is an

exploding wire using an automatic wire setting devices other is plasma

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opening switch using laser plasma. A good reproducibility of the plasma

opening switch has been obtained.

Stefan Rzed et al (1992) have given four different approaches to

develop materials for high energy density and high voltage (10kV) capacitors.

The four different approaches are 1) diamond-like carbon films, 2) chemically

vapor deposited diamonds films, 3) ULTEMB polyetherimide films, and 4)

computer-modeled modified polyetherimide films. They have presented a

brief state-of-the art discussion, the status of the work on these materials,

which includes measurements of resistivity, dielectric constant and loss, and

breakdown strength. They suggested that high voltage capacitors with energy

densities of 4- 15 J/cm3 may be achievable.

Jack Lippert (1993) has manufactured a battery using new

technology called PULSER which can be used in a pulsed power supply, for

rail gun application. He has suggested that by using PULSER technology, the

power and energy density of battery can be increased and it allowing the total

volume reduction. He also has suggested that this technique makes the battery

well suited for pulsed power supply in rail gun application.

Pappas et al (1993) have developed pulsed power supply using

battery energy storage devices called BUS program. This program required to

perform up to two discharges per week. Therefore BUS is designed to be a

low-maintenance, reliable, and fault tolerant power supply. They have

suggested that the Battery Upgraded Supply (BUS) is a reliable and safe

pulsed power supply. The modular design of BUS has allowed simple

simulation of the performance. They have observed that the results from the

simulation showed expected current levels during normal operation as well as

fault currents. They also made a study of available batteries and revealed that

automotive lead-acid batteries are best suited for high current battery power

supply systems.

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Sunil Murphy et al (1994) have investigated multiphase rail guns

(electromagnetic launchers) powered by multiphase compensated pulsed

alternators (compulsator). They have suggested that poly phase system offers

several advantages over the single phase system. They also have mentioned

that the multiphase compulsator relaxes the strong dependence between the

current pulse width necessary for the rail gun and the design parameters of the

generator (number of poles, rotor diameter and tip speed) thus allowing the

compulsator to be designed for optimum power density and electromechanical

energy conversion.

Esposito et al (1995) have investigated the performances of an

electromagnetic launch system constituted by an arc driven rail gun powered

by a MHD generator. The analysis of the rail gun and generator has been

carried out by means of a lumped parameter equivalent network model that

takes into account drag force and ablation effects, and allows the evaluation

of the main electrical and thermodynamic quantity distributions of the plasma

arc. The behavior of a Faraday and a Hall MHD generator driving a small

bore plasma rail gun for fusion fuel pellet injection have been examined and

compared. They suggested that the Hall type MHD generator have better

performances than those of the Faraday type generator. Moreover, the results

show that a plasma armature driven by a Hall type generator has an E/B

velocity limit higher than the same armature driven by an inductive supply.

Kanter et al (1995) have discussed the system approach to the

inductive storage design. They have made an attempt to optimize the existing

battery inductor technology and it has been achieved at a coil stress that is

significantly lower than the tensile strength of the conductor. They have made

a parametric trade-off study for the prime power battery and the coil to reduce

the volume occupied the power supply. They have considered brook coil and

jelly coil to make the trade of study. They have shown that the minimal

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volume of the battery-coil system can be achieved with a Brooks coil. They

also have suggested that a jellyroll coil is preferable to a pancake one in view

of higher transfer efficiency. They also have calculated the fringe field of

cylindrical and quasi toroidal coils by dipole approximation. They have

measured the discharge efficiency and fringe field and they have observed a

good agreement with the theoretical analysis.

Singh (1995) has made a comparison between the switching

devices for their ability to conduct high peak current at high coulomb levels

while operating in a mobile tactical system having severe volumetric

constraints. He has taken solid switching and non solid state switching for

comparison with their ability. He has concluded that for series-parallel

arrangement of silicon controlled rectifiers was considered to offer the best

approach for the tactical system.

Kitzmiller et al (1997) have described the CCEMG pulse power

supply configuration and highlights important features of the commissioning

test plan. They have presented test results from mechanical runs, stand alone

compulsator (CPA) rectifier tests, short circuit tests, and single shot live fire

tests. Finally, CPA performance have been compared with predictions for the

single shot tests and they have observed that the entire pulsed power system

has performed extremely well so far with the CPA developing power per

original predictions.

Murphy et al (1997) have given the state of the art rotor dynamic

analysis methods successfully applied to the design of air core compulsator.

They have used advanced finite element techniques to model the rotating

assembly, and a special purpose computer program was used to calculate rotor

dynamic critical speeds and imbalance response. The rotor dynamic model

was used to help select a bearing technology best suited to the application

(angular contact ball bearings in conjunction with squeeze film dampers). The

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rotor dynamic model was also used to calculate optimum properties for the

squeeze film dampers to minimize the machine’s sensitivity to residual

imbalance throughout its speed range. The CCEML rotor has also been run

multiple times through a rotor critical speed, showing no effect on vibration

performance.

Pratap et al (1997) have reported the method of obtaining flexible

wave shape by using different phase system like single phase, two and multi

phase compulsator. They have suggested that each system has its own

advantage and disadvantages. The single phase system has the problem of

poor control and flexibility and also higher machine mass. The two phase ac

rail gun system requires an extra set of rails (anti-augmenting rails) to achieve

the desired acceleration ratio. This implies higher losses in the two phase A.C

system. In general the A.C system requires more reactive power than the

staged discharge system or the single phase system because the magnetic

energy is oscillating in and out of the rail gun during each cycle. The three

phase A.C rail gun system also has the additional problem of an eccentric

force which is not favorable from the interior ballistics view point. Finally

they have concluded that the three phase staged discharge system has better

features from a control and flexibility stand point than the two phase staged

discharge system.

Cook et al (1998) have described the design, construction, and

testing of three scaled composite rotors. Results from the three studies were

reviewed in detail. Techniques developed at the Center for Electro mechanics

for determining composite rotor performance are also discussed. The design

and testing of these rotors, has demonstrated that the next generation of

compulsator are based upon reliable engineering design. They also have

suggested that continuing component research of this type will increase this

reliability.

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Cletus Kaiser (1998) has addressed different types of capacitors and

he has given some guidance in their applications.

Walter et al (1998) has discussed the recent trend in capacitor

application and operating characteristics. He also has discussed about the

different types of capacitor briefly. He has made comparisons between the

multi kilojoules pulsed power supply. He also has suggested that Modern

capacitor technologies generally retain potential for increased power and

energy densities by factors of 2- 5 times , depending upon the specific

technology. Implementation of these potentially ever more compact designs

rests primarily upon cost consideration in the consumer, commercial, and

industrial sectors.

Guido Picci (2000) has discussed the current performance of

metalized polypropylene film capacitors. He has confirmed that pulses having

high peaks of current but short duration produce the same degradation level in

the capacitor than pulses having low peaks of current but long duration. He

also has suggested that an increase in the capacitor’s compactness seems to be

a good way to increase the capacitor’s power pulse performance reducing in

the same time the loss in the capacitance.

Walls (2002) has summarized current trends in high performance

pulsed rotating machine development, and discussed some of the trade-offs

involved in the selection of an appropriate rotating machine approach to a

given set of application requirements. He has suggested that in a system level

view, including energy recharge, output power conditioning, and auxiliary

support systems, must be considered to minimize overall power supply weight

and volume. He also has suggested that use of the improved composite fibers,

innovative machine topologies, and advanced solid state switching devices

will allow these systems to be applied to a broad range of pulsed power

applications.

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Wang Ying et al (2004) have given the theory-mathematical model

in which some characteristics of the MHD generator were expressed. This

helps us to understand the relationship between various physical quantities

about the generator and provides a basis to research their mutual influences.

In addition, in physical design of the circuit, they adopted a proper high

energy density capacitor as auxiliary energy storage. Hence, the high energy

capacitor is charged directly by the generator and energy store within the

capacitor is realized, so as to form a generator-capacitor combined high power

pulsed power supply, which can be used by high energy electric launchers.

Ling Dai et al (2005) have produced the sample of the high voltage

multi layer capacitor. They tested their electrical characteristics in a pulse

energy discharge circuit. From the result they have derived the relations

between the changes of capacitance, dielectric loss, the charge frequency, and

the lifetime. They concluded that, MLC is suitable for making high energy

density capacitor, which can endure high reverse voltage, high current, and

possesses long lifetime.

Kirk Slenes et al (2005) have developed a novel dielectric material

called TPL in support of compact power systems for EML applications. The

material offers a unique combination of high dielectric constant and high

dielectric strength. They observed that the projected performance of

capacitors for use in future EML power systems support a factor of three

increases in energy density over current technologies. They also projected the

integration of the polymer/paper film technology into full-scale capacitors.

Sitzman et al (2007) have designed, constructed, and tested a

working slow transfer of energy through capacitive hybrid (STRETCH) meat

grinder system that can be output a current of over 20 kA. This system was

then used to successfully fire a small rail gun.

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( c ) Modelling of rail gun

Kerrisk (1981) has developed a model to analyze one and two

dimensional, nonlinear current diffusion in rail gun conductors. The nonlinear

current-diffusion equation that accounts for the temperature dependence of

electrical conductivity has been developed from Maxwell's equations. He has

used a finite difference heat transfer computer program to solve the current-

diffusion and thermal diffusion problems for rail-gun conductors in one and

two dimensions. He has calculated the rail gun key parameters for various rail

dimensions and then compared with other researcher’s values have shown a

good agreement between the results.

Jerry Kerrisk (1984) has calculated rail gun key parameters such as

inductance gradient and temperature distribution in a rail using finite

difference method. He also has developed a lumped electrical model to

calculate the rail current and projectile position as a function of time. He has

observed that calculated values and measured values have shown a good

agreement between the results.

Patch et al (1984) have given the design methodology of rail

gun, based on wide spectrum of computational tools for analyzing the multi

faced barrel performance. They have discussed the key feature of barrel

design process, analysis technique and optimized barrel design. They have

used 2 - D A.C method with high frequency limit, using finite element

method analysis to carry out this investigation. They have observed that

iteration between the design and analysis cycles are a critical interplay, for

rail gun barrel development.

Sadedin (1984) has calculated the efficiency of rail gun for constant

current distribution .The energy stored in the rails, energy dissipated in the arc

rail resistance, and the resistance per unit length was taken into account to

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calculate the efficiency. He has found that, the constant resistance per unit

length has lower losses in the projectile region, but diffusing current can

attain lower loss in the rail behind the projectile. He also has made a

comparison between the constant resistance per unit length and diffusion

current and has observed that there is not a large difference in efficiency,

given a common initial condition at constant temperature.

Honjo et al (1986) have developed BUS 3D code to calculate the

force acting on the each conductor in a rail gun model. They have suggested

that the BUS 3D code is useful in designing bus bar configuration for EML

system. They also have proved that the BUS 3D code could be versatile and

able to handle very complex arrangements of current carrying bars in three

dimensions.

Long (1986) has presented one possible approach to solve magnetic

field and current density in a simple rail gun. He has suggested that high

armature speed will cause damage to the rails through ohmic heating and

internal forces. He also has suggested that significant changes in rail and

armature design must be consider, if a solid conducting medium is to be used

between the rails.

Sharder et al (1986) have described the effect of number of turns in

the bore, the bore size, and lithium arc package on gun velocity. They have

conducted series of exploratory test and have calculated the velocity by

varying the above three parameters. They have observed that as the number of

turns in barrel increases, the velocity of the armature decreases. They also

have observed that as the bore surface area increases, the velocity of the

armature increases.

Atkinson (1989) has used finite element software, called MEGA, to

calculate the current density distribution using 2 D finite element analysis. He

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also has studied the current distribution in rails and armature using 3 D

analysis. He has used rectangular and C shaped armature to estimate the

current density distribution inside the rails and armature using mega theory.

He has observed that high temperature rises along the inside of the edges of

rails and armature, and it consistence with data obtained from firings

REMGUN.

Drake et al (1991) have described a model which can be used to

analyze current and temperature development in the return rail of an EML

during the launch by incorporating temperature dependent electrical and

thermal material properties. Due to these temperature dependencies and the

non-linearity’s, they have introduced derived equations, and solved

numerically by using ADI method, in which the nonlinearities in governing

equations accounted by assuming stepwise constant behavior in time.

Comparisons of the current and temperature responses are made with the

results of previously published researchers. They have argued that designing

rails by using only one-dimensional models for predicting current and

temperature, histories stipulates far more stringent, and sometimes

unattainable, requirements for survival than would designing rails using their

more physically correct model.

Huerta et al (1991) have calculated the inductance gradient of rails

in the short time flight, where the skin depth is much smaller than any other

rail dimensions. They have given the solution based on the Schwartz

christoffel transformation that maps the boundaries of the problem into a

small shape. They have observed that the calculated values of L’ have shows

a good agreement with other researchers values.

Azzerboni et al (1992) have developed a three dimensional

model of electrical and thermal response of the rails of electromagnetic rail

guns. The model have included the specification of time dependent material

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properties of rails and of the arc-armature, and takes into account the voltage

drops between the fixed and moving conducting parts. They have calculated

electric and thermal stress on a moving conductor and fixed conductors part

by solving differential equations using a Gear method and they have observed

that calculated values has a good agreement with the values obtained by other

researchers.

Azzerboni et al (1993) have developed a numerical code, called

FEMAN, to calculate the force acting on a conductor in rail gun system. They

have suggested that the FEMAN program is a useful code in analysis of

electromagnetic accelerator systems, because it can be able to perform the

calculations of the potential vector, magnetic field, self and mutual

inductance, and forces for the system composed by structure formed by one or

more massive conductors.

Ellies et al (1995) have made a study to explore a range of bore and

rail geometry and look at their effect on key rail gun system parameters such

as parasitic mass, inductance gradient of the rails, linear current density,

required PFN size, and barrel mass. Numerical code was developed to carry

out this investigation. They have taken rectangular, square and circular bore

geometries to calculate the above parameters and they have suggested that

rectangular bore geometry has more advantage than square and circular bore

geometry.

Hsieh et al (1997) have presented the electromagnetic simulations

based on a common problems including current density, magnetic field,

temperature and driving body force density with stationary armature, and

moving armature along with a discussion of skin effects.

Moyama et al (1997) have calculated the L’ values of rails,

considering the non linearity of electrical conductivity of the rails and the

22

magnetic property of the ferromagnetic component using FEM analysis. They

have observed that the calculated L’ values are little lower than the measured

one. They also have observed that the L’ values changes with peak current

values. Through the parametric study, they have obtained important

information related to barrel design such as the coupled effect on L’ of the

magnetic property and conductivity of barrel component, and they have

proposed the idea of a thin steel wire wound barrel from the results.

Alexander et al (1999) have designed and fabricated monopole

antenna probe to measure the pulsed E field environment. The calibration

shows a linear response to frequencies of interest for rail gun operation. Then

they also have developed a theoretical model to evaluate the electric field

environment produced by a rail gun. The magneto static approximation was

used and forms the basis of circuit theory by neglecting displacement current

in Maxwell equation. The currents have considered in the model for the

calculation of the vector potential were those following only in the rail and

armature conductor. They have observed significant disagreement between

theoretical predictions and measured value of E field.

Alexander et al (1999) have developed a quasi static model for the

in bore field B from the Biot savart’s law, based on the launcher and armature

current conducted in a thin sheet. They also have measured the azimuthal

component of the magnetic field ahead of the armature. The obtained data’s

are in good agreement with the model predictions. They have suggested that

the interior and exterior electric field and magnetic field is complicated and is

dependent on the system configuration. They also have addressed the in bore

field issues relative to the functionality of an in bore electronics packages for

stationary armature. It was suspected that the time derivative of the electric

field and magnetic field will be more pronounced, particularly at the time of

projectile exit.

23

Bok-ki kim et al (1999) have investigated how rail and armature

geometry affect the current density distribution and L’ of the rail gun system.

They have concluded that the relative position between the contact leading

edge and the root trailing edge is most important geometrical parameter since

it determine lower inductance path.

Asghar Keshtkar (2005) has investigated how the rail dimensions

and space affects the current density distribution, magnetic flux density and

inductance gradient of the rails using finite element method. He has varied

rail separation, rail width and height to calculate the inductance gradient of

the rails. He has suggested that to increase L’, the thickness and width of rails

must be decreased where as separation between rails ought to increase. He has

used transient analysis technique to carry out this investigation.

John Powell et al (2007) have developed two-dimensional

model for investigating current and heat transport in rail guns. They have

developed a mathematical model using Maxwell’s equations to perform the

electromagnetic and thermal analysis rail gun. The model is then used to

investigate current diffusion into a pair of parallel rails such as might be

appropriate in a rail gun behind the projectile.

Majid Ghassemi et al (2009) have formulated governing nonlinear

equation, Maxwell, energy, and Nervier equations are applied to rails under

dynamic load to investigate the effect of body force as well as temperature

distribution on the displacement of the rails in an EML. They have developed

nonlinear governing differential equations using finite difference base code

and then the force distribution in a rail and armature has been calculated.

They have observed that the maximum volumetric forces take place where the

highest magnetic field gradient occurs. In addition, they also have observed

that the maximum magnetic force is accumulated at the trailing edge of the

armature and portions of the rail interior. The thermal stress distribution

24

follows the same trend as the displacement due to the temperature behavior of

the rails.

Asghar Keshtkar et al (2009) have derived an empirical formula

that can be used to compute the inductance gradient value of rails by using

IES method. The obtained L’ values using empirical formula have well

agreement with other researcher values.

(d) Capacitor based pulsed power supply design

Deadrick et al (1982) have developed and validated simulation code

at the Lawrence Livermore National Laboratory (LLNL) to predict the

performance of a rail gun electromagnetic accelerator. The code is called

MAGRAC (magnetic rail gun accelerator), models the performance of a rail

gun driven by a magnetic flux compression current generator (MFCG). The

MAGRAC code employs a time-step solution of the non-linear time varying

element rail gun circuit to determine rail currents. He has concluded that the

MAGRAG model has provided valuable insight and data which have directly

benefited the design, operation, and diagnostics of MFCG rail gun systems

used in the LOS Alamos research project. They also have observed the

calculated value of rail gun parameters such as velocity, projectile position

and acceleration of the projectile shows a good agreement with experiment

results.

Alexey Alexeev et al (1992) have developed the PFN complex

program for obtaining a preset shape current in the rail gun launcher by

calculating parameters of the pulse forming network. They have suggested

that for the creation of a required current shape in the rail gun launcher with a

preset quantity of capacitor modules, one can offer different schemes of the

pulse forming network differing by the quantity of capacitor module groups

and values of pulse forming inductances. They also have shown that the

25

scheme of the pulse forming network with start switches triggering together is

the simplest scheme for the formation of a quasi-rectangular current pulse in

the rail gun launcher.

Bhasavanich et al (1993) have described a flexible 4.5 MJ pulse

power supply (PPS) for use as a driver for experimental electro thermal guns.

The PPS consists of 18 identical pulse forming modules which can be set to

discharge independently at predetermined intervals. The system features 1 %

capacitor bank charge repeatability from shot to shot and an ability to

generate short and long pulses for each of the modules using a combination of

pulse shaping inductors, crowbar resistors and diodes. Fiber optic isolation for

the controls and diagnostics provides a high level of noise immunity from the

main gun circuit. Critical components were selected with ample safety

margin, to allow for reliable operations and ability to fire through a gun

breech short circuit fault.

Strachan et al (1993) have designed a transportable 1 MJ energy

storage bank designed for electro thermal gun driver. They have also

described the layout and operational parameters of the system and strategies

implemented for fault mitigation. Performance of storage bank, for a dummy

load and a short circuit has also been presented. They have observed

discharging the system in dummy load a maximum current of 60kA achieved

at 0.15ms after ignition. The pulse shape is over damped and the total pulse

duration about 2ms. They also have observed that the discharging the system

into a short circuit leads to a ringing output current with a maximum current

of 200kA.

Tatake et al (1994) have developed a rail gun powered by a

capacitor bank to launch hypervelocity projectiles. They also have developed

a simulation code, using Pascal language, to predict the performance of the

rail gun. The rail gun has been modeled as a time-varying impedance to

26

determine the currents and the voltages from the power source. They have

calculated the rail parameters such peak current value at exist, the energy

distribution in a rail gun at exist, velocity, pressure, force and effective barrel

length of rails using the developed simulation code and they have observed

that the results obtained from simulation and experiment shows a good

agreement between the results. They also have suggested that even very low

impedances of the order of milli-ohm and micro-henry are substantial sources

of energy losses.

Emelina et al (1995) have described the pulse formation of a

programmable multi-stage pulsed power supply for electric rail guns. This

power supply allows optimal operation of the rail gun by maintaining a near

constant acceleration force over the launch period. This constant force is

gained by matching the voltage of the power supply to the variable inductance

and resistance of the launcher. They also have presented the way to estimate

the load inductance of rail gun.

Lehmann et al (1995) have presented an overview of what can be

done to enhance the efficiency of a rail launcher fed by capacitor banks

adjusting the rail design, the launcher caliber and length in view to accelerate

payloads of several kilograms up to velocities of few km/s with minimum of

charged electrical energy. They have also shown that the inductance gradient

L’, which has a great influence on the launcher performance, can be improved

by choosing an appropriate profile of the rails. They have also observed that

the overall efficiency of rail gun increases when L’ increases. Finally, they

have optimized the rail gun design in order to accelerate the projectile with a

fineness ratio of L/D =30.

Wey et al (1995) have developed the capacitor bank, consisting of

two stages, is used for experiments with a 50mm round bore rail gun at a

maximum current of 2MA. The rail gun is fed at two different points in order

27

to test DES rail gun concept. An appropriate design and material choice of

metallic projectiles, accelerated form the rest position, allow the current to be

injected at the front side and to be distributed over whole the armature

discussed. They also have developed electromechanical model of rail gun

using PSPICE based code to predict the peak current value and velocity of the

projectile. They have observed that the calculated values and experiments

values have show a good agreement between the results. Voltages and energy

distribution in different parts of circuit are also having compared to obtain

information of the loss mechanism in rail gun.

Antonino Musolino et al (1997) have presented the procedure for

the design of a PFN feeding an electromagnetic launcher. For the given the

design parameters (pulse duration, pulse rise time, pulse current amplitude

and load equivalent resistance), they have given the procedure to get the value

of the inductances and capacitances for an optimal design of L- C ladder

feeding network to get a required pulse shape of current. They have used an

analytical procedure that speeds up the optimization process and takes into

account the parasitic effects has been developed assuming a linear equivalent

resistor for the rail gun. The initial values of the network parameters are

estimated by means of an auxiliary network free of parasitic elements.

Calculated results to optimize the L-C branches in order to obtain a given

trapezoidal current pulse have been presented.

Ian McNab (1997) has described the pulsed power requirements for

electric guns. He also has discussed the preferred technologies for energy

storage and pulsed compression. He has suggested that by choosing the

correct technologies to study depends on financial constraints and the

definition of which gun and mission approaches should be the focus for an

electric system that is unlikely to be fielded before 2005 and could be as late

as 2015.

28

Jack Bernardes et al (2003) have developed a generic design PPS

based on state-of-the-art power supply, capacitor, and switching technologies.

The capacitor-bank and rail gun transient performance have been simulated

using Micro-Cap VI, an electrical circuit analysis software package. They

have calculated the rail gun parameters such as velocity, acceleration,

armature current value, and energy dissipated in rails by using the Micro-Cap

VI simulation package. The circuit simulation results show that a 160-MJ

capacitor-based PPS adequately drives a 63-MJ notional naval rail gun.

Analysis of the energy dissipation has showed that approximately 10% of the

stored energy is deposited as heat in the pulsed power components. Finally

they have concluded based on performance and physical characteristics this

type of capacitor based PPS is a feasible option for driving a long-range

Naval, rail gun.

Dwight Warnock (2003) has explored the design options for a 1.2-

m rail gun power supply capable of accelerating a 150-g to 250-g projectile to

1000 m/s. In order to accomplish this task he has developed a MATLAB

model to conduct trade-off studies between various power supply

configurations in an attempt to maximize the system performance. The final

design shows that by distributing the system capacitance between four equal

size banks and firing them sequentially the total system capacitance can be

reduced by more than half.

Miguel Del Guercio (2003) has designed a 4.5-MJ capacitor-based

pulsed power supply (PPS) and installed at the U.S. Army Research

Laboratory (ARL), Aberdeen Proving Ground, MD, for rail gun operations.

The system consists of 18 independent modules, each with an energy capacity

of 250 kJ. Simulations were conducted for a variety of load conditions using a

Spice-based code and peak current value and velocity of the projectile have

29

been calculated. They have observed that the predicted currents and velocities

have shown a reasonable agreement with measured quantities.

Wisken et al (2003) have given layout of a compact capacitive PPS

system influenced by many different parameters. They have suggested that

the geometrical parameters can be determined by the electric requirements.

Especially the capacitor and inductor design have to be adjusted for the

application. They also have presented capacitive pulsed power module for

large caliber ETC application has an energy density in the range between 0.8–

1.0 MJ/m3. They used new technologies and components such as high energy

density capacitors, light activated thyristors, and a toroid inductor to build up

a compact PPS module.

Timothy Wolfe et al (2004) have described preliminary design

assessments associated with the 200 MJ Naval PoC Facility rail gun. They

have discussed facility requirements, PFN modeling and component technical

assessment. Additionally the facility layout, capacitor bank modules and

bussing requirements have been illustrated. The circuit model was created,

using MicroCap™ software, to validate PFN performance at each of the

installation increments. The model was validated against existing shot data

from actual firings at the Green Farm Test Facility Advanced Armature

Program (AAP) predictions and some Pro Basic™ modeling.

Jiannian Dong et al (2005) have designed a 600kJ capacitor-based

pulsed power system with two independent triggered modules, each with an

energy capacity of 300 kJ, as a basic facility for testing pancake coils systems.

The PPS consists of the capacitor banks, spark gap switch, a PWM high-

voltage charger, crowbar switch and the control system. The power supply

has been tested individually by varying the pulse shaping inductance. They

also have carried out the experimental researches on discharging character of

PPS and they have observed that, in all cases, performance of PPS is

30

satisfactory with waveform as predicted. They have suggested that the

duration of the current pulse can be extended by varying the inductance and

capacitance of capacitor.

Spahn et al (2008) have given the development of a 10MJ power

supply which consists of 200 units with 50kJ each. To analyze malfunctions,

simulations with the electrical code P-Spice have been used. The simulations

results show that by carrying out small modifications, the PFN should be

qualified as energy source for ETC-experiments

Shi Zhengjun et al (2009) have proposed a novel two-objective

optimization design model for pulsed power supply. Transient electric circuit

model for the PPS have been built using the electrical circuit analysis

software Saber™. The model is created in a modular approach and is

structured in a top down building block format, which organizes the system

into a hierarchy of intermediate circuit schematics. They have taken two

objectives such as muzzle velocity and the stored energy to analyze the

performance of rail gun model. The design variables include the operating

voltage and the trigger delay times between segments. The optimization

results for the muzzle velocity and the efficiency separately shows that (1)

the acceleration constraint has great influence on the performance; (2) wide

current pulse yields high velocity but low efficiency; and (3) the operating

voltage has to be increased to accelerate a heavier projectile to a certain

velocity, or at a certain efficiency.

31

1.6 GUN PROPULSION TECHNIQUES

In a broad sense the gun propulsion techniques to launch projectiles

are

1. Electro Magnetic(EM) rail gun

2. Electro Thermal (ET)gun

3. Electro Thermal Chemical (ETC)gun

1.6.1 Electro Magnetic Rail Gun

Figure 1.2 shows a simple rail gun model without a power supply.

The rail gun uses the electromagnetic energy to drive a projectile (Hammon

et al 1992). The rail gun consists of a two parallel conductors called rails

separated by a distance and connected by a movable conductor called an

armature. The magnetic field is set up, when high current flows through the

two rails and an armature. The armature current interacts with the field

produced by the rail current and accelerates the projectile due to the Lorenz

force. The entire energy comes from the power source for the electromagnetic

rail gun and no propellant is used.

Figure 1.2 Rail gun models without a power supply (Jerome Tzeng et al

2004)

Based on the capacitive energy storage and pulse forming option

the basic characters of electromagnetic rail gun are

32

(a) Load impedance

Load impedance is the impedance offered by a launcher

when the current flows into the launchers. Depending on the energy

conversion method, the impedance offered by the launchers is going to

be varied. In electromagnetic rail gun the force acting on the projectile is

given as

21'

2F L I N (1.1)

where L’is the inductance gradient of the rails (µH/m);

I is the current that flowing through the armature (Amps)

and

Acceleration of the projectile is given as

21'

2

Fa L I

m mm/s

2 (1.2)

From the equation (1.2), it is observed that the force acting on the

projectile is proportional to inductance gradient of the rails. This L’ is the load

impedance of the rail gun. The load is initially a very low inductance and

resistance. The inductance is increased rapidly as the projectile is accelerated.

The rate of change of inductance is the key parameter contributor to the

impedance, particularly for lower mass projectiles (Hammon et al 1992).

Figure 1.3 shows the load impedance curve for Electromagnetic

launchers. The load impedance of the rail gun increases linearly as the

time increases. Normally the load impedance of EML is in the range of

milliohm.

33

Time(ms)

Imp

edan

ce (

m)

Figure 1.3 Load impedance of rail gun (Hammon et al 1992)

(b) High current is required

The source current is the only thing to consider in rail gun system

instead of source voltage, because the acceleration of the projectile is

proportional to the square of the current (Equation (1.2)). However, the source

voltage should always be greater than the load voltage (induced e.m.f in

armature called back e.m.f). The maximum allowable current through the

barrel is limited by its pressure rating, but may also be limited by the

allowable current density flowing from the rails into the projectile. For a

given system, a roughly constant current should be provided. The rise time of

the current should not be too fast (Hammon et al 1992).

Figure 1.4 shows the load current of EM rail gun. To get higher

acceleration and utilize the entire barrel length of the rail it needs constant

current pulse.

Time (ms)

Cu

rre

nt

(MA

)

Figure 1.4 Load current wave form for rail gun (Hammon et al 1992)

34

1.6.2 Electro Thermal (ET) Gun

Figure 1.5 shows the simple schematic diagram of electro thermal

gun. This is similar to the conventional gun. The projectile in ET gun is

propelled by the expansion of hot gases generated from an endothermic inert

material by impinging high temperature plasma in a plasma cartridge. The

hyper velocity of the projectile is achieved by injecting enough electrical

energy to the ET gun. The entire energy for ET gun comes from power source

like rail gun. This leads to large system complexity and reduces it

attractiveness (Hammon et al 1992).

Figure 1.5 Electro thermal guns

Based on the capacitive energy storage and pulse forming option

the basic characters of ET gun system are as

(a) Load impedance

The load impedance of ET gun fairly high resistance initially, it

reaches to lower value in the middle of the pulse, and then increases to higher

value of resistance at the end of the pulse as shown in the Figure 1.6. The load

inductance is low value and roughly constant in entire operation of ET gun.

The load impedance of ET gun is greater than electromagnetic gun ( Hammon

et al 1992).

35

Res

ista

nce

(m

)

Time (ms)

Figure 1.6 Load resistance of ET Gun (Hammon et al 1992)

(b) High current is not required.

The acceleration of projectile in ET gun depends on the expansion

of hot gas generated inside the barrel that depends on power supplied by the

power source. So the ET gun does not need higher current to accelerate the

projectile. In principle, the plasma chamber design can be selected to operate

at any voltage within a fairly broad range, allowing the gun designer to trade

voltage for current while holding power constant (Hammon et al 1992).

Pow

er (

W)

Time(ms)

Figure 1.7 Power pulse for E T gun (Hammon et al 1992)

36

Figure 1.7 shows the desirable power pulse for the ET gun. In order

to maximize the launch energy for a given barrel in ET gun, the pressure

inside the barrel has to keep in roughly constant. This means during the

launch a constant increasing power is to be delivered by the plasma source

this leads the power source to provide a constant increasing power.

1.6.3 Electro Thermal Chemical (ETC) Gun

Figure 1.8 shows the simple schematic diagram of electro thermal

chemical gun. It is a hybrid gun, formed with a combination of ET and EM

propulsion concept. It utilizes electrical and chemical energy to accelerate a

projectile this offer enhancement in gun lethality increased kinetic energy and

improve the performance as compared to solid propellant gun (Young- Hyun

(2002).

The internal ballistic process of ETC involves a discharge of high

electric current from pulse forming network into a plasma cartridge. This

causes vaporization and subsequent ionization of a fuse wire in to plasma.

Figure 1.8 Schematic diagram of ETC gun (Gus Khalil et al 2007)

The high electric current is continuously discharged from PFN in to

plasma cartridge causes ohmic heating and transforms a portion of electric

energy into thermal energy. This also ablates and ionizes a wall material of

37

the plasma cartridge and the results in a substantial pressure rise in the

cartridge. A pressure gradient between the plasma cartridge and combustion

chamber is developed. This allows venting the plasma in combustion. ETC

offers advantages like substantial reduction in electrical power, increased load

density and reduced vulnerability. Based on the energy storage and pulse

forming option the basic characters of the ETC gun are as

(a) Load resistance

The load resistance of an electro thermal-chemical (ETC) depends

on the thermodynamic state of plasma and propellant gas in the gun chamber.

It is difficult to analyze the load resistance theoretically because the

complicated flow equations, which nonlinear electric energy distribution.

Figure 1.9 Load resistance of ETC Gun (Young- Hyun 2002)

Figure 1.9 shows the load impedance obtained from experiment.

From the figure, it is observed that initially the load resistance of ETC gun is

of higher value, then it decreases as the time increases, at the middle of the

Load

res

ista

nce

()

Time (ms)

38

pulse once again it increases to a higher value and then it decreases to a lower

value at the end of the pulse (Young- Hyun 2002).

(b) Need moderate high current and high voltage

As the ETC gun utilizes the electrical energy and chemical energy

to accelerate the projectile, it needs moderate high current and high voltage.

1.6.4 Comparison of Electric Gun Technologies

The required breech input energy for different gun propulsion

technology are obtained from the mission requirements via the projectile

energy required on target, the aerodynamic losses in flight, and the gun

efficiency (Ian McNab 1997). A notional set of breech input energy

requirements for several electric gun technologies for a typical FMBT large

bore gun is given in Table 1.1.

Table 1.1 Comparison of various electromagnetic launchers (Ian McNab

1997)

Electric

gun concept

Energy

(MJ)

Voltage

(kV)

Current

(kA)

Efficiency

(KEout/

EEin

Pulse

length

(ms)

Average

power

(kw)

ETC gun 3-5 12-18 30-50 5 3-4 250

EM rail gun 60 - 90 5-7 3000-4000 0.5 4-6 4500

Pure ET gun 30 – 40 22-80 50-100 0.2 3-4 2000

From the Table 1.1, it is observed that the energy and average

power required for electro thermal and chemical gun are less compared to EM

gun to achieve higher velocity of the projectile. But the rail gun requires

substantially higher energies than either of the ETC and ET gun but it

operates at a lower voltage. In ETC and ET gun the projectile is accelerated

39

by generating large pressures behind the projectile inside the barrel. The

pressure inside the barrel is increased or the time is extended over which the

pressure is applied to get higher velocity in conventional gun systems. The

first method requires building stronger barrels with a practical limit being

reached as the weight of the gun exceeds that which can be used in tactical

environment. The second method involves extending the length of the barrel

thereby extending the time over which a given pressure is applied. This leads

to large system complexity and reduces their attractiveness. But the

Electromagnetic gun requires electric current to accelerate the projectile this

can be generated by several ways none of which require new volatile material.

The absence of projectile propellant is another attractive characteristic of EM

rail gun. Due to absence of propellants, 75% of space in EM gun is free,

which could then be used to keep the energy storage machinery and additional

projectile. While projectile velocity is a high priority the design and operating

characteristics of EM gun make them an excellent choice where specification

call for high projectile velocity, low system weakness, low firing signature,

extended projectile shelf life, selectable lethality, simplicity of projectile

storage, handling, and resupply, and minimal environmental impact (Fred

Charles Beach 1996).

1.7 THEORY BEHIND ELECTROMAGNETIC RAIL GUN

AND ITS PULSED POWER SUPPLY SYSTEMS

1.7.1 Basic Concept of Rail Gun

The concept of electromagnetic launchers has been in existence

since the early 1900s. In order to get the better success of the electromagnetic

launcher for the past century, the designs and goals have changed. The

electromagnetic launcher, also known as a rail gun, has had the considerable

developments in the last two decades (Bryan Mcdaniel 1996). Applications

that have been envisioned include everything from replacing the antiquated

40

steam system for rapidly accelerating carrier based aircraft, to launching

orbital platforms, welding or coating surfaces, acting as fuel pellet injectors

for nuclear fusion, and firing hypervelocity projectiles as weapons. While

many of these applications seem viable from a physics standpoint, the

problem of translating concept into design has been riddled with numerous

challenges (Matthew Schroeder 2007).

Figure 1.10 illustrates a schematic diagram of rail gun. The rail gun

consists of two parallel conductor called rails and electrically conductive

armature. The rails are connected to an electrical power supply. The closed

circuit is formed in rail gun system when the electrically conductive armature

is inserted between the rails. Once voltage is applied by the power supply,

electric current is flows through one rail and return through second rail via an

armature as shown in Figure 1.10(a).

(a) (b)

Figure 1.10 Concept of electromagnetic rail gun (Jerome Tzeng et al 2004)

The EML becomes a powerful electromagnet when the electric

current flowing through rail and armature creates the electromagnetic field

around them. The supplied current is interacting with resulting

electromagnetic field which result the electromagnetic force on armature

called Lorentz force. This is the driving force that accelerates the armature

along the rails. Since the rails also carry an electric current, they also

experience electromagnetic force and this is illustrated in Figure 1.10(b). The

41

electric current flows into the one rail in the negative X direction, and it flows

out from the second rail in the positive X direction. These two current creates

magnetic field between the rails in opposite direction which result repulsive

force on two rails.

1.7.1.1 Analysis of rail gun force and magnetic flux density

distribution in a rail (matthewmassey.com/RailgunTheory.pdf)

The force acting on a moving charge in a magnetic field and

electric is described using Lorentz force law

.F qE q v B (1.3)

where F is the force acting on the charge N

E is the electric field intensity V/m

B is the magnetic field intensity (T)

v is the charge velocity m/s

q is the charge (C)

Generally in a rail gun system, a large electric current in a

conducting armature is due to moving charge, hence the first term in equation

(1.3) can be neglected and then the force acting on the projectile is given as

.F q v B (1.4)

The amount of charge transfer through the projectile and across the

magnetic field, when the projectile moves with a velocity v and distance

traveled across the projectile l as shown in Figure 1.11, can be expressed as

lq it i

v(1.5)

42

Figure 1.11 Drift velocity and length through the projectile

Substituting the equation (1.5) into equation (1.4), then the force is given

.l

F i v B i l Bv

(1.6)

Using the cross product rule, the equation (1.6) can be further expressed as

. . sinF i l B (1.7)

is the angle between the magnetic field and current flows through the rail.

In a rail gun operation the magnetic field and current are

perpendicular to each other. So the equation (1.7) can further be reduced to

. .F i l B (1.8)

From the above equation, it is inferred that the current in the rails

and magnetic field created by the rails decides the force on the armature. For

a given current the force along the armature varies along its length, and the

magnetic field varies according to the length of the rails.

The magnetic field produced by the rail gun conductors can be

calculated by using the Biot - savart law. As per Biot savart law, the magnetic

field due to a current carrying conductor at any point is given as

0

24

ridl a

Br

(1.9)

vl

43

where dl an element of length along the current path through the

projectile

r is the radial distance from rails

ra is unit vector

Figure 1.12 Magnetic fields created by current in the rails

Assuming that the rails are constructed of thin wire that extended to

infinity long and then the magnetic field created by the rail current can be

closely approximated as shown in the Figure 1.12, then the magnetic field for

a straight wire can be given as

02

iB a

r (1.10)

Where r is the radial distance from the wire

For a semi-infinite straight wire, B will be1

2 of an infinitely long

wire and then the B can be given as

04

iB a

r(1.11)

B

2Rw

44

The magnetic field contribution from the first wire at any point is

being equivalent to equation (1.11) and for a given rail separation of width w,

the magnetic field contribution from the second wire is

04

iB a

w r(1.12)

The total magnetic field at a point along the armature is obtained by

adding the equations (1.11) and equation (1.12) and given as

0 04 4

i iB a a

w r r (1.13)

In order to prevent spurious results for magnetic field due to an

assumption of thin long wire, the radius of the wire must be taken into

account to calculate the magnetic field strength at the ends of the armature.

Taking into account the radius R of the rails, equation (1.13) can be expressed

as

0 04 4

i iB a a

R w r R r(1.14)

Subsisting equation (1.14) into equation (1.8), the differential force

acting on the armature can be obtained and given as

0 0

2

0

. .4 4

1 1. .

4 4

i idF i dl

R w r R r

i dlR w r R r

(1.15)

45

The total force acting on the armature can be obtained by

integrating equation (1.15) over the rail separation w between rails and given

as

2 2

0 0

0

1 1ln

4 2

wi i R w

F drR w r R r R

(1.16)

From equation (1.16), the term L’ is derived and given as

0' lnR w

Lw

(1.17)

It is important to note that, L’ has units of H/m, is not an actual

inductance of the system, but rather a magnetic field factor. The inductance

gradient of the rail is only dependent on the geometry of the rail gun and it

does not change once the gun has been constructed. By substituting equation

(1.17) into equation (1.16), the Lorentz Force (F) on the projectile can be

expressed with the following simple equation:

21'

2F L i (1.18)

The acceleration of the projectile can be obtained by dividing

equation (1.18) by mass of the projectile and it can be given as

21 '

2

L ia

m (1.19)

Velocity of projectile can be obtained by integrating the

acceleration of the projectile and given as

v adt m/s (1.20)

46

The distance traveled by the projectile can be obtained by

integrating the velocity of the projectile and given as

d vdt (1.21)

In order to obtain an exact solution to these equations, it is

necessary to know the initial velocity and position of the projectile.

1.7.2 Basic Concept of Pulsed Power Supply

The energy source plays an important role in a rail gun design as it

determines the constant current delivered to the load. Mission goals, such as

projectile kinetic energy and velocity, define armature and launcher

requirements, which in turn specify the rail gun’s input power. The power

supply is then built or adapted to meet this need. The system’s total size,

weight, and cost are usually dominated by the power supply, and so it is a

major constraint in developing mobile systems for the future battlefield.

Depending upon the energy source connections, the rail guns are

classified in two types

1. Breech fed rail gun

2. Distributed Energy Storage (DES) fed rail gun.

Figure 1.13 shows schematic diagram of breech fed rail gun. The

front end of the rail is called breech end where as the end of rail is called

muzzled end. The area where the armature is located is called the bore. In

Breech fed rail gun the power supply is placed in nearer to breech end.

47

Figure 1.13 Breech fed rail gun

The Distributed Energy Storage (DES) rail gun system as shown in

Figure 1.14 has the more complex electromagnetic launcher design. In DES

rail gun, the power supply is placed at certain points along the rail gun. The

advantage of the DES rail gun is that the electrical efficiency can be improved

because inductive energy is only being stored in the last section of the rail.

Figure 1.14 Distributed Energy system rail gun

Also the ohmic loss due to rail resistance is decreased because the

current from each energy source is restricted to the resistance seen from that

stage and onto the muzzle (Bryan Mcdaniel 2006).

Rail

Rail

Energy

Source

Bore

Muzzle endBreech end

Armature

Energy

SourceEnergy

Source

Muzzle end

Rail

Rail

Energy

Source

Bore

Breech end

Armature

48

1.8 BRIEF DESCRIPTION ON THIS THESIS

Chapter 2 gives an overview of the existing types of energy storage

system used primarily for electric gun. A detailed feasibility study was made

in this chapter on different available energy storage devices to select a

suitable candidate to design a 500kJ pulsed power supply. For each energy

storage device, the technical challenges involved in designing the pulsed

power systems and research activity taken to improve the corresponding

pulsed power system are discussed. It is found that each energy storage device

has its own advantages and disadvantages. So a logical compromise has been

made taking into account of the constraints which are posted by the desired

energy requirement. The most feasible energy storage device is chosen by

studying all the technicalities of the system. Based on the resources and the

intended application it was decided that the 500kJ pulsed power supply will

be designed as a capacitor based system.

Chapter 3 gives importance of rail gun design parameters such as

such as current distribution over a rail cross section, magnetic flux density

between the rails, inductance gradient of the rail, temperature rise over rail

cross sections. The rail gun design parameters are mainly affected by rail

geometry and design. In this chapter the effect of rail dimensions on rail gun

design parameters are studied using computer package called Ansoft field

simulator. A.C high frequency method has been used to compute the rail gun

key parameters. The eddy current field solver is employed to perform

electromagnetic analysis and thermal field solver is employed to perform the

thermal analysis of rail gun. Finally this chapter gives the optimum rail

dimensions of rail gun design based on the rail gun design parameters values

obtained from the simulation results.

Chapter 4 gives the method of extracting the empirical formula

which can be used to compute the inductance gradient of rails for different

49

rail geometries. In order to calculate the inductance gradient of rails so for the

researcher has been used either of numerical method or analytical method. As

these two methods are time consuming, a simple method is needed to

calculate the L’ of the rails. In this chapter an empirical formula which can be

used to compute L’ of rails is extracted using regression analysis technique

for different rail geometry. The empirical formula for L’ is extracted for

rectangular geometry and circular geometry rail design. Finally L’ values

obtained from empirical formula are compared with other researcher values to

validate the extracted empirical formula.

Chapter 5 discusses the design of 500kJ pulsed power supply using

computer packages. In order to design 500kJ pulsed power supply in this

chapter the basic electric requirements of electromagnetic guns to be fulfilled

by the appropriate PPS systems are studied. From these requirements, design

criteria for high energy discharge modules and their auxiliary systems are

derived. Finally, the 500kJ PPS is designed using computer simulation

packages called PSPICE and MATLAB to accelerate the projectile with a

velocity of 1 to 1.5 km/s. In PSPICE simulation trade off study was made to

find out the optimum number of stages to get desired pulse shape and rail

parameters. MATLAB was used to obtain optimum values of rail parameters

such as muzzle velocity, current at exit, effective barrel length. Finally, this

chapter gives some basic considerations on volume and weight requirements

of 500kJ capacitive PPS systems to be applied for rapid fire of

electromagnetic rail guns.

Chapter 6 summarizes the overall work done in this study and

scope of the feature works.

50

1.9 SUMMARY

The main objective of this thesis is to design a 500kJ pulsed power

supply system which can be used to accelerate a projectile with a velocity of

1000 m/s to 1500 m/s. In order to carry out this study, in this chapter,

different types of electric gun propulsion technology which can be used to

accelerate a projectile with high velocity are studied. Based on energy storage

and pulse forming network the characteristics of each technologies have been

studied. It has been concluded that the design and operating characteristics of

EM gun make them an excellent choice because it has high projectile

velocity, low system susceptibility, low firing signature, selectable lethality,

simplicity of projectile storage, handling and resupply, and minimal

environmental impact. Then different types of energy fed rail gun system such

as breech fed rail gun and DES rail gun are studied to understand the concept

of pulsed power systems. It has been concluded that DES rail gun system has

more advantages than the breech fed rail gun system as it has low inductive

losses. Then the problems involved in design of rail gun and its pulsed power

supply are discussed. Based on the discussions, it has been concluded that,

before the rail gun system became synchronous, simulation has to be carried

out well in advance to predict the performance of rail gun and its pulsed

power supply system. Methodologies adopted to carry out these problems are

also discussed. Based on discussion, it has been concluded that the

performance of rail gun can be analyzed by using FEM software where as the

performance of pulsed power supply can be analyzed using PSPPICE and

MATLAB software.