Rahul Singh Dhari,Aravind Sekar

aDepartment of Mechanical Engineering,Pandit Deendayal Petroleum University,Gandhinagar,382007,IndiabDepartment of Mechanical Engineering,Dhanalakshmi College of Engineering,Chennai,601301,India

Split warhead simultaneous impact

Rahul Singh Dharia,*,Aravind Sekarb

aDepartment of Mechanical Engineering,Pandit Deendayal Petroleum University,Gandhinagar,382007,India
bDepartment of Mechanical Engineering,Dhanalakshmi College of Engineering,Chennai,601301,India

Mathematical formulations Aerodynamics Military technology and weapons systems Projectile and target fragmentation Warhead Split warhead

A projectile system is proposed to improve efficiency and effectiveness of damage done by anti-tank weapon system on its target by designing a ballistic projectile that can split into multiple warheads and engage a target at the same time.This idea has been developed in interest of saving time consumed from the process of reloading and additional number of rounds wasted on target during an attack.The proposed system is achieved in three steps:Firstly,a mathematical model is prepared using the basic equations of motion.Second,An Ejection Mechanism of proposed warhead is explained with the help of schematics.Third,a part of numerical simulation which is done using the MATLAB software.The final result shows various ranges and times when split can be effectively achieved.With the new system,impact points are increased and hence it has a better probability of hitting a target.

1.Introduction

The weapon system development is one of many factors that involve in proving a nation superior among a group of powerful nations.The World War I has been dawn of new era of the fire poweramong various nations.Beforethis,the kingdoms werethere using normal projectile weapons like canons and mortars fired manually.Then World War II which saw ambitious German army on one hand and highly populated American army on the other allied with many nations.P R de Wilde[1]claims the projectile motion to be used in firing artilleryand missiles.The Germans were so good at development of newartillery weapon systems in front of which the resource of the Americans had quite a struggle.But then the German dominance came to an end due to the air power of Americans.Both these world wars had been a beginning for evolution of currently existing modern weapon systems.Stevenson and Caven[2]invented incendiarycharges which enable the charge to burn for a longer time to ensure deeper penetration.

A new projectilewas introduced by Giljharus and Vien[3]which can detonate the explosive charge without any separate fuse which enabled toconnect multiple warheads toa single bore and a charge.A multi-platform/multi-role weapon system is a one which can be usedforany kind of terrain and be fired fromany type of Launchpad that is available and capable of carrying multiple warheads.Development of such weapon system will add on the advantage of revolutionizing defense technology.These weapon systems can deliver a better damage and be compatible with various available launchers and terrains.They are also considered as time saving and economic when compared to the normally existing weapon systems.

1.1.Multiple round simultaneous impact weapon system

This idea was mainly initiated from type of attacks carried out during world wars with the help of mortars and cannons by varying angle of the projectiles that are fired.The process of varying the motion of projectile is based on angle of the turret during time of initiation of attack done by each projectiles launch.This can be achieved in two ways,one of the ways is launching ‘n’number of projectiles froma particular point towards the target all at the same time byonlyvarying the angle of launch and anotherbylaunching a single projectile that is capable of firing multiple rounds at one point of its trajectory.

The process of modifying launch angle and velocity for each warhead and thereby making all projectiles hit the specific target area at a varied time is said to be the Multiple Round Simultaneous Impact(MRSI)weapon system[4].

The MRSI can be superior to a single round attack that is launched on the target because the MRSI can be used against all countermeasures that are launched from the target that is supposed to be destroyed.But if seen closer,major drawback exists in the place where the launch pads are less in number and situation of attacking being non-supportive to the requirements for making an attack using MRSI system.So in order to overcome this,a new weapon system with an entirely new idea designed and developed.This weapon system should be capable of making a possible damage on a specific target from anywhere at any time and also be able to carry multiple warheads with it to engage the target.Thus the new weapon system designed will be overcoming the drawback of handling and problem prevailing due to the shortage cases in an MRSI weapon system.

2.Proposed warhead weapon system

The multi-warhead projectiles have become necessary in battlefield applications for providing a better functionality and higher handling capacity.Providing greater target damage for a given thermonuclear weapon payload.Several small warheads cause much more target damage area than a single warhead alone.This,in turn,reduces the number of missiles and launch facilities required for a given destruction level-much the same as the purpose of cluster munitions.

With all these Multi-projectile warheads present,we propose a new(Anti-Tank Missile)Multi-projectile warhead capable of splitting into “n”(initially 2)warheads and causing damage.This can save precious time of reloading,aiming and shooting of tank crews.And not to mention the stress caused during this time.

This system,can use a single missile to hit a target as compared to multiple rounds in the traditional approach.As shown in illustration,if the tank/target moves from its place after launch in the MRSI system,rounds are miss-hit or wasted.However,in new SWSI approach,there's still a chance for a round to hit as the round splits into two warheads and at least anyone of the warhead will hit the target.Along with suitable change in time of split we can increase or decrease the distance between the impact of two warheads(See Fig.1).

3.Ballistic projectile motion

Projectile motion is a form of motion in which an object or particle(called a projectile)thrown from a surface moves along a curved path under the action of gravitational force.This gravity is the only force that acts on the object,acting downwards to cause a downward acceleration.In addition to gravity the drag force acting on the projectile will also affect the motion of the object.

The basic equations of a projectile motion should are carefully studied using the MATLAB program and a proper mechanism is crafted to be used to improvise such a design idea in a proper way.These equations of projectile are taken from the basic laws of the Newtonian physics.

3.1.Equations

Since the projectile launched comes across drag force when in air.The equations to find the position and velocity of the projectile at a point(x,y)should also be re-written considering the drag force equations.

Drag forceFcan be written as

Since,we cannot calculate acceleration and velocity directly,it's better to divide them into Vertical and Horizontal Component.Where,

ρis the density of air in kg/m3;Cis the Co-efficient of Drag;Ais the Area of cross-section in m2;mis the mass of object in kg;vxandvyare the horizontal and vertical component of velocity respectively in m/s;axandayare the horizontal and vertical component of acceleration respectively in m/s2;Δt=Change in time in seconds.

We get,the following equations

Substituting the eqn.(2)in(3).

Horizontal component of velocity,

Vertical Component of velocity

3.2.Mathematical model

Equations mentioned in the previous section are used to construct a mathematical model for the trajectory of weapon system.The model is then solved using Newton-Raphson Method.Newton-Raphson Method ischosen foritsaccuracyand robustness.

From equations(2)-(4)

The numerical model is run for various time increments （Δt）to obtain consistency.Time increments are kept as very small values(1μs to 1 ms)to ensure the accuracy as well precision of the code.

3.3.Algorithm

For a target at a distance ofXmetres,gunner has the target in sight.Ordnance is fired upon,the tank changes its position either forward to some 5 m.Then,in case of ordinary missile it will miss the target.

But,with proposed system the movement of tank is taken into account.Warhead will split after the designated time/range to ensure it has two(or more)point of impacts.Possible conditions to split is calculated using the MATLAB program and presented in the next section.

In order to achieve multiple point of impacts in the conventional MRSI System,morethan one roundsare tobe fired at various angles such as 15°,30°or 45°.Which means more ordnance,more time and more stress for the tank crew.

Inthe battlefield,Tank crewsdevisevarious maneuverstododge the missiles and rounds shot at them.A single round fired at them can be evaded.Crew needs to be on their toes and alert to hit a moving tank.With the SWSI,this work can be reduced to an extent as points of impact are increased.

3.4.Warhead schematics

E.L.Nooker[5]suggested that there can be multiple warheads stored in a single missile or a projectile.A similar concept is applied here.However,warheads get separated in mid-air to hit the designated area.Migliaccio[6]claims projectiles with extra sensitive warhead which has a detonation fuse in the nose.This can be implemented here as well.The missile can either have nose fuse like Migliaccio[6]or single fuse like Giljahrus[3]claims.Following is schematics of the new projectile missile we are developing.Projectile consists of two warheads of weights initially,assumed as 3 and 1.5 kg to ensure a total warhead weight of 4.5 kg.Initially,A combination of weights of two warheads was taken as 3 and 1.5 kg as arbitrary values with respect to the total weight of the warhead currently used.However,if analysis has to be performed for different sizes of missiles a suitable combination of weights can be assumed.

The warheads are considered to be of a cylindrical shape and hence suitable Drag Co-efficient has been assumed as 0.87[7].The Drag Co-efficient will further decrease with an increase in the launch velocityof a missile.However,we are dealing with velocities only up to 300 m/s[8].

The shell primarilyconsists of two parts-Propellant Casing and the Shell Casing.The Propellant Casing houses an explosive charge needed to shoot or fire the shell.The fuse of explosive is attached from bottom and can be removed or assembled from the bottom surface of the shell.This is done to ensure high efficiency inspections and safety measures.

The Shell casing is in two halves and is inserted into propellant casing.It contains various parts such as control rod which has avionics,warheads,fuse which can be inserted and removed from the sides.

The control rod contains electronics necessary to pin point the shell to its target.Its main components are RF Receiver,GPS for telemetry,Timer,Switch,Laser Detectors,and a battery to power all avionics.The control rodisattached to acircular bracketat centreof shell which gets created when both halves are shell casing are joined.

The warhead is having shape of a semi cylinder of outer diameter 110 mmwith a groove at the centre to facilitate the control rod.The warhead is 375 mm long.

There are 3 fuses in total on the shell.One for the propellant charge and one each for warheads.All can be accessed from surface and hence the shell can be easily disarmed for storage purposes.

Connection between casing and control rod is achieved using ejection rods.There are two ejection rods one each for a half of shell casing.The type and size of the rod can be of different dimensions depending upon the variants of the shell(See Fig.2).

4.Results and discussion

MATLAB program is written to calculate trajectories of projectiles.Basically,the split is classified in two types:

1.Based on time(“t”seconds after launch).

2.Based on distance(%of range).

The warhead is split into 2 projectiles and their path has been calculated using the program.The mainwarhead weighs 4.5 kg and it gets split into 2 warheads of 3 and 1.5 kg respectively.Aim is to make both projectiles hit within 9-10 m(normal length of a tank)to ensure a hit or kill.

A MATLAB program is written based on derivations that are made from basic equations of a projectile motionwith drag force as a major consideration.

4.1.Split based on time

The projectile(see Fig.3)was launched at 30°,velocity 300 m/s and the split was achieved at 20 s after launch.The main warhead and split projectile impacted within 50 m.The Range of split projectile is 2376 m.And range of main warhead is 2423 m.

Considering the aim of the system,this case is not true.Similarly more than 30 possible combinations were tested.With each having 1000 or more iterations for a second to reach on good result as shown later on.

The projectile(see Fig.4)was launched at 5°,velocity 300 m/s and split was achieved at 4 s after launch.The main warhead and split projectile impacted within 04 m.

Hence,the launch was successful for operations within Line of Sight.The Range of split projectile is 1033 m.And range of main warhead is 1029 m,which makes missile successfully impacting within 10 m.

4.2.Split based on range

The plots are made for the projectile to split based on the range as the determining factor.This is done by the specific MATLAB code written from the derivation made with basic equations and the range of the projectile as a vital parameter to simulate the program in a realistic manner.The program basically depends on initial parameters such as speed,launch angle,and velocity.

Fig.2.Warhead schematics.

Fig.3.Failed plot for time based split.

Projectile(see Fig.5)was launched at 45°,velocity 280 m/s and the split was achieved at 80%of range after the launch.Main warhead and split projectile impacted within 8 m.Range of split projectile is 8000 m.And range of main warhead is 8008 m,which makes the missile successfully impacting within 10 m.

Whereas,this projectile(see Fig.6)was launched at 45°,velocity 280 m/s and split was achieved at 90%of range after launch.The Range of split projectile is 8000 m.And the range of main warhead is 8454 m,which makes missile successfully impact 454 m after each other.Even this way system can do good harm.But considering the aim of system,it's a failure.

This system can be further enhanced by studying even more combinations of launch angle,range and time.

Fig.4.Successful result for a time based split.

4.3.Effectiveness and comparison

Let's compare the SWSI system with MRSI.While,in combat situations a tank usually fires multiple rounds at the target.The Target might be moving or stationary.The moving target mostly a Tank or an APC can easily dodge the rounds fired from the tank and hence multiple rounds should be fired to ensure a kill.At an average,an Arjun MBTcan fire6 to8 rounds per minute[9]whereas a T-90 tank with autoloader can fire a round every 5-8 s[10].Hitting the target and ensuring a kill within a time frame is important.With SWSI we can split warhead into two(or more)pieces.So,in case of moving target,the split warhead has two or more chances to hit the target as compared to the existing single warhead missile.That way we can save a lot of ordnance and time,both of which plays a crucial role in the battle field when precious lives are at stake.

Dividing the ordnance into several fragments might reduce the damage and the impact radius of the missile,but at the same time we are able to hit two places with a single launch.Even a hit at one of the impact will easily compensate against the conventional round being a total miss-hit.So,if a single warhead of weight 4.5 kg makes an impact radius of some x meters.Impact radius of warheads weighing 3 and 1.5 kg would be proportional tox in variation with its weight.They will make an impact radius of 0.6× and 0.3×respectively.But,the missile is hitting the target and which means the target is crippled or destroyed with launch of just one missile and hence saving ordnance and time.

ArjunTank can fire 6 to 8 rounds per minute[9].That means one round can be fired every 8-10 s.The Probability of hitting with the first shot on target at a stationary tank,assuming the laser rangefinder and computer to be as effective as those in Western tanks is 35-40%for a range of more than 3 km[11].L R Cerrato concludes the probability goes below 0.5 as distance increases beyond 4 km[12].However,if target moves forward or backward after firing off round,round might miss target.But with this split warhead concept,we are achieving that even if tank moves from his position(see Fig.1),either any of the two warheads can hit or both of them can hit which results in the increase of probability of a kill.It is also possible to split the projectile to hit multiple targets with a single launch.But that will require changing of parameter-time of split or range at split.

Fig.5.Successful result based on split by distance.

Fig.6.Failed plot for split by distance.

5.Conclusion

The SWSI weapon system has a better capacity to make a collateral damage on a target as specified above.If this experimentation comes into implementation then the tank warfare will become more revolutionized and any type of target can be engaged with an ease.For implementing the above system the above MATLAB plots will be a vital need and specifications along with possible splitting mechanism can lead to design and development of the first prototype.According to MATLAB plots,projectile with a maximum range of around 8 km and a speed of around 280 m/s to 300 m/s.For a successful and efficient attack,splitting of warheads should occur at 80%of range.This system with compatible hardware can be very much successful for operations within the line of sights.Results show a split after 4 s of launch can cause missile to make an impact at 2 places within a difference of 4 m which makes missile more capable of destroying a tank or a moving armored vehicle.Another application of this system could be scatter bombings or hitting more than one targets which are close to each other.Thus,approach of analysis can be used as a base to study further,the aspects of split warhead missiles.

Supplementary video related to this chapter can be found at http://dx.doi.org/10.1016/j.dt.2017.06.004.

Acknowledgement

Authors are grateful to Dr.Nirav Patel,Assistant Professor,Department of Mechanical Engineering,School of Technology,Pandit Deendayal Petroleum University,Gandhinagar,India for his insights and guidance on various aspects of the paper.

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4 February 2017

in revised form 16 June 2017 Accepted 26 June 2017 Available online 29 June 2017

?2017 The Authors.Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.

E-mail address:rahul4194@gmail.com(R.Singh Dhari).

Peer review under responsibility of China Ordnance Society.