Method of ballistic control and projectile rotation in a novel railgun

Bo Tang,Ying-tao Xu,Gang Wan,Jiang Yue,Yong Jin,Hai-yuan Li

National Key Laboratory of Transient Physics,Nanjing University of Science and Technology,Nanjing,210094,Jiangsu,China

Keywords:Ballistic control Railgun Rotation Spin-stabilized projectile

ABSTRACT In order to realize the ballistic control of the railgun and the flight stability of the projectile,a new type of railgun is designed,which can control the muzzle velocity and rotation rate.The method of the muzzle velocity and overload control is to adjust the voltage or other parameters of pulse power supply.It would be easy to change velocity accurately in large wide.Another widespread concern problem is launching the spinning stability projectile by railgun.This paper designed a new structure of additional rails to generate an unsymmetrical magnetic field to produce rotational torque in armature.The structure is simple and can control the rotation rate by linear changing the barrel parameters.The calculation formulas of interior ballistic are derived by Biot-Safar law.The important parameter is the deflection angle of the additional rails relative to the symmetry plane of main rail.The larger the angle,the greater the rotation torque generated in the armature.To maintain the flight stability of the projectile,the barrel structural parameters should be proportional to the projectile structural parameters.When changing the muzzle velocity,the rotation rate will also be the equal proportion change.So that the gyro stability is the same.The experiment proves that the railgun designed in this paper can launch the projectile to rotate.And the rotational projectile may not cause the transition or much arcs.This method expands the application of the railgun.

1.Introduction

With the development of electromagnetic launch technology,a series of problems are gradually solved[1],so that the railguns are close to practical.Electromagnetic launch has some advantages[2],in addition to the high muzzle velocity,the control of the ballistic is also an important advantage.Just control the current waveform,the ballistic is easy to adjustment[3].The accurate control of the ballistic is a large improvement to conventional weapons.In the future,the railguns may automatically design the best ballistic according to the launch conditions of environment and shooting angle.No need to master the knowledge of adjusting the sight or firing table(Fig.1).

The control of ballistic has lots of application demand[4].For example,in the police firearms,there are often occur accidentally injures.When face to a suspect,whether to use the gun is often confusing the policeman,as it always leads to a mis-shot.On the other hand,if the policeman using non lethal weapons,they could not fight back with the armed criminals.This problem will be solved after using the ballistic controlled railgun.In the face of unarmed suspects,the ballistic could be regulated as a non lethal model.Good ballistic control will be significance(Fig.2).

The control of muzzle velocity also requires the projectile satisfying the flight stability.At present,the most common in electromagnetic launch is the tail wing projectile[5].Because the current electromagnetic gun now cannot make the projectile rotating at high speed.It most uses the tail wing stable mode.This method uses armature to push the projectile,and the armature is separated from the projectile after the exit.It is disadvantageous as the armature will cause additional damage.Therefore,this paper proposes an integrated projectile without the separation of armature and projectile.For the stability of the flight,the projectile must be rotating at high speed[6].It may be used in various projectiles,such as high explosive shells,small caliber projectiles and kinetic energy projectiles(Fig.3).

The method of driving the projectile to rotate is using electromagnetic force.And the armature moving forward is also driven by electromagnetic force.By controlling the electromagnetic force,it can control the muzzle velocity and the rotation rate of the projectile.A new design method of railgun is proposed in this paper.The muzzle velocity and rotation rate are proportional to the structure of the barrel,projectile and the parameters of the pulse power supply(PPS).Besides,the muzzle velocity is proportional to the rotation rate,if a velocity sat is fies the stability condition.When adjusting the velocity,it can still satisfy the stability condition.Experiments show that the method can stabilize the small caliber projectile and achieve the purpose of ballistic control.It provides a novel idea for the development of railgun.

2.Theoretical analysis

2.1.Design principle

The principle of electromagnetic launchis simple.Taking railgun as an example,the current in rail generates magnetic field and action with the armature to generate electromagnetic force.The innovative idea of this paper is adding additional rails to control the interior ballistics.It is simple to generate rotating torque in armature and enhance the launch efficiency[7].

As shown in Fig.4,the additional rails are located above and below the main rails and can be shifted laterally,which is different from the usual series structure.The center of the additional rails forms a certain angle relative to the symmetry plane of the main rail.The additional rails of this structure will generate the x direction magnetic field in the armature,thus forming a rotational torque to drive the armature rotation.The main influence od rotational torque is dh which is the distance between the additional rails and the center symmetry plane.Or saying the offset angle.The rotation rate can be regulated by adjusting the offset position of the additional rails.

According to Biot-Safar law,the magnetic induction intensity in the y direction at the center of the armature is

In the formula,Ilinerepresents the current in a line in the rail,Blinerepresents the magnetic induction intensity produced by the line current[8].Theαindicates the angle between the line and the armature center.Theθand r can be seen in Fig.4.The magnetic field in the y direction acts with the current in the armature to generate the forward electromagnetic force.

The magnetic field in the x direction generated by the additional rails at the armature tail arm is a formula which produces rotational torque in the armature.

In Formula(2),subscript 2 and 3 represent two additional rails seen in Fig.4.The magnetic field in the x direction is mainly generated by the additional rails and forms the rotational torque.Because the main rails are symmetrical relative to the armature,the force generated by x direction magnetic field is also symmetrical,and there is no rotation torque.So it may just calculate the additional rails.

2.2.Principle of muzzle velocity control

The control of muzzle velocity depends mainly on the current waveform,as the voltage of PPS.For the multi module,it can generate the square current waveform to control the overload.The power supply system consists of N modules,each module capacitance is Ck,the initial voltage is Uck,the Inductance value is Lk,the equation group is[9]

If UBis used as the voltage at ends of the rail,the circuit equation of the barrel system is written as follows

The magnetic induction intensity of two main rails in the y direction is

The Formula(5)is difficult to write specific expressions,and the final solution can be obtained by numerical calculation.

The magnetic flux density of two additional rails in the y direction is

Add the magnetic field generated by the additional rails to the main rails

All parameters in the formula are the structural parameters of the barrel seen in Fig.4,they can be regarded as constants when calculating.

2.3.Principle of rotating speed control

The principle of rotating torque can be simply understood as deflection of two additional rails.Which generate magnetic Bxin the tail arm of the armature,as shown in Fig.5.The Bxinteracts with current in the armature tail to generate torque.After the armature is rotated,the current is still in its original position,thus continue accelerating armature rotation.

The magnetic flux density of the additional rails in the x direction generated one side of the armature tail is

Where

According to the ampere force formula,the electromagnetic force and torque are obtained

The muzzle velocity and rotation rate of armature or projectile can be obtained by

The m and C represents the mass and moment of inertia of armature and projectile.The v is muzzle velocity,˙r is rotation rate.

2.4.Ballistic stability

For the small caliber railgun,the useful ballistic of a projectile is mainly the straight line.First consideration is gyroscopic stability represented by gyro stability factor Sg[10]

The A means the moment of inertia of the projectile equator,kzmeans the coefficient of projectile turning moment.To be stable,it needs Sg＞1.

For the relationship of muzzle velocity and rotation rate

If it want to be stable,it needs Sg＞1,so

When the parameters of the launcher and the projectile are determined,muzzle velocity and rotation rate can be regarded as the product of the additional rails deflection coefficient and current integration

In Formulas(24)-(25),the coefficient can be obtained from the previous formula,which is related to the structural parameters of the barrel.Therefore,if we want to satisfy the flight stability of the projectile,we need to satisfy the following formula

The item on the left side of“＞”is related to the structural parameters of the barrel,on the right side is related to the structural parameters of the projectile.Which means muzzle velocity and rotation rate arefixed proportion relation.This indicates that when change the muzzle velocity of the projectile,the rotation ratio will automatically follow the change.The flight will be stable

The kzcan be estimated by formula.kmz(M)can be obtained by checking the tables[11],Mzis the turning moment,h is distance of pressure center and centroid of projectile,d is diameter,δis angle of attack,ρis air density,H(y)means height.

3.Discuss

3.1.Controlling of muzzle velocity

The muzzle velocity of the projectile is related to the value of current.For the capacitive energy storage pulse power supply the current is proportional to the voltage of PPS.Therefore,adjusting the voltage can obtain the required current.Then the muzzle velocity may be controlled.Fig.6 shows four kinds of muzzle velocity and four corresponding current waveforms in the same linetype.The velocity curve is with circle mark.The faster the speed,the shorter the launching processes time.The muzzle velocity of projectiles can be controlled very accurately in theory.But at present,for the electrical contact and power system errors such reasons,it is not easy to realize.

3.2.Controlling rotating speed

When the two additional rails are shifting from the main rail symmetry,the magnetic induction intensity is obtained as shown in Fig.4.The magnetic field is deflection,and the magnetic field has downward direction component at the tail of the armature shown in Fig.7.That generates rotational torque and driving the armature rotation.

The direction of current in the armature is shown in Fig.8.The current flows into the central part of the armature from the tail arm,which produces rotating torque with the magnetic field.In order to keep this direction of current,there should be some slots in the rear of the armature.This structure also has another advantage,the tail arm has the outward expansion electromagnetic force.It can make the armature contact with the rail closely,increasing the electrical contact[12].

The influence of the deflection angle of the additional rails tothe symmetry plane of the main rail on the forward electromagnetic force and rotation torque is shown in Fig.9.The forward electromagnetic force decreases slightly with the increase of the deflection angle when the current is constant,the influence of the deflection angle on the forward electromagnetic force is not large.

3.3.Relationship of muzzle velocity and rotating speed

As shown in Fig.11,when the parameters of the barrel are determined,the muzzle and rotation rate are increasing with the voltage of the pulse power supply.The stable factor Sgis basically a constant value.Which means that the flight stability is satisfied at one muzzle velocity,the other muzzle velocity will meet the stability conditions too.Do not need to match the parameters of the barrel and projectile again.It is proved that electromagnetic launch is suitable for the control of muzzle velocity.

4.Experiment analysis

In previous papers,there have been many analyses of the effects of pulse power parameters on muzzle velocity[13,14].This experiment did notrepeatagain.For the experiment of rotation projectile launched by rail is seldom to see.In the experiments of Challita,many times of projectiles rotation were observed in the round bore railgun[15].It is believed that it was caused by electromagnetic force.But they did not want the rotation projectile,as some solutions to avoid rotation was proposed.

In this experiment,it is mainly to study the feasibility of the rotating of the projectile driven by electromagnetic force.The structure of the launcher,as the principle of this paper,has been designed for the experiment,shown in Figs.12-14.

This launcher has a detachable structure.It can change the structure of the rails.The arc control device is installed at the muzzle.The internal structure is like the principle described in Fig.4.

Using the capacitive PPS as the energy source,the total current is

The rotation torque increases linearly with the deflection angle.According to the formula,to meet the condition of the gyroscope stability,the rotation torque relative to the electromagnetic force should be more than a certain value.In Fig.9,the torque value on the left of the stable point is smaller than the certain value,it can not be spin stability.On the right the projectile would be sable.

The rotation rate of the projectile is also proportional to the initial voltage of the PPS,as shown in Fig.10.The higher the voltage,the greater the deflection angle,the higher the rotation rate.The adjustment range of the rotation rate is large,high voltage and little angle is suitable for the low rotation rate fin-stabilized projectile.Which means the method proposed in this paper is suitable for rotation rate control.about 140 kA.At the beginning of the muzzle voltage,there is a negative current due to induced eddy current.The voltage always keeps a low amplitude during the launching,which indicates that the projectile has no transition and proves that the projectile has good electrical contact properties.

The movement of the projectile is photographed by high speed camera.From Fig.15,the projectile has good attitude and flight stability and the projectile has rotated during the flight.It can be read from the high-speed camera pictures,the rotating angle is about 30o,the experiments have got the rotation rate is over 100000o/s,more than tens of thousands rounds per minute.This proves that the electromagnetic force can drive the projectile to rotate.Besides,there is no arc around the projectile just like conventional projectile flight.Which means that the rotational projectile did not cause the transition or produce much arcs.This proves the rotational projectile is feasible for railgun.

5.Conclusions

The ballistic control of the railgun has a good application prospect.In the future,the railgun will be able to set the optimal ballistic automatically and achieve the firing accuracy.For the muzzle velocity and rotation rate control,this paper designs a new type of railgun.Which produces asymmetrical magnetic by additional rails and generates rotation torque in armature.The structure is simple to realize,and the rotation rate can be controlled conveniently by changing the deflection angle.Which can be accurately controlled within a large range.In principle,it is feasible to adjust the muzzle velocity and rotation rate control before or during the launch.Changing current wave or the barrel parameters can achieved by electronic control or mechanical action.

According to the analysis,to maintain the flight stability of the projectile,the structure parameters of the barrel and the projectile are required to satisfy a proportional relationship.If the flight stability is satisfied at one muzzle velocity,the other muzzle velocity will meet the stability conditions too.Usingthe voltage of PPS and the deflection of the additional rails will easy to control the muzzle velocity and rotation rate.The experiment proves that the railgun designed in this paper can launch the projectile rotating and ensure the flight stability.Also proves that the rotational projectile may not cause the transition or produce much arcs.