Comparison of the recoil of conventional and...

141

Comparison of the recoil of conventional andelectromagnetic cannon

Edward M. SchmidtArmy Research Laboratory, Aberdeen ProvingGround, MD 21005-5066, USA

The recoil from an electromagnetic (EM) railgun is discussedand compared with that from conventional, propellant gasdriven cannon. It is shown that, under similar launch condi-tions, the recoil of the EM gun is less than that of the powdergun; however, use of a muzzle brake on a powder gun canalter this relative behavior.

1. Introduction

Electromagnetic launchers have experienced re-newed interest over the past ten to fifteen years. Theyhave the potential to deliver both hypervelocity and hy-perenergy launch while eliminating the potential haz-ards associated with gun propellants and reducing thesize of the cartridge. The two main classes of elec-tromagnetic launcher are the coil gun and the railgun.Within the latter, there are many configurations of railssuch as simple, augmented, transaugmented, contra-augmented, etc. For the present paper, only simplerailguns are considered, Fig. 1. These have two con-ducting rails separated by adjacent insulators that runthe complete length of the launcher. The projectile isaccelerated by the Lorentz Force developed from theinteraction of the magnetic field (generated by currentflowing up one rail and down the other) with the cur-rent passing through the armature. The Lorentz Forceis expressed as FL = qv × B. In the railgun, themagnitude of this force is FL = L′I2/2, where L′ isthe inductance gradient of the rails (typical values are0.35–0.55 µH/m) and I is the current in amperes. Thecurrent is provided by a suitable pulsed power system.This could be a capacitor bank, battery-inductor array,or a rotating machine such as an homopolar genera-tor or compulsator. Typically, L ′ is a constant and Ivaries with time depending upon the characteristics ofthe pulsed power system in use. Since there is current

flowing in the rails which are immersed in the magneticfield of their partner, a rail repulsion force is developedwhich must be resisted by the structure of the launcher.

2. Recoil

With a powder gun, the accelerative force is providedby the high pressure gases generated from the propel-lant combustion process. Clearly, the recoil force istransmitted at the breech by the propellant gas pressure.The time integral of this force is the recoil impulse andfor a powder gun is equal to the momentum impartedto both the projectile and the propellant gases as theyexit the muzzle.

In the case of EM, there is neither a breech nor pro-pellant gas. As such the recoil impulse is simply equalto the momentum imparted to the projectile at shot exit,It = mpVo, but where is the recoil force applied? Thefact that EM guns must recoil is obvious from first prin-ciples and has been measured by mountin g an EM gunin a ballistic pendulum [1]. Witalis [2] postulates thatthe recoil force is transferred in part at the rails them-selves. Marshall and Wood [3] counter that the rela-tivistic effects Witalis claims for rail recoil are simplyto small to account for the actual recoil levels. Theyplace the recoil forces at the buswork and power sup-ply. Clearly, the buswork connecting the power circuitto the gun experiences substantial loads as is evidencedby the frequent failure of these components in test. Itwould be of interest to conduct a careful experimentto define the location of the recoil force. It will be as-sumed in this paper that the position taken by Marshalland Wood is correct.

To make a comparison with the powder guns, theirrecoil impulse is estimated as the sum of the projectilemomentum and powder gas momentum efflux at theweapon muzzle [4]:

It = mpVo + mc(RTo)1/2(2/(γ + 1))3/2

(1)(1 + (γ + 1)mc/(12γmp)) [N · s]

Shock and Vibration 8 (2001) 141–145ISSN 1070-9622 / $8.00 2001, IOS Press. All rights reserved

142 E.M. Schmidt / Comparison of the recoil of conventional and electromagnetic cannon

C u rre n t A rm a tu re

P ro je c t ile

F o r c e

R a il R e p u ls io n F o rc e

C o n d u c tin g R a il

x x x x x x x x xM a g n F ie ld x xx x x x x x x x x

Fig. 1. EM railgun schematic.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.5 1 1.5

mc/mp

Vo (

m/s

x 1

0-3)

Fit: V = 3050( /[ + 3])1/2

= mc/m pµ

µ µ

Fig. 2. Velocity vs charge to mass ratio for a wide range of powder guns.

RTo = RTad − 0.26(1/6 + 4mp/7mc)V 2o

(2)[m2/s2]

where mp, mc are the projectile and charge masses;Vo is the projectile muzzle velocity; R, γ are the gasconstant and ratio of specific heat; and Tad, To adiabaticflame and average gas temperatures at shot exit. As asimple means to develop the trend in the impulse withvelocity, a fit [5] to the correlation presented in Fig. 2is used.

Using the fit above, Eqs (1) and (2) are rearranged to

It/mp = 3050(µ/[µ + 3])1/2 + µ(RTo)1/2

(2/(γ + 1))3/2(1 + (γ + 1) (3)

µ/(12γ)) [m/s]

RTo = RTad − 2.4 × 106(1/6 + 4/7µ)(4)

(µ/[µ + 3]) [m2/s2]

A sample calculation is made on a 20 mm cannonusing WC870 propellant. For this case, γ = 1.25, R =365.5 m2/s2K, and Tad = 2577 K. The variation inthe impulse ratio for a powder gun is computed andcompared to that for an EM gun, It/mp = Vo, in Fig. 3.This ratio could be considered the impulse imparted infiring a constant launch mass. It can be seen that therecoil impulse of the powder and EM are quite similarat low velocities; however, beyond 1800 m/s the recoilimpulse ratio for the powder gun begins to increasedramatically as the propelling charge mass grows.

Often, comparisons are made by assuming that thegun muzzle energy is constant across the range oflaunch velocities, Fig. 4. The EM gun behavior simplyreflects the fact that the recoil momentum varies as theenergy divided by the velocity. For the powder gun,the recoil impulse is similar to that of the EM gun until1800 m/s where it begins to climb. However, for theconstant energy case, the increase is less dramatic than

E.M. Schmidt / Comparison of the recoil of conventional and electromagnetic cannon 143

0

2000

4000

6000

8000

10000

0 500 1000 1500 2000 2500

Vo (m/s)

I t/m

p (m

/s)

Powder Gun

EM Gun

Fig. 3. Impulse ratio vs velocity.

I t (N

-s)

Fig. 4. Constant energy case energy case.

in Fig. 3. For powder guns, there is the potential todecrease the recoil impulse through the use of a muzzlebrake.

3. Muzzle brakes

Muzzle brakes deflect the exhausting propellantgases laterally thereby recovering axial momentum.The M109 brake, Fig. 5, is a high efficiency device em-ployed on a 155 mm self-propelled howitzer. Baur andSchmidt [6] measured the recoil attenuation of 20 mmscale models of M109 and M198 brakes, Fig. 6. Thebrake momentum efficiency factor is defined

β = (Iwo − Iw)/(Iwo − mpVo) (5)

The numerator is simply the difference in total re-coil impulse with and without the brake in place andthe denominator is the total momentum available in the

Fig. 5. M109 muzzle brake.

propellant gases. This ratio can exceed 100% sincethe gases may be both turned rearward and further ex-panded. The behavior of β in Fig. 6 reflects this. Forthe 20 mm cannon as the launch velocity increases, themuzzle pressure also increases. The dimensions of thepropellant gas exhaust plume grow with muzzle pres-sure. The M198 brake is only 1.6 calibers in radius

144 E.M. Schmidt / Comparison of the recoil of conventional and electromagnetic cannon

βM109 Brake

M198 Brake

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

400 600 800 1000 1200

Vo (m/s)

Fig. 6. Muzzle brake efficiencies.

-100

0

100

200

300

400

500

500 1000 1500 2000 2500

Vo (m/s)

I t (N

-s) Powder Gun

EM Gun

Powder Gunwith Brake

Fig. 7. Constant muzzle energy case with muzzle brake.

and is swept away from the muzzle; thus, its outer edgeallows gases to escape as the plume grows. However,the M109 brake has a radius of 2.0 calibers and is swepttoward the muzzle. This baffle captures more of theplume as pressure increases and the brake efficiencygrows. Eventually, the supersonic core of the plumeshould fully envelop both brake surfaces and variationwith velocity (pressure) should level out. These datamay be used to estimate the impulse imparted to thecannon.

By fitting the M109 data in Fig. 6 and extrapolatingto velocities up to 2500 m/s, the impulse of a powdergun with a high efficiency brake may be comparedto the impulse of an EM gun over a similar range,Fig. 7. Since the efficiency of the M109 brake is greaterthan one, the total impulse imparted to the powdergun with the brake installed is lower than the impulse

imparted to the EM gun, i.e., the momentum impartedto the projectile. There are drawbacks to employing amuzzle brake. The M109 brake is quite massive andaffects the gun dynamics and the design of the elevatingand traversing mechanisms. Also, the employmentof a muzzle brake greatly increases the muzzle blastoverpressure behind the weapon. This may not bea problem with a vehicle having a closed hatch, butinfantry moving with an armored fighting vehicle couldbe injured.

4. Conclusions

The recoil characteristics of an electromagnetic rail-gun are considered and compared with those of a pow-der gun. The EM gun is shown to have less recoil

E.M. Schmidt / Comparison of the recoil of conventional and electromagnetic cannon 145

impulse than does a powder gun, particularly at highvelocities. However, the installation of a muzzle brakecan alter this comparison to the point where the re-coil imparted to a powder gun equipped with a highefficiency brake is lower than that of an EM gun.

References

[1] A. Zielinski, private communication of results presented at the11th EM Launcher Association Meeting, Sep. 1998, pp. 93.

[2] E. Witalis, Origin, Location, Magnitude, and Consequencesof Recoil in Plasma Armature Railgun, IEEE Proc. A 142(3)(1995).

[3] R. Marshall and L. Woods, private communication of draftpaper responding to Witalis, 1996.

[4] C. Lang, Muzzle Devices, AMCP 706-251, AMC, Alexandria,VA, May, pp. 68.

[5] E. Schmidt, A Ballistic Evaluation of Electromagnetic Launchand Flight, Proceedings of 17th Int’l Symposium on Ballistics,NDIA, Arlington, VA, May, pp. 98.

[6] E. Baur and E. Schmidt, Relationship between Efficiency andBlast from Gas Dynamic Recoil Brakes, AIAA Paper 85-1718,July, pp. 85.

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