Recoil in Electromagnetic Railguns

RECOIL IN ELECTROMAGNETIC RAILGUNS

By: W. F. Weldon M. D. Driga H. H. Woodson

Third Symposium on Electromagnetic Launch Technology, Austin, TX, April 20-24, 1986.

IEEE Transactions on Magnetics, vol. 22, no. 6, November 1986, pp. 1808-1811

PR- 52

Center for Electromechanics The University of Texas at Austin PRC, Mail Code R7000 Austin, TX 78712 (512) 471-4496

©1986 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. ©1986 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. 1808 IEEE TRANSACTIONS ON MAGNETICS, VOL MAG-22, NO. 6, NOVEMBER 1986

RECOIL IN ELECTROMAGNETIC RAILGUNS

Wm. F. Weldon, M. D. Driga, and H. H. Woodson

Abstract - Gun designers have longaccepted and Perhaps thesimplest i1 lustration of the forces at work in arailaun is the understoodthe fact that guns experiencerecoil when I response of a flexible fired, and many ingenious mechanisms have been devised cablecarrying a large current (Fig. 2). When the to cope with the problem.But hope springseternal, current is passedthrough the cable, the cable expands and when confronted with a revolutionary new technique toinclude the largest area possible, typically a cir- for accelerating projectiles, where theaccelerating cle if nototherwise constrained. It canbe enviy mechanism may be somewhat mysterious,the gun designer sioned that since the current flowing in the cable hopefully asks, "Does it recoil?"; knowing in his produces a uniform amount of flux per unit length of heartthat it does. The more difficultquestion with cable,the flux density is somewhat higherinside the regardto the electromagnetic (EM) railgun is "Where circle than outside due simply to the curvature of the and how dothese recoil forces appear and can their cable.Furthermore, application of the familiar location and distribution be controlled?"That is the "right hand rule" will show that the flux contribu- topic of this paper. tions for various sections are additive (in the same direction) inside the circle and subtractive outside BACKGROUND thecircle. Both of these factors result in a higher magnetic flux density inside the circle than outside, When a thermodynamicgun is fired, the recoil is and anet "magnetic pressure" causing the cable to caused primarily by the pressure of the combustion expand into a circle. productsagainst the breech closure (Fig. 1). Whereas the lateral forces due to gas pressureare reacted against each otherby the "hoop strength" of the gun barrel,the gas pressureacting against the breech block is uncompensated (except by friction between the projectile and bore) andpushes the gun barrel back- wardas theprojectile is accelerated forward. An additionalsource of recoil is therocket-like action of the combustionproducts leaving the muzzle after theprojectile exits. Overall, of course, the pre- vailingrequirement is theconservation of momentum. Because the system started initially (prior to firing) withzero net momentum (both gun and projectile at rest) the net momentum of the system must remainzero. This means of course that

so that as the projectile acquires forward momentum throughthe action of gas pressure on its base, the gun acquires momentum in the opposite direction throughthe action of gas pressure on thebreech plug. Fig. 2. Response of a flexiblecable We shall see that an analogous situation occurs with to a large current. therailgun. More rigorously,the force is equal tothe deriva- tive of the magnetic coenergy with respect to general- ized coordinate x

The force, acting locally oneach element ofthe flexible cable, is in adirection to increase, by local contributions,the inductance of the loop, thereby, Fig. 1. Recoil in aconventional gun. expanding it into a circle.

The localforces will be higherat the points and alongthe directions where theinductance gradient is higher:

-F = -I12 grad L = -I12 VL. Manuscriptreceived March 17, 1986. 2 2 The authorsare with the Center for Electromechanics at The University of Texas atAustin, Austin, TX 78758-4497.

0018-9464/86/1100-1808$01.00@1986 IEEE ©1986 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. 1809

The integral of a gradientover any closedcurve @ 0 is zero.This shows that Newton's third law is r--7- respected in a global sense.

SIMPLE RAILGUNS

These same relationships can be more specifically appliedto the railgun as shown inFig. 3. Of course the force on any part of the railgun circuit is simply thevector product of the current in that part and the magnetic flux density at that point; commonly called theLorentz force. To theextent that the railgun is J 0 symmetricalalong the center line (Fig. 3), theforces a b a tending to sepa#ratethe rails are symmetrical also and may be convenientlyreacted against each other in the containmentstructure. This leaves the Lorentz force Fig, 4. Recoilforces in a more complex railgun. on thearmature to be reacted upon the portion of,the circuit which"closes the breech," in this case the power supply! Inthe simple railgun shown in Fig. 3 the recoil situation is analogous to that for the con- ' ventional gun inFig. 1, therecoil force is applied tothe circuit conductor at the breechclosure. Of course few railguns are laid out as simply as that in Fig. 3, the power supplyoften comprising several com- ponentsinstead of the simplified ideal current source shown.

Fig. 5. Anotherapproach tothe recoil problem.

In this instance of what we shall call the side- fed rails it is a bit more difficult to trace the recoilforce. It is doublyimportant to do in this case,however, because ofthe consequences. If the Fig. 3. Simplifiedrailgun, schematic. magnetic field around the breech of the railgun in Fig. 5 is plotted (as inFig. 6) thenthe recoil force can be characterized. More importantlythe side load MORE COMPLEX CONFIGURATIONS on the projectile resulting from this geometry becomes apparent.Figure 7 shows thedirection of the Lorentz The admonitionthat "the recoil forces appear upon force on thearmature and the resultant recoil force the power supply," if takentoo literally, may lead on the railgun for three positions of the armature. one astray.Applied for example tothe somewhat more In Fig. 7a, the bus fromthe power supplyacts asa realistic railgun circuit in Fig. 4a, the gun designer railgun and no forwardforce is applied to the arma- mightjoyously conclude that the recoil force would be ture'atall. It is simplyforced against,the insulat- directed downward! Alas, we must applythe lesson of ingsidewall of the railgun. Even withthe armature Fig. 3 in more detailto determine the true nature of forwardof the power supply bus (Fig. 7b) a signifi- therecoil forces for the railgun in Fig. 4. In a cant fraction of the Lorentz force is applied against simplified sense the parallel sections of the gun thesidewall. As the.armaturetravels down therai- itself (1 and 2) canbe reactedagainst each other as lgun(Fig. 7c) the Lorentz force vector rotates to before, ascan theparallel sections of the'power sup- become more nearly aligned with the railgun. ply bus (3 and 4). Using this same logicthe power Obviously this casemust be avoided since the possi- supply (5) can be reactedstructurally against section bility of locking the projectile in the breechsection (6) ofthe buswork. This means thatthe accelerating ofthe barrel exists. At thevery least, substantial force on thearmature (7) must reactagainst section 8 damage tothe sidewall insulator will result. The ofthe busworkwhich "closes the breech," at least in problem of the side-fed railgun can be solvedby feed- the electromagnetic sense. ing it symmetricallyfrom both sides (Fig. 8) in this case thetransverse components of the Lorentz force Unfortunately this situation has led more than will cancelleaving only the longitudinal component to one novice railgunner to consider the configuration act on theprojectile. Greatcare must be taken how- shown in Fig. 5 in an effort to redirect the recoil ever toinsure equalcurrent distribution in both legs force. By making thebreech transition from the edge of the power supply bus. of the rails rather than the ends, thebreech closure is avoided.While this is certainly an advantage for attaching an autoloader, what happens to the recoil forcein this case?Perhaps it is eliminated?

Fig. 8. Symmetricallyside-fed railgun.

\4 i fF Fig. 6. Magnetic flux distribution for sid-fed railgun.

Fig. 9. Currentpath inrail-to-armature transition.

ends of the rail, a tensile load is applied to the b rail and it is importantfor the gun designer torec- ognize this.

Havingestablished that electromagnetic railguns do indeedexperience recoil forces in much the same way as conventional guns; we will offer one interesting possibility of what mightbe done in the way of recoil management that is not practical with conventional guns. Railguns poweredby pulsedrotating machinery(homopolar generators (HPGs) or compulsators) must dealwith the substantial discharge torque of the rotating machine as well as the recoil of the gun. Of coursethe net discharge torque canbe reduced to zero by the use of counter rotating genera- torrotors, but for the compulsators [l] atleast an interesting possibility exists for the single rotor Fig, 7. Armature and recoilforces in a machine. Unlikethe HPG which must charge an interme- side-fedrailgun. diateinductive store, the discharge torque profile of thecompulsator canbe made to exactly match the recoil force profile of therailgun during the launch OTHER CONSIDERATIONS time.This suggests the interesting configuration shown in Fig. 10. If therailgun is solidly mounted We have nowcome to see that regardless of to the compulsator stator; the railgun recoil can be geometry, therailgun recoil force appearswherever the reactedagainst the compulsator discharge torque. breechof the railgun is "closed" in the electromag- Unfortunatelythis does not result in a cancellation netic sense. As neexamine theproblem in more detail ofthe forces, but does result in the recoil of the a few otherinteresting aspects present themselves. railgunappearing as a lateral force at the base of Forexample, if we examine thecurrent path from the thecompulsator. Dissipative losses in the system may railgun rail into the armature(Fig. 9) or power bus preventthe compensation from being perfect, but the we find that there is some transverse component of technique does offer the promise of substantially current in the rail itself and thereforea longitudi- reducingthe overturning moment of a high performance nal component of force applied to the rail conductor compulsator-driven railgun mounted on a vehicle. atthis point. Since this phenomenon occursat both

RAILGUN RECOIL p RAILGUN

COMPULSATOR REACTlCNTDRWE

COMPULSATOR

COMPULSATOR REACTIONTORQUE

uFig. 10. Compulsator drivenrailgun recoilconsiderations.

CONCLUSION

Recoil forces in EM railguns appearwherever the breech of the railgun is closed electromagnetically. This means recoil forces may appearon power supply leads, switches, or power supply componentsthem- selves. Carefulattention is required on thepart of the railgun designer to control the location of the recoil loading and provide means for sustaining the loads.Careless design can result in undesirable forces being applied to the projectile armature as well. On theother hand a thoroughunderstanding of whereand how recoil forces are generated can be used to good advantage in some EM gun systems. In closing we offer aspiring railgun designers one bit of advice originally offered to HPG machine designers by Hr. B. 0. Lamme in 1906, "You can'tfool the flux."

REFERENCES

[l] M. L. Spann, et al., "Rapid Fire, Compulsator-Driven Railgun System," presented at The 3rd Symposiumon Electromagnetic Launch Technology, April 20-24, 1986, Austin, TX.