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
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1808
IEEE TRANSACTIONS ON MAGNETICS, VOL MAG-22, NO. 6, NOVEMBER 1986
RECOIL I N ELECTROMAGNETIC RAILGUNS
Wm. F. Weldon, M. D. Driga, and H. H.
Abstract - Gun designers have longaccepted and
u n d e r s t o o dt h ef a c tt h a t
guns e x p e r i e n c e r e c o i l when
f i r e d , and many ingenious mechanisms have been devised
hope s p r i n g se t e r n a l ,
t o cope with t h e problem.But
and when c o n f r o n t e d w i t h a r e v o l u t i o n a r y
new technique
foracceleratingprojectiles,
where t h e a c c e l e r a t i n g
mechanism may be somewhat mysterious,the gun designer
h o p e f u l l y asks, "Does it r e c o i l ? " ; knowing i n h i s
h e a r tt h a t it does. The more d i f f i c u l t q u e s t i o n w i t h
r e g a r dt ot h ee l e c t r o m a g n e t i c
(EM) r a i l g u n i s "Where
and how dothese r e c o i l f o r c e s appear and can t h e i r
l o c a t i o n and d i s t r i b u t i o n be controlled?"That
i s the
t o p i c o f t h i s paper.
BACKGROUND
When a thermodynamicgun
is fired, the recoil is
caused p r i m a r i l y b y t h e p r e s s u r e o f t h e c o m b u s t i o n
1 ) . Whereas
productsagainstthebreechclosure(Fig.
thelateralforces
due t o gas pressurearereacted
against each other by the
"hoop s t r e n g t h " o f t h e
gun
b a r r e l , t h e gas pressureactingagainstthebreech
b l o c k i s uncompensated (except by f r i c t i o n between t h e
p r o j e c t i l e and bore) andpushes t h e gun b a r r e l backwardas t h ep r o j e c t i l ei sa c c e l e r a t e df o r w a r d .
An
i s t h er o c k e t - l i k ea c t i o n
a d d i t i o n a ls o u r c eo fr e c o i l
o f t h e combustionproductsleavingthemuzzleafter
t h ep r o j e c t i l ee x i t s .O v e r a l l ,o fc o u r s e ,t h ep r e momentum.
v a i l i n gr e q u i r e m e n t i s t h ec o n s e r v a t i o no f
Because t h e system s t a r t e d i n i t i a l l y ( p r i o r t o f i r i n g )
w i t hz e r on e t
momentum (both gun and p r o j e c t i l e a t
r e s t ) t h e n e t momentum o f t h e system must remainzero.
T h i s means o f c o u r s e t h a t
so t h a t as t h e p r o j e c t i l e a c q u i r e s f o r w a r d
momentum
throughtheactionof
gas pressure on i t s base, t h e
gun acquires momentum i n t h e o p p o s i t e d i r e c t i o n
throughtheactionof
gas pressure on thebreechplug.
We s h a l l see t h a t an analogous s i t u a t i o n o c c u r s w i t h
therailgun.
F i g . 1.
Recoil i n aconventional
gun.
Woodson
Perhaps thesimplest i1l u s t r a t i o n o f t h e f o r c e s
a t work i n a r a i l a u n i s the response o f a f l e x i b l e
c a b l ec a r r y i n gal a r g ec u r r e n t( F i g .
2).
When t h e
c u r r e n t i s passedthroughthecable,thecable
expands
toincludethelargestareapossible,typicallyacirI
t canbeenviy
c l e i f nototherwiseconstrained.
sionedthatsincethecurrentflowinginthecable
produces a uniform amount o f f l u x per u n i t l e n g t h o f
c a b l e ,t h ef l u xd e n s i t y
i s somewhat higherinsidethe
c i r c l e t h a n o u t s i d e due s i m p l y t o t h e c u r v a t u r e o f t h e
c a b l e .F u r t h e r m o r e ,a p p l i c a t i o no ft h ef a m i l i a r
" r i g h t hand r u l e " w i l l show t h a t t h e f l u x c o n t r i b u tionsforvarioussectionsareadditive(inthe
same
direction) inside the circle
and s u b t r a c t i v e o u t s i d e
t h ec i r c l e .B o t ho ft h e s ef a c t o r sr e s u l ti nah i g h e r
magnetic f l u x d e n s i t y i n s i d e t h e c i r c l e t h a n o u t s i d e ,
and anet"magneticpressure"causingthecable
to
expand i n t o a c i r c l e .
I
Fig. 2 .
Response o f a f l e x i b l ec a b l e
t o alargecurrent.
i s equal t o t h e d e r i v a More r i g o r o u s l y , t h e f o r c e
with r e s p e c t t o g e n e r a l tive of the magnetic coenergy
ized coordinate x
The f o r c e , a c t i n g l o c a l l y
oneach element o f t h e
flexiblecable,isin
ad i r e c t i o nt oi n c r e a s e ,b yl o c a l
contributions,theinductanceoftheloop,thereby,
expanding it i n t o a c i r c l e .
The l o c a l f o r c e s will be h i g h e r a t t h e p o i n t s
alongthedirections
where the inductance gradient
higher:
Manuscriptreceived March 17, 1986.
The authors are with the Center for Electromechanics
a t The U n i v e r s i t y of Texas a t A u s t i n , A u s t i n ,
TX
78758-4497.
0018-9464/86/1100-1808$01.00@1986 IEEE
F = 1 I
2 grad L = -I
1 2VL.
2
2
and
is
©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 i n t e g r a l o f a gradient over any closedcurve
i s zero.This
shows t h a t Newton's t h i r d law i s
respected i n a g l o b a l sense.
@
0
r
7
-
SIMPLE RAILGUNS
'
These same r e l a t i o n s h i p s can be more s p e c i f i c a l l y
a p p l i e dt ot h er a i l g u n
as shown i n F i g . 3 . O f course
t h e f o r c e on any p a r t o f t h e r a i l g u n c i r c u i t i s s i m p l y
t h ev e c t o rp r o d u c to ft h ec u r r e n ti nt h a tp a r t
and t h e
magnetic f l u x d e n s i t y a t t h a t p o i n t ;
commonly c a l l e d
theLorentzforce.
To t h e e x t e n t t h a t t h e r a i l g u n i s
3 ) , theforces
symmetricalalongthecenterline(Fig.
b
t e n d i n g t o sepa#ratethe r a i l s a r e s y m m e t r i c a l a l s o
and
may be conveniently reacted against
each o t h e r i n t h e
containmentstructure.ThisleavestheLorentzforce
on thearmature t o be reacted upon t h e p o r t i o n o f , t h e
c i r c u i t which"closesthebreech,"
i n t h i s case t h e
power supply!
I nt h es i m p l er a i l g u n
shown i n Fig. 3
the recoil situation is
analogous t o t h a t f o r t h e
conv e n t i o n a l gun i nF i g .
1, t h er e c o ifl o r c ei sa p p l i e d
Of
t ot h ec i r c u i tc o n d u c t o ra tt h e
breechclosure.
course few r a i l g u n s a r e l a i d o u t
as simply as t h a t i n
comFig. 3, t h e power supply often comprising several
ponentsinsteadofthesimplifiedidealcurrentsource
shown.
Fig. 3.
S i m p l i f i e dr a i l g u n ,
schematic.
MORE COMPLEX CONFIGURATIONS
The a d m o n i t i o n t h a t " t h e r e c o i l f o r c e s
appear upon
may lead
the power supply," i f t a k e n t o o l i t e r a l l y ,
one a s t r a y .A p p l i e df o r
example t o t h e somewhat more
realistic railgun circuit in Fig.
4a, t h e gun designer
might joyously conclude that the recoil force
would be
d i r e c t e d downward! Alas, we must applythelessonof
Fig. 3 i n more d e t a i l t o d e t e r m i n e t h e t r u e n a t u r e o f
t h er e c o i lf o r c e sf o rt h er a i l g u ni nF i g .
4. I n a
s i m p l i f i e d sense t h e p a r a l l e l s e c t i o n s o f t h e
gun
i t s e l f (1 and 2 ) canbe reacted against each other as
before, ascan t h e p a r a l l e l s e c t i o n s o f t h e ' p o w e r
supUsing t h i s same l o g i ct h e power
p l y bus (3 and 4 ) .
supply ( 5 ) can be r e a c t e d s t r u c t u r a l l y a g a i n s t s e c t i o n
( 6 ) o ft h e buswork. This means t h a tt h ea c c e l e r a t i n g
8
f o r c e on thearmature ( 7 ) must react against section
o f t h e busworkwhich"closesthebreech,"
at least in
the electromagnetic sense.
Unfortunatelythissituation
has l e d more than
one n o v i c e r a i l g u n n e r t o c o n s i d e r t h e c o n f i g u r a t i o n
shown i n F i g . 5 i n an e f f o r t t o r e d i r e c t t h e r e c o i l
force. By making t h eb r e e c ht r a n s i t i o nf r o mt h e
edge
oftherailsratherthanthe
ends, thebreechclosure
i s avoided.While
t h i s i s c e r t a i n l y an advantage f o r
a t t a c h i n g an autoloader, what happens t o t h e r e c o i l
it i s eliminated?
f o r c ei nt h i s
case?Perhaps
J
0
a
Fig, 4 .
Recoilforces
Fig. 5.
Anotherapproach
i n a more complex r a i l g u n .
t ot h er e c o i l
problem.
I n t h i s i n s t a n c e o f what we s h a l l c a l l t h e s i d e f e d r a i l s it i s a b i t more d i f f i c u l t t o t r a c e t h e
I
t i s doublyimportantto
do i n t h i s
r e c o i lf o r c e .
case,however,because
o ft h e consequences. I f t h e
magnetic f i e l d around t h e b r e e c h o f t h e r a i l g u n i n
Fig. 5 i s p l o t t e d (as i n F i g . 6 ) t h e nt h er e c o i lf o r c e
can be characterized.
More i m p o r t a n t l yt h es i d el o a d
on t h e p r o j e c t i l e r e s u l t i n g from t h i s geometry becomes
7 shows t h ed i r e c t i o no ft h eL o r e n t z
apparent.Figure
f o r c e on thearmature and t h e r e s u l t a n t r e c o i l f o r c e
on t h e r a i l g u n f o r t h r e e p o s i t i o n s o f t h e
armature.
I n F i g . 7a, t h e bus from the power supply acts asa
r a i l g u n and no forward force i s a p p l i e d t o t h e armaIt i s s i m p l yf o r c e da g a i n s t , t h ei n s u l a t t u r e ' a ta l l .
i n gs i d e w a l lo ft h er a i l g u n .
Even withthearmature
forwardofthe
power supply bus ( F i g . 7b) a s i g n i f i cant fraction of the Lorentz force is applied against
As the.armaturetravels down t h e r a i t h es i d e w a l l .
l g u n( F i g .7 c )t h eL o r e n t zf o r c ev e c t o rr o t a t e st o
become more n e a r l y a l i g n e d w i t h t h e r a i l g u n .
Obviously t h i s casemustbe
avoided since the possibility of locking the projectile in the
breech section
A t t h ev e r yl e a s t ,s u b s t a n t i a l
o ft h eb a r r e le x i s t s .
will r e s u l t . The
damage t ot h es i d e w a l li n s u l a t o r
problem o f t h e s i d e - f e d r a i l g u n c a n
be solvedbyfeed8 ) in this
i n g it symmetricallyfrombothsides(Fig.
case the transverse components o f t h e L o r e n t z f o r c e
w
i
l cancelleavingonlythelongitudinal
component t o
a c t on t h e p r o j e c t i l e .
Greatcare must be taken however t o i n s u r e e q u a l c u r r e n t d i s t r i b u t i o n i n b o t h l e g s
o f t h e power supply bus.
©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.
1810
Fig. 8 .
i
\4
Fig. 6 .
Symmetricallyside-fedrailgun.
Magnetic f l u x d i s t r i b u t i o n f o r
sid-fedrailgun.
f F
a
Fig. 9.
i nr a i l - t o - a r m a t u r e
ends o f t h e r a i l , a t e n s i l e l o a d i s a p p l i e d t o t h e
gun designer t o r e c r a i l and it i s i m p o r t a n t f o r t h e
ognize this.
b
Fig, 7 .
Currentpath
transition.
Armature and r e c o i lf o r c e s
s i d e - f e dr a i l g u n .
in a
OTHER CONSIDERATIONS
We have nowcome
t o see t h a t r e g a r d l e s s o f
geometry, t h e r a i l g u n r e c o i l f o r c e
appearswherever
the
breechoftherailgunis"closed"intheelectromagn e t i c sense. As neexamine theproblem i n more d e t a i l
a few other interesting aspects present themselves.
Forexample, i f we examine the current path from the
9 ) o r power bus
railgunrailintothe
armature(Fig.
we f i n d t h a t t h e r e i s
some transverse component of
current in the rail itself
and t h e r e f o r eal o n g i t u d i n a l component o f f o r c e a p p l i e d t o t h e r a i l c o n d u c t o r
a tt h i sp o i n t .S i n c et h i s
phenomenon occursatboth
Having established that electromagnetic railguns
do indeedexperience r e c o i l f o r c e s i n much the same
i
l o f f e r one i n t e r e s t way as conventional guns; we w
i n g p o s s i b i l i t y o f what mightbe done i n t h e way o f
r e c o i l management t h a t i s n o t p r a c t i c a l w i t h
convent i o n a l guns. Railguns poweredby p u l s e dr o t a t i n g
machinery(homopolargenerators
(HPGs) o r comp u l s a t o r s ) must dealwiththesubstantialdischarge
torque o f t h e r o t a t i n g machine as w e l l as t h e r e c o i l
o f the gun. O f coursethenetdischargetorque
canbe
reduced t o zero by t h e use o f c o u n t e r r o t a t i n g genera[l] a t l e a s t an
t o rr o t o r s ,b u tf o rt h ec o m p u l s a t o r s
interesting possibility exists for the single rotor
machine. U n l i k et h e HPG which must charge an intermediateinductivestore,thedischargetorqueprofileof
the compulsator canbe made t o e x a c t l y match the
r e c o i l f o r c e p r o f i l e o f t h er a i l g u nd u r i n gt h el a u n c h
t i m e .T h i ss u g g e s t st h ei n t e r e s t i n gc o n f i g u r a t i o n
mounted
shown i n Fig. 10. I f t h e r a i l g u n i s s o l i d l y
tothecompulsatorstator;therailgunrecoil
can be
reacted against the compulsator discharge torque.
U n f o r t u n a t e l y t h i s does n o t r e s u l t i n a c a n c e l l a t i o n
oftheforces,but
does r e s u l t i n t h e r e c o i l o f t h e
base o f
railgun appearing as a l a t e r a l f o r c e a t t h e
thecompulsator.Dissipativelosses
i n the system may
preventthecompensationfrombeingperfect,butthe
technique does o f f e r t h e p r o m i s e o f s u b s t a n t i a l l y
reducing the overturning
moment o f a h i g h performance
compulsator-driven railgun mounted on a vehicle.
©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.
1811
RAILGUN
RECOIL
p RAILGUN
u
COMPULSATOR
REACTlCNTDRWE
COMPULSATOR
COMPULSATOR
REACTIONTORQUE
Fig. 10.
Compulsator drivenrailgun
recoilconsiderations.
CONCLUSION
Recoil forces i n EM railguns appearwherever the
breech of the railgun
i s closed electromagnetically.
This means recoil forces may appearon power supply
leads, switches, or power supply componentsthemselves. Carefulattention i s required on thepartof
the railgun designer to control the location of the
recoil loading and provide means for sustaining the
loads.Careless
design can r e s u l t i n undesirable
forces being applied t o t h e p r o j e c t i l e armature as
well. On theother hand a thoroughunderstanding o f
whereand how recoil forces are
generated can be used
t o good advantage i n some EM gun systems. I n closing
we o f f e r a s p i r i n g r a i l g u n designers one b i t o f advice
o r i g i n a l l y o f f e r e d t o HPG machine designers by Hr. B.
0. Lamme i n 1906, "You can'tfooltheflux."
REFERENCES
[ l ] M. L. Spann, e t al.,
"Rapid Fire,
Compulsator-Driven Railgun System," presented a t
The 3rd Symposiumon Electromagnetic Launch
Technology, A p r i l 20-24, 1986, Austin, TX.