A method of obtaining the relationship between various parameters governing the ricochet phenomenon of a projectile has been described. The experimental procedures for determining such parameters and their use have also been discussed

Battacharyya, A. R.

Kohli, S. L.

Venkatesan, N. S.

English

Defence Science Journal

A NOTE OR THE DETERMINATION OF WZCOGHET TRACE OF SMALLA RMS AMMUNITION Terminal Ballistic8 Research Laboratory, Chandigarh {Received 1 December 1973 ; revised 1 1  August 1976) . A method of obtaining the relationship between various parameters governing the ricochet phenomenon of a pro- jectile has been described. The experimental procedures for determining such parameters and their use have also been discussed. The problem of ricochet of any projectile when it fails to hit the target or ifter its impact on the target, is of great importawe for the services as well as for the police personnel. The ricochet process is of cons- tant concern for the Airforce authorities also during air to ground attack, due to the chances of hit to own a h a &  from own fire. Whenever any bullet hits the pound short of target, it may deflect considerably from its original path due to high energy it possesses. The ricochetted projectile may travel in a direction quite different f om its original one and up to  a distance which depends on a number of factors related to the ammunition, nature of ground, angle of impact and initial velocity of bullet etc. Though some classi- fied literature is availahle for calculatillg the ricochet distance and ricochet heiqht in the case of APDS pro- jectiles, nothing of this sort is available to predict the same for small arms ball ammunition, where the pro- jectile undergoes deformation on impact. d The ohject cfthis paper i 3  to high light the basic parameters governing the ricochet process of small arms ball ammunition, their relationship with the initial condition of fire. The basic parameters which play vital role during ricochet have been given in Fig. 1 which is self explanatory. The set up used for determining these parameters is shown in Fig. 2.- Post ricochet angle (0) = tan-1 - 3'2 - y, { ( X ,  - XJ2  + (2, - 2A2 )lj2 (1) x2 - XI Azimuthal deflection angle (a) = tanw1 -  Z, -- Z, (2, height of the rifle Muzzle Angle of incidence ( i) = tan-1 Distance between point of impact and Muzzle (3) Angle of total deflection (43, =; cos-14,sin e sin. i + cos 0 cios i cos u) (4) X-axis is horizontal, perpendicul~r to the line of fire, Y-axis is vertical and Z-axis is horizontal, ~arallel  to t$e line of fire. (XI, Y1, 2,) and (X2, Y,, 2,) are cowdinates of the points of impact of the bullet on ground and on recording panel. Tlje ricochet process mainly depends on the pre-ricochet qonditions viz. angle of impact, pre-ri- cochet velocity and nature of ground while the post ricochet oonditions mainly depend on the post-ricoche$ ANGLE OF ce, PROJECTILE IN FLIGHT (AFTER RICOCHET ) - RICOCHET (BEFORE RICOCHET ) (RECORDING PANEL (3 rn m THICK) IIEN(TH Fig. I-Geometrical derivation of the values of, total Fig. 2-Experimental . set-up for 'determining different deflection (8)  post ricochet angle (e) and azimuthal ricochet parameters. deflection (a). 6' angle of departure e, loss of velocity on impact, the extent of deformation of the bullet and the angle of deflection from the line of fire. In order to determine the extent of loss in velocity on impact, it is observed that a relationship of the form . (V/ZC) = 1 - K$ (5) where u, v are pre and post ricochet velocities respectively, gives a good fit. /3 r<epresents the angle of total deflection, which, from definition, includes in it all ricochet parameters. R a m  practical trials it has been seen that the value of the constant K is related to the nature of ammunition and ground. The case of 'No Ricochet' is explained in two ways, (i) either through complete dispersal of energy or (ii) through non-emergence from the ground. The former case would occur, as indicated from (5), when /3 = 1 The case of non-emergence will depend only on the angle af iwqact. It has been ~bserved that ricochet occurs upto a certain critical a*ngle of impact after which the shot penetrates; nto the ground. This prompts one to relate the angle of the incidence i with angle of total deflection as itself signifies post ricochet events. The observed values of /? corresponding to different values of i were fitted to obtain aparabola of the form ,B = a, i + b, i2 (6) by the method of least square. As pointed.out earlier, the ricochet phenomenon in the-case of ;ma11 arm ammunition differs from that of APDS shots etc, in the sense that in the former case the projedtile deforms. Compared to the range usually achieved by small arm ammunitions this factor cannot be ignored. Due to tbis, the change in ballistic coefficient of the projectile cannot be neglected . In the case of ammunition; of kigher calibre (longer range) the ballistic coefficient can be a~surned to be constant. The ballistic oo-efficient of the deformed shot alongwitheother parameters can be determined either from the field trials or inaclosed range by measuring the post ricochet velocities at two different points and using the space functions. The correlation between post ricochet conditions and variation of ballistic coefficient was analysed and it was seen that there exists a close relationship of the form (70 = a, + b2 B + C2 B2 (7) The value of the constants were obtained by employing the method of least square. Thus when all the parameters relating to the pre and post ricochet conditions are determined with the , help of above relationships, i t  is possible to draw a ricochet trace as explained below. D R A W I N G  O F  R I C O C H E T  . T R A C E  - From any impact conditions i.e. for certain i and zc we know /3 from (6). For any arbitrary values of a and /3 (/3 > a) from (4), the value of v is obtained from (5) and value of post ricochet angle of depar- ture (e)  is determined from & e =  - sin i 00s /3 zk &os2 i oos2 a (sin2 j? - cos2 i sin2 a) (1 - cos2 i sin2 a) (8) since, e < 4 2 ,  only + sign of square root need be taken, the Ballistics Coefficient is determined from (7). Knowing all tbese, the ricochet range isdetermined. The terminal conditions at the end of first ricochet will serve as the initial conditions for the second ricochet. This process will continue tillthe ricochet ceases either due to loss of energy or due to the penetra- tion of the bullet. The extreme ranges achieved by the bullet for different values of a may then joined to get the ricochet trace. D I S C U S S I O N  As pointed out earlier it is seen from (6) that extrem; value of B occurs when i = - a,/2 b, (9) since /3 = 0 for i = 0, it is obvious that extreme value is maximum. Further from (6) it is obvious that ricochet will cease due to non-emergence from ground for a value of i =(al - l)/bl (10) The value of i given by (9) is greater than the value of i given by equation (10) if a,> 2 which is true for all practical cases. From equation (6) there will be no ricochet through complete dispersal of energy if P = l / d K  1 The method outlined here may well be applied to determine the ricochet safety trace for ammunition of higher calibre also. 68 

A Note on the Determination of Ricochet Trace of Small arms Ammunition

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A Note on the Determination of Ricochet Trace of Small arms Ammunition

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