Vibrations of Rifle Barrels. 



337 



Diagram 11 shows the curves represented by the function 



? si "t ~ Sin # from 4> = to * = 2* and q = 0-6 to q = 4. 

 1 - q 2 



When q = 1 this expression takes the form of a . which, evaluated 

 in the usual way, gives • 



I will now apply the above results to examine the form of the Lee- 

 Enfield rifle at the moment the shot leaves the barrel, assuming that 

 the pressure developed during the explosion is that shown in fig. 10, 

 taking into consideration the first three terms of the harmonic series 

 for that curve and the first three modes of vibration of the rifle. 



For this rifle it was found by experiment* that a couple of 1 foot-lb. 

 acting at the nodes caused at the muzzle the following deflections : — 



In the authorised ' Text-book for Military Small Arms ' the initial 

 pressure in the chamber of the Lee-Enfield is given as 15 tons per 

 square-inch. 



The area of the base of the shot is 0*0725 square-inch, so that the 

 initial pressure on the shot is 1 -09 tons or 2450 lbs. Since the weight 

 of the shot itself is 215 grs., the force acting on it is -VV/- x 2450, 

 nearly 80,000 times its own weight. Multiplying this by g. the 

 acceleration which the shot would undergo in the absence of friction 

 in the barrel is 2,560,000 feet per second per second. 



In case 3 (14) the initial pressure was found to be 2,320,000 feet per 

 second per second, so that, allowing for the force required to press the 

 shot into the rifling and the friction in the barrel, it seems probable 

 that the pressure curve of case 3 represents with some degree of 

 approximation the actual acceleration which the shot experiences. 



* It would occupy too much space to describe these experiments in detail. They 

 were made by loads suitably placed on the rifle, and the deflections caused by them 

 were measured by optical means. The deflections so found were reduced to what 

 they would have been had the action of the couples been concentrated at the nodes. 

 In virtue of the approximate straightness of the free end of a vibrating rod, the 

 angular deflection at the muzzle was taken as equal to the angular deflection at the 

 nearest node. Hence the deflections above given are rather less than the true 

 values. 



</> cos - sin <f> 



2 



Mode I 

 Mode II 

 Mode III 



0! = r-13 

 9 2 - 0'-765 

 6 3 = 0'-565 



