PRINCIPLES OP GUNNERY, 
37 
In the same way, the place of contact between the body of the shell 
and the lands of the gun can be found. In this case 
nl 
l — h 
144, 
or Ji — 90*07 ins. from the muzzle; 
i.e,, 28*93 ins. from the breech end of rifling. 
When the motion of projectiles fired from rifled ordnance comes 
under consideration, it is necessary to distinguish between the motion 
of translation and the motion of rotation. 
Motion of translation refers to the motion of a projectile travelling 
through the air; the motion of rotation to its spinning round its longer 
axis. 
Both these motions are combined in the motion of an elongated pro¬ 
jectile fired from rifled ordnance; but they are quite independent of 
one another, and may be considered separately. 
The velocity of translation of a projectile is usually measured by its 
linear velocity in feet per second. 
The velocity of rotation of a projectile is usually measured by its 
angular velocity in units of circular measure per second, The angular 
velocity of a projectile making one turn in one second is r. 
Now, if o) be the angular velocity of a projectile per second, and s 
the number of turns it makes in a second, then 
..( 1 ) 
i.e.j the number of revolutions per second is proportional to the angular 
velocity. 
Also, if the projectile makes one revolution in n calibres— i.e., in 
nd inches, where cl is the calibre of the gun in inches, and V the muzzle 
velocity in feet per second—then the number of revolutions of the 
projectile per second as it leaves the muzzle of the gun is 
\2V 
Equating (1) and (2), it will be seen that 
247 tV 
to= - ; 
■( 2 ) 
(3) 
or the angular velocity of a projectile is directly proportional to the 
muzzle velocity, and inversely proportional to the length of twist. 
The linear velocity of rotation of any point in a rotating projectile is 
the product of its angular velocity into the distance of that point from 
the axis of rotation; or if <o be the angular velocity, and r the distance 
of the point from its axis of rotation in inches, 
linear velocity of rotation = wr = 
2irVr . P 
-=- m teet per second. 
nd 
Example.— To find the number of revolutions per second, the angular 
velocity, &c., of the IG-pr. shell at the muzzle. The muzzle velocity 
The motion 
of transla¬ 
tion and 
rotation of 
a projectile 
fired from 
rifled 
ordnance. 
Velooity of 
translation. 
Velocity of 
rotation. 
Linear 
velocity of 
rotation. 
