PRINCIPLES OP GUNNERY, 
363 
The front part of the projectile is, then, meeting the air in directions 
parallel to GT. The resultant of the resistance of the air opposed 
to this motion does not usually (owing to the form of head) act in 
exactly the opposite direction, but in a direction inclined to it, as RC. 
The point C, where the direction of the resultant of the resistance 
intersects the axis of the projectile, is called the “ centre of resistance.” 
The resultant R acts in the direction RC in the plane passing through 
the axis of the projectile and the tangent to the trajectory. 
The resultant, R , acting at G may be replaced by an equivalent force, 
R, acting at G , the centre of gravity of the projectile, and parallel to 
RC, and a couple whose moment is proportional to R x GC. The 
tendency of the couple, as drawn in Fig. 1 (which represents the case 
of an ogival-headed projectile) is to raise the point of the projectile — i.e., 
to give the projectile rotation round its shorter axis passing through 
its centre of gravity, and perpendicular to its longer axis. 
The combination of this rotation and the rotation impressed on the 
projectile round its longer axis by the spiral grooves in the bore, gives 
rise to the gyration of the axis of the projectile round a tangent to its 
trajectory. If the moment of this couple is increased from any cause, 
the velocity of rotation of the projectile must also be proportionally 
increased, in order to keep the axis of the projectile as close to the 
trajectory as possible; or, in other words, to keep the semi-amplitude 
of the gyration within moderate limits. 
The magnitude of the resultant resistance for a projectile of given 
diameter depends principally on the velocity and form of head of the 
projectile. Hence, when a projectile is fired with a high muzzle 
velocity, since the moment about the centre of gravity increases with 
the magnitude of the resultant resistance, a higher velocity of rotation 
is required to keep it steady under similar circumstances. 
Flat-headed projectiles, for the same reason, require a higher velo¬ 
city of rotation than ogival-headed projectiles.* In experiments made 
by Colonel Owen, R.A., “on the derivation of elongated projectiles,” 
it was found “that the velocity of rotation given by the rifled 
B.L. 40-pr. was not sufficiently high to keep a flat-headed shot steady 
during flight, except at very short ranges.”! 
The moment of the couple tending to produce rotation round the Position 
shorter axis, depends on the relative position of the centre of gravity treofgra* 
and the centre of resistance— i.e., on the distance GC, in Fig. 1. The Vlty ‘ 
greater this distance is, the greater will be the tendency to upset the 
projectile, and the greater must be the velocity of rotation, in order to 
keep the projectile steady in flight. If the centre of gravity of the pro¬ 
jectile were purposely brought towards the base, the tendency of the 
projectile would be to fly base foremost, unless it were counteracted by 
a much greater velocity of rotation than would be necessary under 
* The coefficient of resistance of flat-headed shot is much greater than for the ogival head (vide 
p. 241). For flat-headed shot, K = 139*6. 
f Vide Owen’s “ Modern Artillery,” p. 245. 
