THE AERODYNAMICS OF A SPINNING SHELL. 
369 
projectile leaves the gun, which may prove of value. Owing to the effect of the 
initial oscillations on the ranging of the shell, it is important to determine whether, 
in general, the initial disturbance takes place at, or nearly at, the same orientation. 
Secondly, it is important to determine whether the initial oscillations may be regarded 
as caused by an impulsive couple whose size is independent of the twist of the rifling. 
If this is so, the amplitude of the initial oscillations of a shell can be cut down 
indefinitely by sufficiently increasing the spin. If, however, as appears to be the 
case from a rough survey of the data of the present trial, the initial circumstances 
are such that the impulsive couple (or its equivalent) increases in proportion to the 
twist of the rifling, then no increase of spin will reduce the oscillation below a 
certain definite limit. This conclusion would be technically important, as in the 
later stages of flight the spin is always in excess of requirements, and so the initial 
spin should be kept down as much as possible. 
5.13. Wind Effects. —In calculating the effect of wind on a shell it is usual to 
assume that the shell at once turns its nose to the relative wind. This is not strictly 
correct, and the true angular motion in a wind when the velocity is known at every 
point can be determined by our theory, since the forces acting on the shell depend 
only on its motion relative to the air. Consider, for example, the special case in 
which a shell suddenly enters a cross-wind region from a region of still air; it 
starts its relative trajectory with a yaw S given by the equation 
tan S = w/v, 
where w is the wind velocity and v the velocity of the shell. At the same time 
S' = 0 and f — 0. The equations of § 3.6 enable the subsequent motion to be 
properly traced, and the errors in the usual treatment calculated. 
§ 5.2. Effect of Size and Shape of Shell. 
The jump card trials described in this paper were carried out with shells of two 
different shapes only. The differences between the two shells may he seen from fig. 6 
to be considerable, form A having an ogival head of roughly 2 calibres radius, while 
form B is of 6 calibres radius. For form B the experiments determine the moment 
coefficient only, for a single position of the centre of gravity, and give no information 
as to the cross-wind force. As experiments of this type are expensive and laborious 
to carry out, it is of importance to examine how far these results may be applied to 
shells of other shapes and sizes. 
From the results of § 1.1 it appears that there is no evidence that the size (repre¬ 
sented by the radius r of the shell) enters into any of the factors on which the force 
coefficients depend, so that the coefficients ,/ K , f M , f L may be considered as entirely 
independent of size. It is therefore sufficient to make experiments on shells of as 
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