THE AERODYNAMICS OF A SPINNING SHELL. 
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1.33. Differences Between the Shell and Tap Movements. —We now proceed to 
consider the factors, so far neglected, which cause the angular motion of the 
shell to differ from that of the corresponding top. These may be enumerated as 
follows:— 
(1) The effect of the cross-wind force in causing the centre of gravity to follow 
a curve of helical type. 
(2) The effect of the force components denoted in §1.11 and § 1.12 by 
H, J, and K. 
(3) The effect of the diminution of forward velocity caused by the drag. 
(4) The effect of gravity. 
These effects will be considered in turn. 
1.331. The angular oscillations of the shell give rise to a cross-wind force, which 
varies in magnitude and direction as the yaw varies, and this modifies the straight 
line motion along the direction of projection into motion of a helical type. If this 
helical motion could be observed with accuracy it would give valuable data for the 
cross-wind force coefficient f u but unfortunately the amplitude of the oscillations 
is too small to allow of this. Hence the most important effect, from the point of 
view of these experiments, is the reaction of the sideways motion of the centre 
of gravity on the angular oscillations of the shell. This helps to damp out the 
oscillations. 
1.332. The yawing moment factor H has a similar damping effect as it is always 
opposed to the transverse, angular velocity. While the effect of the former factor 
is to damp the slow period oscillation and slightly augment the quick oscillation, this 
latter has exactly the reverse effect. In combination, they, in general, damp out 
the oscillations of both periods. For the 3-inch shells, used in this trial, the yawing 
moment damping factor is of gre'ater importance than the cross-wind force damping 
factor, and the general effect is to diminish the maximum values of the yaw, and at 
the same time to convert the initial rosette motion into the slower steady precessional 
motion. # The force component, J, due to the spin, has no appreciable effect on the 
angular motion, but the corresponding couple K might act as a small additional 
damping factor. 
1.333. The head resistance or drag slowly diminishes the forward velocity, and so 
increases the stability factor s, by diminishing m . The change in s diminishes the 
amplitude of the oscillations to a limited extent, and so assists the other damping 
factors. 
1.334. Gravity affects the angular motion of the axis of the shell by producing 
curvature in the trajectory. In taking account of the gravity effect it is necessary to 
* Ther.e are two possible types of steady precessional motion at constant yaw, one with a quick and the 
other with a slow precessional velocity. 
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