THE AERODYNAMICS OF A SPINNING SHELL. 
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great as 700 f.s. For higher velocities it is necessary to fall back on the second method 
which is the principal subject of this paper. 
For this purpose the shell is fired horizontally through a series of cards such as 
are used for measuring the jump* of the gun on firing. From the shape of the holes 
in the cards the actual motion of the axis of the shell can be reconstructed. Initial 
disturbances at the muzzle give rise to angular oscillations of the shell of sufficient 
amplitude for accurate measurement. These oscillations are very similar to those of 
the axis of a spinning top under gravity. If, as a first approximation, we regard the 
centre of gravity of the shell as constrained to move uniformly in a straight line over 
the range containing the cards, and ignore frictional damping forces in both cases, 
then the angular motion of the axis of the top and the axis of the shell are identical, 
provided that (l) the top and shell have the same axial spin and axial moment of 
inertia ; (2) the transverse moment of inertia of the top about its point of support is 
equal to the transverse moment of inertia of the shell about its centre of gravity ; 
and (3) the moment of gravity about the point of the top is equal to the moment of 
the force system on the shell about its centre of gravity. 
In this approximate case the formal solution of the two problems is identical. As 
is explained in § 1.3, from the periods of the oscillations of the axis of the top or 
shell, we can deduce the moment of the disturbing couple and vice versa. In the 
same way the nature of the decay of the oscillations can be used to determine the 
damping forces. 
In conclusion, we feel that a word of apology may be needed for the length of the 
introductory part of this paper. We do not here emphasise the applications to 
practical gunnery of the results obtained, but these are of some importance. We 
have, therefore, thought it desirable that the results should be presented in such a 
form as to be available to those who are concerned with the practical results, but 
who are not prepared to follow in detail the arguments of Parts III. and IV. At 
the same time it has been necessary to avoid statements which, without explanations, 
might convey little meaning to those who have not been technically concerned with 
ballistics and aerodynamics. It does not appear possible to achieve these objects 
except at the expense of a somewhat lengthy Introduction and Part I. 
Part I.—A General Description of the Motion of a Spinning Shell and 
the Principal Experimental Results. 
§ 1.0. The Classical Theory of the Plane Trajectory. 
According to the classical theory, a shell is supposed to move in a resisting medium 
like a particle on which the only forces acting are gravity, and a resistance tangential 
to its path, depending only on the velocity of the particle and the state of the 
* The angle between the axis of the bore before firing and the initial tangent to the path of the centre 
of gravity of the shell. 
