THE AERODYNAMICS OF A SPINNING SHELL. 
297 
of pressure distribution over the surface of the shell, material is provided on which a 
successful attack on the hydrodynamical problem may some day be based. A first 
contribution to a knowledge of the force system is made by the present paper. It is 
hoped to make a similar contribution to a knowledge of the pressure distribution in 
another place.* * * § 
The problem proposed for discussion is of course by no means novel, f In the 
earlier work which is summarised by Cranz (cf. (4)) the treatment of the equations 
of motion is often open to criticism, in view of the lack of sufficient justification for 
the necessary simplifying approximations. The classical theoretical results, such as 
Mayevski’s equation for the drift], (see § 4.2, equation (4.204) ) have therefore hitherto 
justly commanded little confidence. The discussion, moreover, is of necessity based 
on a prion assumptions as to the nature of the complete force system. Unless the 
results of these assumptions are brought to the test of detailed experiment, the 
assumptions themselves must remain unjustified and unjustifiable. It shoidd be stated 
here that the theory and experiments described in this paper confirm the classical 
theoretical results. Cranz’s own experiments (cf. (5)) were expressly designed to 
explode the fallacy that the axis of the shell, in steady motion, precesses right round 
the direction of motion of its centre of gravity. In this they are successful, but they 
were only carried out at low velocities, and give little in the way of quantitative 
results. The only real comparison of theory with experiment, which lias hitherto 
been made, is the comparison of the observed and calculated§ values of the drift. 
But the observed drift is the integrated result of the disturbing forces over a 
considerable arc of the trajectory, and moreover, can only be disentangled with 
difficulty from the effect of any cross wind that may be blowing. The observed drift 
does not therefore serve to determine the force system with any success, though it 
may be used to check the values of the components otherwise determined (§4.21). 
It may, therefore, be stated in general terms that, up to the present, there is no 
* “The Pressure Distribution on the Head of a Shell Moving at High Velocities,” ‘Roy. Soc. Proc.,’ A, 
Vol. XCVIL, p. 202. 
T See for example :— 
P. Charbonnier. (1) ‘ Traite de Balistique Exterieure,’ ed. 2, Bk. V., Ch. IV. (2) ‘ Balistique 
Exterieure Rationnelle,’ vol. II., Ch. IX. 
C. Cranz. (3) ‘Lehrbuch der Ballistik; Aeussere Ballistik,’ 1917, Ch. X. (4) ‘ Encyklopadie der 
Mathematischen Wissenschaften,’ vol. IV., Part II., p. 185, Art. 18, “Ballistik.” (5) ‘ Zeitsehrift 
fiir Mathematik und Physik,’ vol. XLIII., pp. 133, 169. 
J. Prescott. (6) ‘ Phil. Mag.,’ Ser. 6, vol. XXXIV., p. 332. 
Further references to previous authors will be found in (4), and the best account of Cranz’s own work 
in (5). 
f The lateral departure of the projectile from the vertical plane containing the initial tangent to the 
path of the centre of gravity of the shell. 
§ Actually, also, the important term in the calculated drift depends only on the ratio of two components 
of the force system, and not on their absolute values. 
2 T 2 
