304 MESSRS. R, H. FOWLER, E. G. GALLOP, C. N. H. LOCK AND H. W. RICHMOND: 
when v/a <0-7. With regard to their dependence on 8 we are not here concerned 
experimentally with f n . We shall assume for the purpose of analysing our experiments, 
where only a rough value of f R is required, that f R (v/a, 8) is independent of 8 for small 
values of SA For the usual position of the centre of gravity of the shell, f M at low 
velocities is remarkably nearly independent of $ for all values less than 10 degrees, 
and then diminishes as 8 increases beyond this value. On the other hand, at low 
velocities, y L (v/a, 8) behaves curiously for small values of 8. The wind-channel value 
of f L (v/a) is in consequence uncertain. Typical curves showing f R , f L and as 
functions of 8 at low velocities are shown in fig. 2. It is the main purpose of the 
experimental part of this paper to determine f L (v/a), and f M (v/a) as functions of 
v/a, when v/a >0*7. 
1.11. The Effect of the Angular Motion of the Axis of the Shell. —In practice the 
direction of the axis of the shell relative to the direction of motion changes fairly 
rapidly. By analogy with the treatment of the motion of an aeroplane, we assume, 
tentatively, that the components of the force system R, L, and M are unaltered by the 
angular velocity of the axis, but that the effect of the angular motion of the axis of 
the shell can be represented by the insertion of an additional component, namely, 
a couple H, called the yawing moment due to yawing, which satisfies the equation 
(l.lll) H = pvwAfn (v/a, ...), 
where w is the resultant angular velocity of the axis of the shell. The form of (l.lll) 
is chosen to make f R of no physical dimensions 
and is the only one suitable for the purpose. 
The couple H is assumed to act in such a 
way as directly to diminish w (see fig. 3). 
The yawing moment coefficient f H may be 
expected to vary considerably with v/a. It 
may depend appreciably on other arguments 
such as wr/v and 8. This couple is suggested 
by, and is analogous to, the more important of 
the “ rotary derivatives ” in the theory of the 
motion of an aeroplane. It appears from con¬ 
siderations of symmetry that no other couple of 
the “ rotary derivative” type need be considered. 
We shall arrive at rough values of f R from our 
experimental results, and to some degree an a posteriori justification of our 
* By symmetry 0/ E /oS = 0, when 8 = 0, since f R has a minimum for 8 = 0. It might therefore be 
expected that, when 5 is less than 3 degrees (say), / E would be nearly independent of 8. This, however, 
is not the case in wind-channel experiments. The drag at 2 degrees and 3 degrees yaw may be 7 per cent, 
and 10 per cent, greater, respectively, than the drag at zero yaw. Such evidence as exists indicates that 
the same increase may occur also at high velocities. An experimental study of the variation of the drag 
with 8 at high velocities would present no insuperable difficulties with modern apparatus. 
