i6 
A Note on the 
WATER, .-Augubx lo, 1917 
Flight of Shells 
By R. Monteith, S.J. (Chaplain to the Forces) 
W 
HY does the spin of a rifle bullet result in its 
drifting to the left ? " This is, of course, tlic 
same question as " Whv does the spin of a shell 
, , result in its drifting to the right ? " since the 
bullet moves on a left-handed and the shell on a nglU-handod 
screw. Owing to the flat trajectory of rifle bu lets (111 tin-, 
war especially ranges have been very short), the drift and 
rotation of the axis of the bullet are slight, but in tlic case of 
heavv ordnance these factors are of very great importance. 
1-or 'instance a shell under extreme conditions •* said to 
drift as much as a thousand yards to the right. Also the 
rotation of the a.\is mav result in its going wrong end hrst. 
Dr. Proudman discussed the gyroscopic drift of fhe'ls in 
a -mathematical oaper recently read to the Liverpool Mathe- 
matical Society.' The practical value of his work in the.u 
da\s will probably materially delay its i^ublication. 1 ius 
note, though suggested bN' the subject of his lecture, will not 
touch on mathematics. Its purpose is to give an account 
of the causes which tend to produce these rather pu^.zling 
movements of projectiles, not to discuss methods of calcula- 
ting them. The facts to be explained are : 
(a) A shell turns its a.xis to the right ; 
(b) A shell drifts to the right ; 
(c) A shell often turns its point gradually down and so 
lands on it— that is, a shell turns to the right and follows 
its nose. ^ 
\11 shells however, are not so obliging as to go nose hrst, 
and some prefer to land on their tails. In fact, at first sight 
1 think we should expect all of them to do so when fired at 
high angles. , . ^ 1 1 • 
Two reasons might lead us to this false _ conclusion . 
(i) In vacuum a shell would keep its axis parallel to the 
gun which fired it ; also the spin would only tend to steady 
Diagram I. 
the axis in this position. Thus, a shell fired at an angle of 
40° to the horizon, would land on its tail with its axis still 
pointing up at an angle of 40°. (Sec Diagram I.) 
(2) It we consider the action of the air, apart from the 
spin, we see that the forces are disposed as in the shuttle- 
cock. Diagram II. illustrates how the air resistance turns 
the shuttle-cock so that the end which was struck passes 
under the feathers and then leads the way. In Diagram 
Oio^rarn E 
III. the forces tend to the same result, if we disregard the 
spin, and we might expect the shell to turn turtle and alight ' 
wrong end first. This is not the actual result, I believe, in 
the case of our great naval guns. The reason is that the air 
resistance is now apphed to a rotating body whose spin is 
not easily to be checked. 
i \ 
Dr. Proudman asks me to give his more accurate conclusion : — " On 
the whole a shell keeps revolving its nose about a direction which 
keeps a little to the right of that in which it is going, and it tends to 
lollow its nose." 
Two easy experiments carried out with a bicycle will 
illustrate the whole theory. 
Experiment 1 : 
For convenience, fix the catch to prevent the handle-bars 
turning ; grip the bicycle with the left hand towards the 
saddle and the right hand towards the handle bars, lift the 
bicycle just off the ground, and use the pedal to give the 
Diaorxirv IS 
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back wheel a good spin forward, that is, to your right, 
try to turn the bicycle up into the horizontal. (Sec Dia 
IV.) The bicycle will resist and try to turn to the rig 
Experiment 2 : 
Having started the wheel as before, try whilst kcepiiig the 
bicycle vertical to make it turn to the right. Again yoU wili 
find it self-willed with a decided preference to lean ov^er 
away from you out of the vertical. As I have said, these 
two experiments seem to illustrate the tendencies of spinning 
projectiles, which 1 have numbered (a) (b) and (c). Regard 
the hub of the back wheel as the case of a shell pointing aWay 
from you. In Experiment i you have tried to turn it up as' 
a shuttle-cock is turned in the air. It turned its axis to the 
right so that a force couple, similar to the one which made 
the shuttle-cock turn over, w^ill turn the axis of a. spinning 
shell to the right and not up. The shell lias now turned so 
that its nose is to the right of the direction in which it is 
going. (Diagram 3 is now no longer a vertical section.) 
The air resistance will be partly on the left side of the shell. 
One component will still tend to hold the shell back, and 
up, while there will be another causing drift to the right. 
This is movement (b). 
Also just as there was at first an effort of the air to turn 
the point up, so now there will be a tendency to force the 
point still further to the right. In Experiment 2, the cfiect 
of such an effort to turn the axis to the right has been seen. 
The bicycle heeled over away from the operator. The corre- 
sponding motion of the shell is a lowering of the point. This 
is the third motion (c) which we set out to illustrate. 
As far as this third tendency is operative it will check 
the first coming into play, but it depends on the first and is 
secondary to it. We may conclude then that it is likely that 
by properly adjusting the conditions- a shell might be made to 
travel more or less nose first, drifting to the right with its 
nose turned still more to the right end above the tangent to 
its path, but turning over sufficiently for it to alight head- 
first. Of course, nothing but a mathematical treatment 
such as Dr. Proudman's will give us an idea of the relative 
importance of the various factors of this problem. It will 
be noticed that the explanation given makes the aberration 
depend both on gravity and the air resistance and applies in 
general to the whole motion. 
So far the motion of a shell has been illustrated by com- 
parison with the behaviour of a wheel. Now it remains tc 
be explained why a wheel behaves as it does. This may be ol 
more interest as the text-books give only a mathematicaf 
treatment of gyroscopic action. 
It will be necessary to remember that velocity and acceler- 
ation are quite distinct. They may be in opposite directions. 
