i6. 
LAND & WATER 
August lO, 1917 
A Note on the Flight of Shells 
By R. Monteith, S.J. (Chaplain to the Forces) 
'Wi 
'HY does the spin of a rifle bullet result in its 
drifting to the left ? " This is, of course, the 
same question as " Why 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 right-handed 
screw. Owing to the flat trajectory of rifle bullets (m this 
war especially ranges have been very short), the drift and' 
rotation of the axis of the bullet are slight, but in the case of 
heavy ordnance these factors are of very great importance. 
]-or "instance a shell under extreme conditions is said to 
drift as much as a thousand yards to the right. Also, the 
rotation of, the axis may result in its going wrong end first. 
Dr. Proudman discussed the gyroscopic drift of shells in 
a mathematical paper recently read to the Liverpool Mathe- 
matical Society.' The practical value of his work in these 
days will probably materially delay its publication. This 
note, though suggested bv 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 puzzling 
movements of projectiles, not to discuss methods of calcula- 
ting them. The facts to be explained are : 
(a) A shell turns its axis 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. 
All shells, however, are not so obUging as to go nose first, 
and some prefer to land on their tails. In fact, at first sight 
] think we should expect all of them to do' so when fired at 
Irg'i angles. 
i\vo 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 
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°. (See Diagram I.) 
(2) If 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 
D \agrcvm M. 
•^— ::?4r 
III. the forces tend tn 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 applied vj a rotating body whose spin is 
not easily to be checked. 
Dr. Proudman asks me to give his more accurate conclusion --" On 
the whole a shell keeps revolving its nose about a direction -whiuh 
keeps a little to the right of that in which it is going, and it tends to 
• lo.low lis no.io." 
Two easy experiments carried out with a bicycle will 
illustrate the whole theory. 
Experiment i : 
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 u?e the pedal to give the 
Diayniro IE" 
back wheel a good spin forward,' that is, to your right. Now 
try to turn tlie bicycle up into the horizontal. (See Diagram 
IV.) ^The bicycle will resist and try to turn to the right. 
Experiment 2 : 
Having started the wheel as before, try whilst keeping the 
bicycle vertical to make it turn to tile right. Again you will 
.. find it self-willed with a cTecided preference to lean over 
away from you out of the vertical. As I have said, these 
two experiments seem to illustrate the tendencies of spinning 
projectiles, which I 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 j-ou 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, will turn the axis of a spinning 
shell to the right and not up. The shell has 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 sbell. 
One component will still t^nd 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 effect 
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 and 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 notieed that the explanation given makes the aberration 
depend both on gravity and the air resistance and applies in 
general to the wiiole 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 0I 
more interest as the text-books give only a mathematical 
treatment of gyroscdpic action. 
It will be necessary to remember that velocity and acceler- 
ation are quite distinct. They may be in opposite directions. 
