100 PHYSICS: A. G. WEBSTER Proc. N. A. S. 
hole resonator is practically unresponsive to antinodes and to wave trains 
except within ranges from the pipe which are small as compared with the 
dimensions of the room as a whole. 
* Advance note from a Report to the Carnegie Institution of Washington, D. C. 
ON STEERING AN AUTOMOBILE AROUND A CORNER 
By a. G. Webster 
Department of Physics, Clark University 
Read before the Academy April 25, 1921; received April 6, 1922 
The question of so arranging the steering gear of an automobile that 
the front wheels shall skid as little as possible owing to axes not inter- 
secting has been dealt with by A. L. Candy {American Mathematical 
Monthly, Jime 1920) and leads to a geometrical discussion of a high 
degree of complexity. The present somewhat trifling paper has no such 
ambitious purpose, but was suggested by a question asked on the witness- 
stand as to how much an automobile must turn out in order to pass another. 
It was necessary to make some assumption, and this led to the question 
of steering in general, and the principles that should govern it. We shall 
consider only the question of passing from a straight course to another at 
right angles therewith at constant velocity, and inquire how we must 
steer in order not to skid. 
The layman ignorant of geometry and dynamics will suppose that we 
describe a circle, but this is impossible, not only because it is impossible 
to put the helm over suddenly so as to change from zero to a finite curva- 
ture, but also because the sudden change in the centrifugal force from 
zero to a finite quantity would produce a wholly intolerable shock. In- 
asmuch as the question of transition railroad curves has received so much 
attention, it is thought that the treatment of this question for an auto- 
mobile may have some interest to engineers. We shall for the present 
neglect the fact that the rear wheels do not track with the forward ones, 
taking that up later as a correction. Thus we shall examine the curve 
described by a machine of zero wheel-base, like a wheelbarrow, measur- 
ing wheel or monocycle. The condition is evidently that the curvature 
shall begin at zero, increase to a maximum until the tangent has turned 
through an angle of 45 degrees, and then return by a symmetical process. 
The centrifugal force is equal to mv^/ p, where m is the mass, p the radius 
of curvature, v the velocity, and if there is to be no skidding this must be 
less than wg/x where jj, is the coefficient of friction, consequently we must 
have at all times 
V^/p < ixg. 
