30

AERONAUTICS IN THEORY AND EXPERIMENT

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verified, that this simple law breaks down at velocities approaching
that of the speed of sound waves. It has so far been assumed
that the pressures brought into being by the motion are not of
sufficient magnitude to introduce changes in the nature of the flow
due to the compressibility of the medium. Analysis of the flight
of projectiles indicates however that under such circumstances
this condition is violated, and along that path of the trajectory
at which the velocity is in the neighbourhood of or beyond that
of sound waves in air the resistance increases at a much higher rate
than on the remainder of the flight path. The method of deter-
mining this is extremely simple. The position of the shell at

FIG. 21

various times along its path is noted from the times of bursting
of a series similarly projected. If s be the distance measured along
the path, the experiment furnishes a curve showing the variation
of this quantity with time. By differentiating twice the decelera-
tion of the shell is found and by adding to this the component
due to gravity at each point the resistance, and hence the
resistance coefficient, is derived. Plot-
ting this against v/V, where v = speed
of shell and V = speed of sound, a
curve of the type shown in fig. 21 is
obtained.

From an examination of this curve
the remarkable result becomes ap-
parent that for speeds up to about
600 ft. sec. the resistance coefficient
is constant, and consequently the FlCL 22

drag on the projectile is accurately proportional to the square
of the speed. In the region of the speed of sound, i.e. where