When a body moves through air at a uniform speed greater than that of sound, a shock wave is formed which remains fixed relative to the body. This wave is situated on a surface where a very abrupt change in density and velocity occurs. It can be seen as a sharp line in photographs of bullets in flight. In front of this surface the air is stationary, behind it there is a continuous field of fluid flow which may contain further shock waves. The nature of these shock waves is well known and the equations which govern their propagation were first obtained by Rankine. The work of Rankine, however, seems to have escaped the notice of subsequent writers and it was not till some years later that they were rediscovered by Hugoniot to whom they are usually attributed. Rankine’s equations give the relationship between the conditions in front and behind a plane shock wave. They connect the ratio of the density in front and behind the wave with the components of velocity normal to the wave. They have been applied by Meyer to find the flow in the neighbourhood of an inclined plane or wedge moving at high speeds. Meyer begins with a plane shock wave reduced to rest by giving the whole field a suitable velocity perpendicular to its plane. He then gives the whole field a velocity parallel to the wave front. The system is then a steady one, the shock wave remaining at rest, but the direction of motion of the air, which is now oblique to the wave, suffers an abrupt change at the wave front. By combining two such shock waves intersecting at a point, but not continuing beyond the intersection, a system can be devised in which all the air on one side of the pair of waves is moving with a uniform velocity. The air which passes through one wave is deflected, say, upwards, while that which passes through the other is deflected downwards. This system can evidently be bounded by a solid wedge, the faces of which are parallel to the two parts of the deflected air stream.
The air pressure on a cone moving at high speeds.—I