ENIAC U. S. Army
Suppose that we wish to have the ENIAC compute the supersonic airflow past a body of revolution ABC, without yaw. If the Mach number M(velocity in units of sound velocity) is sufficiently large, the nose angle sufficiently small on the curve ABC concave toward the axis, it is believed that there will exist an attacked shock-wave front (surface of discontinuous pressure, density, and velocity) and the velocity will be everywhere supersonic. It is then reasonable to assume that replacing a small Section AE of the nose contour AB by a straight line will have little influence on the flow at a distance from AE. This assumption does, however, have the following effects:
1. If the characteristic (curve making angle (omega) = csc**-1 M with streamlines at each point, or curve of propagation of weak disturbances) from E, making an acute angle with the velocity vector, hits the shock wave at a point F, then the shock front is straight from A to F.
2. In the region AEF, the partial differential equations defining velocity distribution can be satisfied by assuming that the velocity is constant on straight lines through A (G. I. Taylor and J. W. Maccoll, The Air Pressure on a Cone Moving at High Speeds," Proc. Roy. Soc. A139, 278-311 (1938).). Thus u and v are functions of a single parameter in AEF and the partial differential equations become ordinary. It is the solution of these equations for x, y, u, v, and z along EF which we shall choose as an illustrative problem.