Mach waves and the Mach cone

Figure 5.8 shows that the bow shock wave becomes progressively more oblique with increasing distance from the aircraft. As its angle to the free stream flow direction reduces so the shock weakens and the changes in pressure, density, flow direction etc. become less.

At very large distances from the aircraft the wave becomes very weak indeed, like a sound wave. The angle it makes with the free stream direction tends to a particular value known as the Mach angle (Fig. 5.9) and the very weak shock wave is known as a Mach wave. When this happens the velocity component at right angles to the wave is equal to the speed of sound.

The idea of the Mach wave as a line is very important in supersonic flow as it establishes the region of the flow field which can be influenced by a given point on the aircraft surface. For example, if we consider the supersonic flow past a surface (Fig. 5.10), we can imagine a very small irregularity at point A generating a very weak local shock wave, or Mach wave. The flow up­stream of this Mach wave will be uninfluenced by the presence of the surface irregularity.

Flow behind Mach wave

Fig. 5.10 Surface irregularity

In supersonic flow only the area downstream of the Mach wave will be influenced

The angle of the Mach wave to the local stream direction depends only on the upstream Mach number (Fig. 5.9); the Mach wave becomes more swept back as the Mach number increases. Only the downstream flow is affected by the change in geometry. Had the flow been subsonic then the whole of the flow field would have been altered.

For a three-dimensional flow the region which can be influenced by a par­ticular point is given by a surface made up from Mach lines, and this is known as a Mach cone (Fig. 5.11).