Importance of speed of sound – Mach number

It was mentioned above that an aircraft travelling at supersonic speed does not affect the state of the air ahead of the aircraft, while at subsonic speed the disturbance is propagated far upstream. In order to understand the reason for this we need to take a look at how the aircraft is able to make its presence felt as it travels through the air.

Figure 5.2(a) shows the nose of an aircraft flying at subsonic speed. As the flow approaches the nose of the aircraft it slows and the pressure locally increases. The influence of this region of increased pressure is transmitted upstream against the oncoming flow at the speed of sound (approximately 340 m/s at sea level). If the flow approaching the aircraft is subsonic then the disturbance will be transmitted faster than the oncoming flow and the aircraft will be able to make its presence felt infinitely far upstream.

Figure 5.2(b) shows what happens in supersonic flight. The disturbance can only make headway through an area near the nose where the flow is locally subsonic. The flow upstream is separated from this localised region by a shock wave, and is completely uninfluenced by the presence of the aircraft.

As the speed of the flow increases, so the region of subsonic flow at the nose gets smaller and the shock wave gets stronger (i. e. the pressure, density and temperature jumps all become larger).

This is why the speed of the aircraft relative to the speed of sound is the important factor in determining the flow characteristics. This ratio is known as the flight Mach number.

Flight Mach No. = Aircraft speed/speed of sound

Fig. 5.2 Propagation of pressure disturbances

(a) At subsonic speeds pressure disturbances generated at the nose travel at speed of sound and can make headway against oncoming flow (b) At supersonic speed the disturbances can only propagate through the locally subsonic region near the nose

When the flight Mach number is greater than one, then the aircraft is flying supersonically. When it is less than one then it is flying subsonically.

When an aircraft is flying supersonically we have seen that there may be local areas, such as the region near the nose, where the flow speed is locally reduced. Not only is the speed reduced, but the local temperature will rise, thus increasing the local speed of sound. Because of this there will be regions where the flow is locally subsonic (Fig. 5.3(a)).

Conversely, the regions on an aircraft where the flow speed is locally increased, such as the top of the wings, may lead to localised patches of super­sonic flow (Fig. 5.3(b)) even when the flight Mach number is subsonic. Thus we need to define a local Mach number for different areas of the flow.

Local Mach No. = Local flow speed/local speed of sound.

Supersonic ‘patch’ due to local speeding up of flow I (Local M>1)

-"f’] Shock

Fig. 5.4 Change of speed along wind-tunnel duct

If there is a small pressure difference between ends of duct, speed rises to maximum at throat and then decreases

For larger pressure differences speed becomes supersonic downstream of throat