Critical Mach Number

It has already been made clear that the onset of compressibility is a gradual effect, and that things begin to happen at speeds considerably lower than the speed of sound, that is at Mach Numbers of less than 1. One reason for this is that, as explained in earlier chapters, there is an increase in the speed of airflow over certain parts of the aeroplane as, for instance, over the point of greatest camber of an aerofoil. This means that although the aeroplane itself may be trav­elling at well below the speed of sound, the airflow relative to some parts of the aeroplane may attain that value. In short, there may be a local increase in vel­ocity up to beyond that of sound and a shock wave may form at this point. This in turn, may result in an increase of drag, decrease of lift, movement of centre of pressure, and buffeting. In an aeroplane in flight the results may be such as to cause the aircraft to become uncontrollable, in much the same way as it becomes uncontrollable at the high incidence stall at the other end of the speed range.

All this will occur at a certain Mach Number (less than 1), which will be different for different types of aircraft, and which is called the critical Mach Number (Mcr) of the type.

The reader who has followed the argument so far will not be surprised to learn that the general characteristic of a type of aircraft that has a high critical Mach Number is slimness, because over such an aircraft the local increases of velocity will not be very great. This was well illustrated by the Spitfire, a ‘slim’ aircraft that was originally designed without much thought as to its perform­ance near the speed of sound, yet which has proved to have a critical Mach Number of nearly 0.9, one of the highest ever achieved.

We had some difficulty in deciding whether the ordinary stalling speed should be defined as the speed at which the lift coefficient is a maximum, or at which the airflow burbles over the wing, or at which the pilot loses control over the air­craft. They are all related, but they do not necessarily all occur at the same speed. So now with the critical Mach Number – is it the Mach Number at which the local airflow at some point reaches the velocity of sound? or at which a shock wave is formed? or at which the air burbles? or when severe buffeting begins (this is sometimes called the ‘buffet boundary’ of the aircraft)? or at which the drag coefficient begins to rise? – or, again, when the pilot loses control? I do not know – nor, apparently, does anyone else! Authorities differ on the matter, each looking at it according to their own point of view, or sometimes according to whether they want to claim a high critical Mach Number for a pet type of aircraft. However, it doesn’t matter very much; they are really all part of the same phenomenon.

Is it possible for an aircraft to fly at a Mach Number higher than its critical Mach Number? Is it possible for an aircraft to have a critical Mach Number higher than 1 ? These two questions may at first sound silly, but they are not. The answers to both depend entirely on which of the many definitions of critical Mach Number we adopt. If the critical Mach Number is when the pilot loses control, then he can hardly fly beyond it; but if it is when a shock wave is formed, or when the drag coefficient begins to rise, why not? The pilot may not even know that it has happened, any more than he knows whether he is at the maximum lift coefficient in an ordinary stall. Graphs of lift and drag coefficients are all very well, but one cannot see them on the instrument panel when flying. Supposing the pilot can maintain control through all the shock waves, increases of drag coefficient and so on, then the critical Mach Number is higher than 1 or, to be more correct, the aircraft has not got a critical Mach Number in any of the senses that we have so far defined it, except for the one relating to the first appearance of supersonic flow locally or the first appear­ance of shock waves.