Consider the following situation

As subsonic air flow over an airfoil (or wing), it accelerates, reaches a maximum speed and then decelerates toward the trailing edge.

Since T₀ = constant,

Thus, the Mach number of the flow increases and then decreases. The magnitude of this change depends on the airfoil shape and the angle of attack. Thus, it is evident that, as you increase  , the highest local M on the surface may exceed 1 long before  reaches 1.

The value of  at which the highest M on the airfoil first reaches 1 is called the critical Mach number M_cr.

Note

1. M_cr is a value of the freestream Mach number.
2. M_cr is less than 1 for anything with thickness at all.

Calculation of M_cr

We know that

(Isentropic flow relation)

or,

At , M reaches 1 somewhere. The value of c_p at this point can be found by setting M=1.

 
 

Note:

1. For any given airfoil, the value of  can be found from the value of the minimum c_p on the airfoil.
2. If you have only low-speed data on the airfoil, the c_p values can be converted to values at a given subsonic Mach number using the Prandtl-Glauert relations.