Figure 11.5 shows four cases for the flow over the same airfoil wherein M∞ is progressively increased from 0.3 to MCГ = 0.61. Have you wondered where the numbers on Fig. 11.5 came from? Here is your chance to find out. Point A on the airfoil is the point of minimum pressure (hence maximum M) on the airfoil. Assume that the minimum pressure (maximum Mach number) continues to occur at this same point as M∞ is increased. In part (a) of Fig. 11.5, for M∞ = 0.3, the local Mach number at point A was arbitrarily chosen as MA = 0.435, this arbitrariness is legitimate because we have not specified the airfoil shape, but rather are stating that, whatever the shape is, a maximum Mach number of 0.435 occurs at point A on the airfoil surface. However, once the numbers are given for part (a), then the numbers for parts (b), (c), and (d) are not arbitrary. Rather, MA is a unique function of M∞ for the remaining pictures. With all this as background information, starting with the data shown in Fig. 11.5(a), calculate MA when M∞ = 0.61. Obviously, from Fig 11.5(d), your result should turn out to be MA = 1.0 because M∞ = 0.61 is said to be the critical Mach number. Said in another way, you are being asked to prove that the critical Mach number for this airfoil is 0.61.