Question

For an airfoil, which of the relations about the critical Mach number $M_{cr}$ and drag divergence Mach number $M_{dd}$ are correct?

• A. $M_{cr} < M_{dd}$
• B. $M_{cr} < 1.0$
• C. $M_{dd} < 1.0$
• D. $M_{cr} > 1.0$

Hint:

Remember: $M_{cr}$ is the onset of local sonic flow ($<1$), while $M_{dd}$ is the onset of large drag rise ($>M_{cr}$).

Answer 1

The Correct Option is A, B

Step 1: Critical Mach number.
Critical Mach number is defined as the free-stream Mach number at which sonic velocity is first attained locally on the airfoil surface. \[ M_{cr} < 1.0 \] because local Mach reaches 1 before the free stream does.

Step 2: Drag divergence Mach number.
Drag divergence Mach number is the Mach number at which wave drag rises sharply due to shock formation. \[ M_{dd} > M_{cr} \] since shock appears after local sonic condition.

Step 3: Check options.
- (A) True: $M_{cr} < M_{dd}$. - (B) True: $M_{cr} < 1.0$. - (C) False: $M_{dd}$ may be slightly below or above 1 depending on airfoil, but generally $M_{dd} > M_{cr}$ and often near 0.8–0.9 for commercial wings (not strictly $<1.0$ always). - (D) False: $M_{cr}$ is always less than 1. \[ \boxed{\text{Correct statements: (A) and (B)}} \]