Question

Which of the following statements is/are TRUE regarding critical and drag divergence Mach numbers of a wing?

• A. Critical Mach number is the minimum freestream Mach number for which sonic condition is attained somewhere over the wing
• B. Drag divergence Mach number is always higher than the critical Mach number
• C. Drag divergence Mach number is the local Mach number over the wing at which the drag increases drastically
• D. Critical Mach number is independent of the angle of attack

Hint:

Compare where sonic flow first appears (critical Mach) with where the shock-induced drag rise happens (drag divergence Mach); both are defined using the freestream Mach number, and both depend on angle of attack.

Answer 1

The Correct Option is A, B

Step 1: Recall the definitions.
The critical Mach number \(M_{cr}\) of a wing is the freestream Mach number at which the flow accelerating over the curved upper surface first reaches sonic speed (\(M=1\)) at some point on the wing, even though the freestream itself is still subsonic. Below \(M_{cr}\) the entire flow field around the wing stays subsonic.
The drag divergence Mach number \(M_{dd}\) is a freestream Mach number, higher than \(M_{cr}\), at which the local supersonic pocket has grown large enough that a shock wave forms and causes flow separation, and the drag coefficient starts rising very sharply with further increase in Mach number.

Step 2: Check option (A).
Option (A) restates the definition of \(M_{cr}\) exactly: it is the minimum freestream Mach number at which sonic flow first appears somewhere on the wing (usually at the point of maximum thickness or maximum camber, where the local velocity peaks). This statement is TRUE.

Step 3: Check option (B).
Once \(M_{cr}\) is reached, a small sonic pocket exists but the drag rise is still gradual, because that pocket is tiny and often terminates in a weak shock. Only when the freestream Mach number increases further does the pocket grow, the shock strengthens, and separation sets in, producing the sharp drag rise. So \(M_{dd}\) always occurs after (numerically greater than) \(M_{cr}\); the wing always passes through \(M_{cr}\) before it can reach \(M_{dd}\). This statement is TRUE.

Step 4: Check option (C).
This option swaps freestream and local Mach number. \(M_{dd}\) is defined using the freestream Mach number, the number a pilot or a wind tunnel operator actually sets, not the local Mach number over the wing (which is already supersonic at that point, well above 1, and is not the quantity being reported as "the drag divergence Mach number"). Because it names the wrong (local, not freestream) Mach number, this statement is FALSE.

Step 5: Check option (D).
The critical Mach number depends on how much the local flow accelerates above the freestream speed, and that acceleration is controlled by the wing section shape and by the angle of attack. Raising the angle of attack increases the suction peak on the upper surface, so the local flow reaches sonic speed at a lower freestream Mach number, lowering \(M_{cr}\). Since \(M_{cr}\) changes with angle of attack, this statement is FALSE.

Final Answer:
Statements (A) and (B) are true, while (C) and (D) are false. \[ \boxed{\text{(A) and (B)}} \]