A supersonic aircraft has an air intake ramp that can be rotated about the leading edge O such that the shock from the leading edge meets the cowl lip as shown in the figure. Select all the correct statement(s) as per oblique shock theory when the flight Mach number \(M\) is increased.
GATE AE - 2023,
Answer: A
The correct statement is it is always possible to find a ramp setting \(\theta_{RAMP}\) such that the shock still meets the cowl lip.
The shock meets the cowl lip only if the shock angle \(\beta_{SHOCK}\) stays the same. From the \(\theta\)-\(\beta\)-\(M\) relation, a fixed shock angle needs a deflection that increases as \(M\) increases and tends to a finite limit as \(M \to \infty\), never exceeding the maximum deflection for that Mach number. Since the shock angle is fixed and already greater than the Mach angle, which shrinks as \(M\) grows, a suitable \(\theta_{RAMP}\) always exists: the ramp is simply turned to a larger angle.
The other statements are false. With \(\theta_{RAMP}\) held fixed, a higher Mach number makes the weak oblique shock lean further back, so \(\beta_{SHOCK}\) decreases rather than increases, and the shock would fall inside the cowl lip. There is no critical Mach number beyond which the fixed shock angle becomes unattainable, for the reason above. And an oblique shock angle is always greater than the Mach angle, \(\beta \gt \sin^{-1}(1/M)\), with equality only for an infinitely weak wave.
The question is worded “select all”, but the official key gives this single statement.
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