Subsonic and Supersonic Flow over Wings Questions and Answers

Answer: A

Winglets attack induced drag, which dominates in slow flight but is a modest share of the total for a supersonic cruiser, where wave drag and friction lead. The added area and its own wave drag can easily outweigh the induced-drag saving, so the device does not transfer well to that regime.

Answer: B

Linearised supersonic theory divides by the square root of the Mach number squared minus one, and that radical grows with speed, so the slope shrinks. This is the reverse of the subsonic Prandtl-Glauert trend, and it means a supersonic aircraft needs more incidence, and pays more drag, for a given manoeuvre.

Answer: C

Spread, the wing has a high aspect ratio and works well slowly for take-off, loiter and landing; swept, it hides its leading edge behind the Mach cone and cuts wave drag for the dash. The compromise is bought with a heavy, complex pivot, which is why the configuration has largely fallen out of use.

Answer: D

The strong subsonic payoff comes through induced drag, which is a smaller share of the total supersonically. Meanwhile a longer span pushes the tips outside the Mach cone from the apex and adds wave drag. Supersonic wings are therefore short and highly swept rather than long and slender.

Answer: A

Thickness sets how much the flow must accelerate over the section, so thinning it is the most direct way of delaying sonic conditions. Sweep and a supercritical shape both help as well, but neither changes the fundamental relationship between thickness and local overspeed the way thinning does.

Answer: B

The section responds to the component normal to the leading edge, \( M \cos\Lambda = 0.85 \times \cos 35^\circ = 0.85 \times 0.819 = 0.696 \). The wing therefore behaves as though flying at Mach 0.70, comfortably below where a thin section would run into trouble.

Answer: C

The Mach angle is \( \arcsin(1/2) = 30 \) degrees, so the Mach cone lies 30 degrees from the flight direction. Measured from the lateral axis in the usual way, the leading edge must be swept more than \( 90 - 30 = 60 \) degrees to hide behind that cone and stay subsonic.

Answer: D

For a delta wing the aspect ratio is \( 4/\tan\Lambda \). With \( \tan 60^\circ = 1.732 \), that gives \( 4/1.732 = 2.31 \). The low value is characteristic: slender deltas trade the induced-drag efficiency of a long wing for low wave drag and useful internal volume.

Answer: A

Substituting into \( 4/\tan\Lambda \) with \( \tan 45^\circ = 1 \) gives exactly 4. Comparing with the 60-degree case shows how quickly the aspect ratio falls as sweep is increased, which is the geometric price paid for keeping the leading edge subsonic at high Mach number.

Answer: B

The normal component Mach number is \( M \cos\Lambda = 2 \times \cos 60^\circ = 2 \times 0.5 = 1.0 \). The edge is therefore exactly sonic, sitting precisely on the boundary between the subsonic and supersonic leading-edge cases.