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I'm trying to understand why the drag coefficient decreases in the supersonic regime with Mach number. While it is easy to show this using supersonic, potential flow theory, I'm looking for a more physical explanation.

My initial thought is, as freestream Mach number increases, the shocks should become stronger (even though they are more oblique, the normal component to the shock is still larger). Where is this train of thought going wrong?

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  • $\begingroup$ Read this and then let me know if anything is still unclear. $\endgroup$ Jul 23, 2020 at 21:03
  • $\begingroup$ The answer indicates why wave drag occurs, but I'm still a little unclear on why it would decrease with Mach number. It doesn't really dive into why the drag would decrease, just that drag would occur as Mach number increases to sonic velocity and past it. $\endgroup$
    – Nick Hill
    Jul 23, 2020 at 22:12
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    $\begingroup$ With speed well above Mach 1, the change in density is large enough to let the aircraft pass. Only around Mach 1 is the contraction of the streamlines low because the change in pressure and density compensate each other. In fully supersonic flow the change in density is dominant and makes it easier again for the aircraft to squeeze through. $\endgroup$ Jul 24, 2020 at 3:17

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As an airfoil goes from subsonic to transonic to supersonic flow, shocks form on the surface of the wing and then move off of the wing.

Look at the images here.

Most of the drag during the transonic drag rise is actually due to shock induced boundary layer separation. This drag is not technically wave drag.

At higher Mach, there is now a bow shock off the front of a blunt leading edge -- or an oblique shock off of sharp leading edges. There will also be a shock at the trailing edge. The flow separation on the airfoil surface is gone and the drag is reduced.

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From this answer we learn that an increase in flow speed is always coupled to a decrease in density. The ratio between both changes grows with the square of flow speed and equals unity when Mach equals the inverse square root of the ratio of specific heats.

Why is this important? For an airplane to fly through air, this air has to make way for the airplane. At subsonic speed this happens by an increase of local flow speed while at high supersonic speed the air slows down, getting denser. In both cases the air will temporarily occupy less volume so there is space for the airplane to pass.

Think of the air flowing past the airplane as flow through tubes. In order to make way for the airplane, those tubes must shrink in diameter around the airplane so it can fit in. They will do so at subsonic and high supersonic speeds, but much less around Mach 1. That is the reason for the maximum in the drag coefficient between Mach 1 and 1.2.

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