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I am unsure if this is correct but this is my current explanation: Once past supersonic speeds, the larger the speed the larger the divot of air pressure around the plane. Because these divots can get so large at high speeds, control surfaces are ineffective due to the air not flowing close enough to them. When I say divots, I am referring to the "wavefronts" and "shock cone" around the aircraft. Image for reference (from Wikipedia):

Mach cone

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  • $\begingroup$ No, in fact rockets and missiles requires small surfaces (see e.g. SpaceX's grid fins which are very effective on high speed). Air and its (static) kinetic energy are the same per volume (but it varies with altitude and temperature). $\endgroup$ Feb 15 at 8:40
  • $\begingroup$ There may be less longitudinal stability due to (wave) pressure on the nose rather than significant loss of control surface authority. Pressure differential within the "divot" (being a golfer, I like it) is measured in pounds per square foot (divide by 144 for psi). It may be significant at origin and worth study. Early high speed rocket aircraft (the X series) had a tendency to lose stability, but these were flown in extremely thin atmosphere. Loss of stability at higher speeds was known as "divergence". Notice the build of the SR-71 was extremely stable. $\endgroup$ Feb 15 at 12:49

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Once past supersonic speeds, the larger the speed the larger the divot of air pressure around the plane.

There are no divots around the plane. Even at supersonic speeds air keeps on following the plane's contour just like at subsonic speeds. When the airplane comes, air just gets out of the way; at subsonic speeds air begins already well in front of the airplane to move away while at supersonic speeds it does it instantaneously via shock and compression waves.

No matter the speed, lift and drag always follow the well known relationships:

$\begin{cases} L=½ \rho V² SC_l\\ D=½ \rho V² SC_d \end{cases}$

so that, in general, the bigger the speed the bigger the aerodynamic forces.

Anyway both $C_l$ and $C_d$ also change with the speed. In particular, all the rest being the same:

  • $C_d$ at supersonic speed is always bigger than at subsonic speed due to the wave drag;
  • $C_l$ at supersonic speed is lower than at subsonic speed with a ratio that, at least theoretically, for a thin airfoil is 4/2π.

So you're right that

control surfaces effectiveness lowers at supersonic speeds

since $C_d$ is bigger and $C_l$ is lower but this is more than compensate for by the higher speed $V$.

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  • $\begingroup$ One can measure the supersonic cone with Schlieren photography. This has been done with rifle bullets. The angle of the cone can be used to determine Mach number by the formula M = 1/(sine cone angle). $\endgroup$ Feb 15 at 13:12
  • $\begingroup$ What are the values Cd, cl, and S in these equations? $\endgroup$
    – Sam Jones
    Feb 15 at 15:44
  • $\begingroup$ Coefficient of drag, C. of lift, and area. $\endgroup$ Feb 15 at 15:52
  • $\begingroup$ $\frac{1}{2} \rho V^2$ may only be used for incompressible dynamic flow, up to about M= 0.5. $\endgroup$
    – Koyovis
    Feb 17 at 4:34
  • $\begingroup$ @Koyovis: How is the relationship at higher speed? $\endgroup$
    – sophit
    Feb 17 at 10:12
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No. This is not true.

Control surface effectiveness scales with dynamic pressure. Faster means more.

Shocks located on a control surface, or on the hinge line can wreak haovc. However, once you're solidly supersonic, there is no 'divot' in the flow that the aircraft exists in.

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