People on the physics stackexchange recommended I ask here, so I am pasting my question regarding supersonic aircraft.
I stumbled upon an interesting plot; in particular, the dependence of wave drag on the Mach number:
It is curious to see that the drag coefficient drops so abruptly in the supersonic regime, but I am even more curious if the total drag force acting on the airplane also drops, i.e. if the plane starts accelerating in the supersonic regime.
I did some quick analysis of the problem. The drag force is defined as $$F_{\text{drag}} = C(v) v^2 ,$$ onde $C(v) = A C_D(v) \rho(v)/2$ is the newly introduced drag constant with the drag coefficient $C_D(v)$, flight medium density $\rho(v)$, and cross-sectional area $ A $.
Assuming these relations, one can taylor expand the equation for the drag force to find that
$$\Delta F_{\text{drag}} = C'(v)v^2 \Delta v + 2Cv \Delta v.$$
As $C'(v)$ is clearly negative in the supersonic regime, this means that the total drag force drops if $$C'(v) < -\frac{2C(v)}{v}.$$
It seems that this criterion could indeed be satisfied in air, as the right hand term in the inequality is a fairly small number.
Is there anyone that could elaborate further on what actually happens to the drag force as the plane breaks the sound barrier? Do the plane engines lower their power in order to maintain reasonable supersonic cruising speed, and if they didn't, would they be under too much heat load?