Dealing With Mach Tuck
All supersonic aircraft experience some degree of mach tuck.
Historically, recovery from a mach tuck in subsonic aircraft has not always been possible. In some cases, as the aircraft descends and the air density increases, the extra drag will slow the aircraft while the increase in temperature will increase the speed of sound giving a relative reduction of Mach number and control will return.
For aircraft such as supersonic fighters/bombers or supersonic transports such as Concorde that spend long periods in supersonic flight, Mach tuck is often compensated for by moving fuel between tanks in the fuselage to change the position of the centre of mass. This minimizes the amount of trim required and keeps the changing location of the center of pressure within acceptable limits.
Supersonic and subsonic aircraft often have an all-moving tailplane (a stabilator) rather than separate elevator control surfaces. This avoids the shock wave making the control surfaces pitch downwards.
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