High-Speed Cruise and Mach Tuck
A swept-wing business jet is cruising at FL410 with a Mach number of 0.80 and an indicated Mach of 0.80, close to its published Mmo of 0.82. The outside air temperature is ISA +12 °C, so the local speed of sound is higher than standard and the true Mach for a given IAS is different from the standard-day case. The autopilot is holding altitude. The pilot notices a slow, uncommanded nose-down trim change and increasing elevator force, together with a slight buffet. The pilot's instinct is to trim nose-up and add a little power to hold altitude.
1. Explain what is happening aerodynamically and why nose-up trim is the wrong response.
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The symptoms are classic Mach tuck. As the aircraft approaches its critical Mach number, a shock wave forms on the upper surface and the centre of pressure moves aft. On a swept wing the outboard sections reach critical Mach first, so the lift distribution shifts and the aircraft develops a nose-down pitching moment. The increasing elevator force and buffet confirm that the aircraft is at or beyond the point where shock-induced separation is beginning.
Trimming nose-up to hold altitude is the wrong response for two reasons. First, it increases the angle of attack, which raises the local suction peak and pushes the critical Mach number lower, so the shock strengthens and the tuck worsens. Second, it masks the real problem, which is that the aircraft is too close to Mmo for the conditions.
The correct action is to reduce Mach number by reducing power and, if necessary, accepting a shallow descent, and to allow the nose to come down rather than fighting it with trim. The pilot should also check whether the buffet is the high-speed buffet of shock stall rather than the low-speed stall buffet, because the recovery actions are opposite.
2. The aircraft is at FL410 in ISA +12 °C air. Explain how the warmer-than-standard temperature affects the relationship between IAS, TAS and Mach number, and what that means for the margin to Mmo.
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Mach number is TAS divided by the local speed of sound, and the speed of sound depends on temperature: a = √(γRT). In ISA +12 °C air the local temperature is higher than standard, so the speed of sound is higher. For a given TAS, the Mach number is therefore lower than it would be on a standard day.
However, the indicated airspeed is derived from dynamic pressure, which depends on density. At FL410 the density is very low, so a given IAS corresponds to a much higher TAS than at low level. The practical consequence is that the aircraft reaches Mmo at a relatively low IAS, and the margin between the current IAS and the IAS at which Mmo is reached is small. The warmer air gives a little extra Mach margin for the same TAS, but it does not change the fact that the aircraft is already at M 0.80 against an Mmo of 0.82.
The pilot should treat the 0.02 Mach margin as the limiting factor, not the IAS, and should slow down before any further climb or turbulence encounter, because a gust can raise the local Mach above Mmo almost instantly.