Coffin Corner at FL410
A swept-wing business jet of 18 000 kg and wing area 40 m² cruises at FL410 at M0.80. The AFM gives MMO 0.82 and, for this configuration, a high-altitude buffet-onset lift coefficient of 0.60 - the wing's usable CL at high Mach, where CLmax has fallen from its low-speed value of 1.35. ISA conditions apply and the tropopause is at FL360. The crew is cleared to climb to FL430 for a better wind, still at M0.80. In cruise a mountain wave produces a 1 500 ft/min downdraft; the Mach number rises to 0.845 before the autothrottle reacts and the airframe shakes. The captain considers pulling up to stop the descent.
1. Compute the low-speed buffet Mach at FL410 for 18 000 kg using the quoted buffet CL of 0.60 and compare it with MMO. How wide is the usable corridor, and what happens to it at FL430?
Read the worked answer
At FL410 (above the tropopause, ISA): ρ = 0.364 kg/m³, T = 216.65 K, a = sqrt(1.4 × 287 × 216.65) ≈ 295 m/s.
V = sqrt(2W/(ρ S CL)) = sqrt(2 × 18 000 × 9.81 / (0.364 × 40 × 0.60)) = sqrt(353 160 / 8.74) ≈ 201 m/s TAS M = 201/295 ≈ 0.68
So the corridor is M0.68 to MMO 0.82 - about 0.14 Mach.
At FL430 the temperature is the same (still above the tropopause) but pressure has fallen, ρ ≈ 0.331 kg/m³: V = sqrt(353 160 / (0.331 × 40 × 0.60)) = sqrt(44 500) ≈ 211 m/s, M = 211/295 ≈ 0.72.
The high-speed limit does not move because it is set by the wing's Mach number, so the corridor shrinks to 0.72–0.82, about 0.10 Mach. The climb to FL430 buys wind but removes roughly 30% of the low-speed margin.
Note that at high altitude this 'low-speed' boundary is properly expressed in Mach, not IAS. In IAS it falls as altitude rises, which is why high-altitude cruise speeds are always quoted in Mach: the Mach number, not the IAS, tells you where the wing is relative to the buffet.
2. The aircraft reached M0.845 in the downdraft. Explain what happens at that Mach number and evaluate the captain's plan to pull up.
Read the worked answer
M0.845 is 0.025 above MMO. On a swept wing the sequence is:
- the shock on the upper surface strengthens and moves aft, and the boundary layer behind it separates, producing buffet and a loss of lift and aileron effectiveness;
- the rearward movement of the centre of pressure produces a nose-down pitching moment (Mach tuck) that grows with Mach;
- with shock-induced separation the aircraft can lose pitch authority at exactly the moment it needs it.
Pulling up is the wrong instinct for two reasons. First, increasing the angle of attack increases CL, which lowers the buffet-onset Mach, so the separation gets worse rather than better. Second, it raises the load factor, and at FL410 the IAS is only about 260 kt - around 1.3 times the low-speed buffet speed - so an abrupt pull can put the aircraft into an accelerated stall while it is already shaking.
The correct response is to reduce thrust, extend speedbrakes and lower the nose gently to stop the acceleration, accepting the height loss; hold M below MMO until the buffet stops, then reassess mass and level. The aircraft should descend to a level where the corridor is wider, and the event should be reported.
3. Explain the role of the tropopause in this event, and why at constant Mach the angle of attack rises with altitude.
Read the worked answer
Above FL360 the ISA temperature is constant at −56.5 °C, so the speed of sound is constant at about 295 m/s. Two consequences follow:
- For a given Mach the TAS stops falling with altitude. Below the tropopause TAS at constant Mach falls as you climb because the air gets colder; above it, it stays fixed. A continued climb at M0.80 therefore no longer buys a lower TAS.
- Density keeps falling. The lift equation CL = 2W/(ρ V² S) forces CL up: with V nearly constant and ρ falling, CL rises roughly as 1/ρ. A higher CL means a higher angle of attack and a smaller margin to shock-induced separation.
That is why the low-speed buffet Mach rises with altitude (it is the Mach at which CL reaches the buffet value) while the high-speed limit stays at MMO. The coffin corner is simply the two boundaries approaching each other.
A temperature deviation does not change the buffet Mach at a given pressure altitude: dynamic pressure q = 0.5 γ p M² depends only on pressure and Mach, so at a fixed pressure altitude and Mach the wing sees the same CL whether the day is ISA+12 or ISA−20. Temperature does change the TAS, the fuel flow and the climb performance, which is why a warm day hurts the climb but not the buffet margin directly.