Buffet Boundaries and Maximum Altitude

For a jet transport the word ceiling covers several different limits. The flight manual fixes a maximum operating altitude that may never be exceeded. Below it, how high the aeroplane can cruise on a given day depends on two things that change during every flight: whether the engines can still produce the thrust needed to hold the cruise speed, and whether the wing still has room to manoeuvre between the low-speed and high-speed buffet boundaries.

The highest level that satisfies all of these at the current weight and temperature is the maximum altitude the crew, or the flight management system, works with. Understanding how it is built explains why a heavy aircraft on a hot day may be several thousand feet below its certified ceiling, why the buffet margin matters more than the stall warning at cruise levels, and why the band of usable speeds closes into the coffin corner as altitude rises.

Absolute, service and certified ceilings

The classical ceilings come from climb performance. As altitude increases, thrust or power falls with air density faster than the drag at the climb speed changes, so the excess that produces a climb shrinks.

• The absolute ceiling is the altitude at which the maximum rate of climb has fallen to zero. The aeroplane can hold level flight there at only one speed, and the best angle of climb speed Vx and the best rate of climb speed Vy, which move towards each other during the climb, have met.
• The service ceiling is the more practical figure: the altitude at which the best rate of climb has fallen to 100 ft/min for a piston aeroplane. For a jet, EASA ATPL performance material uses 500 ft/min at maximum continuous thrust.

Both are lower at a higher mass and in warmer air. The absolute ceiling is of little practical use, since the climb near it is so slow that it would take an impractically long time to reach.

The maximum operating altitude, often called the maximum certified altitude, is different in kind. It is a fixed limitation established at certification, printed in the limitations section of the flight manual as a pressure altitude, and it does not change with weight or temperature. The A319, A320 and A321 are limited to 39,100 ft without modification and 39,800 ft with one; the Boeing 737 NG and MAX and the Embraer E-Jets to 41,000 ft. Separate, lower limits apply to particular configurations: both the A320 and the 737 NG are limited to 20,000 ft with flaps or slats extended.

Thrust-limited maximum altitude

In cruise, the thrust-limited maximum altitude is the altitude at which the thrust required to maintain the cruise speed equals the maximum cruise thrust available. EASA ATPL performance material often uses the term maximum altitude for this thrust-limited altitude alone. A turbofan's thrust falls roughly with air density, so at FL370 it may produce only about a quarter of its sea-level thrust, while the drag at a given indicated airspeed hardly changes with height. The margin between the two therefore narrows as the aeroplane climbs.

Two factors move this limit during a flight:

• Mass. A heavier aeroplane needs more lift, flies at a higher angle of attack and has more induced drag at any speed, so it needs more thrust. The maximum altitude rises as fuel burns off.
• Temperature. On a warmer than standard day the air at a given pressure altitude is less dense and the engines give less thrust. FAA training material notes that ISA +15 °C can cost several thousand feet of maximum altitude, and it also increases fuel burn.

Low-speed and high-speed buffet

The second family of limits is aerodynamic. At the low-speed end of the envelope the wing approaches its maximum lift coefficient, the boundary layer separates and the airframe shakes: this is low-speed, or stall, buffet. In thin air the wing needs a high lift coefficient simply to support the weight at 1 g, and above about M 0.4 compressibility lowers the lift coefficient at which separation begins, so the low-speed buffet speed rises with altitude. On a flight envelope or buffet chart this low-speed limit is called the stall boundary.

At the high-speed end, above the critical Mach number, shock waves on the wing become strong enough to separate the boundary layer behind them and the result is high-speed, or Mach, buffet. Because the critical Mach number falls as the angle of attack rises, the high-speed buffet boundary moves to lower Mach numbers with increasing weight, altitude and load factor, and with a forward centre of gravity. Both kinds of buffet are described in detail in buffet and buffet margin.

The buffet onset chart

The flight manual of a jet transport presents the buffet limits as a buffet onset chart, also called a buffet boundary chart. For a given weight, centre of gravity and pressure altitude it shows the Mach numbers at which low-speed and high-speed buffet begin at 1 g, and how those Mach numbers converge as the load factor increases.

The inputs are the gross weight, the centre of gravity position, since a forward centre of gravity acts like extra weight, and the planned pressure altitude. The output is either the load factor, or bank angle, at which buffet begins at the planned cruise Mach number, or the pair of Mach numbers between which a chosen load factor is available.

Every factor that raises the angle of attack at a given Mach number, whether weight, altitude, a forward centre of gravity or a turn, narrows the gap between the two boundaries. Crews use the chart, or the flight management system that holds the same data, to check the manoeuvre capability of a level before climbing to it.

The 1.3 g manoeuvre margin

The manoeuvre margin, or buffet margin, is the extra load factor available before buffet onset. It is quoted in g. The 1.3 g buffet margin is the conventional figure used to set the maximum cruise altitude: the aeroplane must be able to reach 1.3 g, 0.3 g more than level flight, before either buffet boundary is met. From n = 1 ÷ cos φ, 1.3 g is the load factor of a level turn at about 40° of bank, and it also covers a moderate vertical gust. Some operations use a lower figure, such as 1.2 g; the operator's policy and the flight manual decide.

Type examples show how the margin reaches the flight deck:

• Airbus A320. The MAX REC flight level on the PROG page of the MCDU gives at least a 0.3 g buffet margin. The FMGS accepts a higher cruise level only if the margin there is still more than 0.2 g. Above 20,000 ft the lowest selectable speed VLS is corrected for Mach so that it keeps a 0.2 g buffet margin.
• Boeing 737 NG. With flaps up, the bottom of the maximum manoeuvre speed amber bar gives 1.3 g of manoeuvre capability to high-speed buffet, and the top of the minimum manoeuvre speed bar gives 1.3 g to the stick shaker below approximately 20,000 ft, and to low-speed buffet above it.

The margin matters most in turbulence. At a level with little margin, a gust or a routine turn can push the aircraft into buffet. The A320 procedure for flight in alternate or direct law at high altitude is to descend, and Airbus notes that about 4,000 ft below REC MAX significantly reduces the occurrence of stall warnings in turbulence.

The aerodynamic ceiling and coffin corner

If the aeroplane keeps climbing at constant weight, the low-speed buffet boundary rises in Mach number and the high-speed boundary falls. Eventually they meet. That altitude is the aerodynamic ceiling, also called the buffet-limited ceiling or coffin corner. There, only one speed can be flown at 1 g without buffet, and the buffet margin is zero: any turn, gust or speed change in either direction produces low-speed buffet on one side or Mach buffet on the other.

The coffin corner is a limit, never an operating point. The 1.3 g rule keeps aircraft well below it, and because the boundaries depend on weight, the aerodynamic ceiling of a heavy aircraft is lower than that of a light one. Some fly-by-wire types add protection at the low-speed edge: on the A320 the angle of attack at which high angle of attack protection begins is reduced as a function of Mach at high flight levels, so that it guards the buffet boundary rather than only the low-speed stall.

View full schematic

Maximum and optimum altitude together

The ceilings can be summarised as follows:

The maximum altitude used in flight is the lowest of the first three, and which one governs depends on the day. A heavy aircraft early in a long flight may be limited to around FL330 while its certified ceiling is FL410.

Optimum altitude is a separate idea: the level at which the specific air range is greatest for the current weight and speed. It too rises as fuel burns off, which is why long flights use step climbs, typically of 2,000 or 4,000 ft, to stay near it; operating within about 2,000 ft of the optimum keeps at least 99 per cent of the maximum specific air range. FAA training material notes that the optimum computed by a flight management system is typically about 2,000 ft below the maximum, and turbulence guidance often recommends staying below the maximum. The economics of the choice are covered in cost index and cruise economics.

Critical Mach number and Mach tuck

Air accelerates over the upper surface of a lifting wing, so the local Mach number there is higher than the free-stream value. The critical Mach number (Mcrit) is the free-stream Mach number at which the local flow somewhere on the aircraft, usually over the wing upper surface, first reaches M 1.0. Nothing is felt at Mcrit itself. Above it a pocket of supersonic flow develops, closed by a shock wave that strengthens and moves aft as speed increases, bringing wave drag, shock-induced separation and buffet (see high-speed flight).

Mcrit is not fixed. Higher weight, higher altitude and a turn all raise the angle of attack and so lower Mcrit, while sweepback and thin wing sections raise it. The maximum operating Mach number MMO, by contrast, is a fixed limit set with a margin below the Mach number at which shock effects become unacceptable. An aircraft that is heavy, high, turning or in turbulence can therefore meet high-speed buffet below MMO.

Mach tuck, also called high-speed tuck or tuck under, is the nose-down pitching tendency that develops above Mcrit on a swept-wing jet. On a swept wing with a thicker root section, shock-induced separation usually begins at the root. Lift is lost inboard and forward, so the centre of pressure moves outboard and, because of the sweep, aft, while the disturbed flow reduces the downwash at the tailplane and so its download. Both effects pitch the nose down, the speed increases and the effect deepens.

Conventional jets fit a Mach trim system that senses Mach number and automatically applies nose-up trim, by moving the elevator or trimmable stabiliser, as the Mach number rises. It works whether or not the autopilot is engaged. Fly-by-wire aircraft such as the A320 compensate within their flight control laws instead. The recovery from an overspeed uses reduced thrust, speedbrakes where permitted and a gentle pull, never an abrupt input; the aircraft manufacturer's procedure governs.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.