Exceeding the Critical Mach Number

The critical Mach number

First the definition, precisely: the critical Mach number,

M_{CRIT}

, is the flight Mach number at which the local flow somewhere on the aircraft (in practice, at the fastest point of the wing's upper surface) first reaches exactly Mach 1. The aircraft itself is still well below the speed of sound; a typical jet transport wing has a critical Mach number around 0.7 or a little above. It is not a fixed property of the aeroplane, and the exam asks what moves it. The logic is one chain used four times: anything that makes the wing work harder (a higher lift coefficient) deepens the suction, speeds the upper-surface flow, and brings the first sonic point earlier:

Angle of attack — a higher α means faster upper-surface flow, so the local Mach 1 point arrives at a lower flight Mach number: increasing α reduces the critical Mach number.

Weight — a heavier aircraft needs more lift at the same speed, hence a higher α: more weight, lower critical Mach number.

Manoeuvres — a turn or a pull-up demands extra lift through the load factor, which is extra α again: manoeuvring reduces the critical Mach number, the same pulling-g-is-a-Mach-event reading as the shock lesson.

CG position — with the CG further forward, the tailplane must push down harder to balance, and the wing must lift that extra download too: more lift, more α: a forward CG reduces the critical Mach number slightly.

Lift above the critical Mach number

Hold the angle of attack fixed and let the Mach number climb, and the lift coefficient traces the left-hand curve below. Through the compressible-subsonic regime

C_L

rises: the compressibility distortions of the speeds lesson deepen the pressure differences, so the same shape at the same angle lifts a little more. The rise continues shortly past the critical Mach number and peaks. Then the shock takes over: strengthening as Mach climbs, it drives the boundary layer behind it into separation: the shock stall, and the lift falls steeply through the transonic regime, recovering only partially as Mach 1 is passed and the flow pattern settles. The same shock-driven separation caps the whole curve family:

C_{L\,max}

falls as Mach rises, and the critical angle of attack falls with it — the wing lets go at a smaller angle when a shock is pressing on its boundary layer.

The falling $C_{L\,max}$ is what bends the stall boundary in the speeds lesson's corridor figure. At low altitude the 1g stalling IAS is effectively constant: the aircraft stalls at the same indicated speed regardless of the day. But at high altitude that constant-IAS stall sits at a high Mach number, where compressibility has already eaten into the maximum lift coefficient, so the 1g stalling IAS rises with altitude in the upper flight levels. The stall wall leans in from the left exactly as the Mach limit leans in from the right.

Wave drag

The drag of the shock system is called wave drag, and it has two parts. The first is the shock itself: the shock lesson showed that part of the total pressure (the flow's recoverable energy) is destroyed across the front, and energy taken from the flow is drag by another name. In the transonic drag rise the second part is usually the larger: the separation the shock provokes, the thickened and detached boundary layer behind it, with all the form drag that brings. On the right-hand curve above, the result reads simply: $C_D$ at constant α runs flat to the critical Mach number, creeps upward just beyond it as the first weak shock appears, and then rises steeply from the drag-divergence Mach number, $M_{DD}$ (conventionally the point where the drag rise becomes serious), peaking around Mach 1. The relation between the two thresholds is exam-stated: $M_{DD}$ lies above $M_{CRIT}$ , typically by a few hundredths of a Mach. On the polar, high Mach hurts both axes: more $C_D$ at every $C_L$ and a lower $C_{L\,max}$ — the polar shifts right and is capped lower, and the origin tangent, the best lift-to-drag ratio, flattens.

Push past drag divergence and the effects arrive as a package; the exam lists four:

Drag rise — steep and getting steeper: holding the speed suddenly demands far more thrust, and without it the speed decays on its own.
Instability — the shocks and their separated regions shift and breathe; lift and pitching moment fluctuate, buffet shakes the airframe, and the aircraft's stability degrades.
Mach tuck — the nose-down pitching tendency of the next section, arriving exactly when the aircraft is already fast.
Shock stall — the shock-induced separation collapsing lift, felt as buffet and, pressed further, as a stall entered from the FAST side of the envelope.

Why cruising past the critical Mach number pays

Given all that, the speeds lesson's claim: transports cruise above their critical Mach number, needs its justification, and it lives in the gap between the two thresholds. Between $M_{CRIT}$ and $M_{DD}$ the drag penalty is still small, and an aeroplane designed for that corner, the supercritical aerofoil of the next lesson, collects three connected advantages there. The speed-to-drag ratio improves: each knot of extra cruise speed costs very little extra drag while the rise is still shallow. Because fuel burn follows drag while distance follows speed, the specific range (the kilometres flown per kilogram of fuel) improves with it. And it buys height: climbing at constant Mach raises the required lift coefficient, and a wing that can carry a high lift coefficient at high Mach without drag divergence can climb until that coefficient sits at its best lift-to-drag ratio, a higher optimum altitude, where the engines and the airframe are at their most efficient. That triangle (speed, range, altitude) is why the entire modern transport fleet cruises a few hundredths above its critical Mach number, on wings built to make that affordable.

Mach tuck

Now the pitching moment. Two movements conspire as the shocks develop. First, the shock lesson's aft march: as the supersonic regions extend rearward, previously idle rear stretches of the chord carry load, and the wing's centre of pressure moves aft, far aft, approaching the half-chord as the wing goes fully supersonic. Lift acting further behind the centre of gravity is a growing nose-down moment. Second, the redistributed lift and the shock-disturbed flow REDUCE the downwash arriving at the tailplane: the tail flies at a higher effective angle, its download fades, and its nose-up contribution weakens. The sum is the tuck under, or Mach tuck: above the critical Mach number, increasing Mach pitches the aircraft increasingly nose-down.

Mach trim

Certification requires that an aircraft resist speed changes with the correct control feel: push forward to go faster, pull back to go slower, all the way to the maximum operating Mach number. Mach tuck breaks exactly that requirement, so aircraft that cruise in the tuck region carry a Mach trim system: an automatic system that, as the Mach number rises, applies progressively more nose-up trim to cancel the growing nose-down moment: on most types by adjusting the trimmable horizontal stabiliser or biasing the elevator, on some designs even by pumping fuel aft to shift the centre of gravity. The pilot feels nothing: the system's whole purpose is to make the stick-force-versus-speed gradient feel conventionally stable through the cruise Mach range.

If the Mach trim system fails, the aeroplane has not become uncontrollable — it has become an aeroplane that must be kept out of the region the system was compensating. The standard corrective measures: reduce Mach and observe the lower maximum operating Mach number the failure procedure prescribes, flying the remainder of the cruise below the tuck region and trimming manually with extra attention to speed excursions.

Controls behind the shock

Last, the controls themselves. A conventional control surface (an elevator, an aileron) works by changing the camber of the aft part of a surface, and in subsonic flow that change telegraphs itself forward: the whole chord's pressure field adjusts, which is where most of the control's power comes from. Above the critical Mach number that telegraph line is cut. Pressure changes cannot propagate forward through the supersonic region ahead of the shock, so deflecting the control re-loads only the stretch of chord behind the shock; only a fraction of the surface's loading responds to the deflection: control effectiveness is reduced. Shock-induced separation over the hinge region blunts the response further, and the interaction can set the surface into a high-frequency oscillation known as control buzz. The design answers (fully powered controls, the all-moving tailplane that moves the whole surface instead of a flap on it) belong to the control module; the aerodynamic problem they answer is this one.