5.2 Critical Mach Number, Shock Waves & Compressibility Buffet

5.2 Critical Mach Number, Shock Waves & Compressibility Buffet

When a swept-wing jet accelerates toward cruise Mach, the wing does not need to fly at M = 1 for serious compressibility problems to begin. EASA Part-66 Module 08 requires you to understand critical Mach number, how shock waves form, and why compressibility buffet appears — because these set $M_{MO}$, buffet margins, and Mach trim requirements on modern transports.

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Critical Mach Number ($M_{crit}$)

Critical Mach number ($M_{crit}$) is defined as the freestream Mach number at which the airflow first reaches Mach 1 at some point on the aerofoil surface — almost always on the upper (suction) side where the camber accelerates flow.

Below $M_{crit}$: entirely subsonic surface flow; shocks absent. At $M_{crit}$: a sonic point appears (often near max thickness, ~30–40% chord). Above $M_{crit}$: a supersonic pocket forms on the upper surface, terminated by a shock wave.

For a typical 1950s straight-wing section, $M_{crit}$ might be ~0.70. A modern supercritical section on a swept wing may permit cruise at M 0.82–0.86 because the shock is weaker and farther aft.

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Shock Waves — Normal and Oblique

A shock wave is a thin region of extremely rapid compression where flow properties change almost discontinuously. Shocks form when supersonic flow must slow to subsonic conditions (e.g., at the downstream end of a supersonic pocket on a wing, or at a pitot intake lip).

  Freestream M < 1                    Supersonic pocket on upper surface
        |                                      ___________
   =====|=====>  subsonic everywhere          /           \  supersonic region
        |                                     |     |       \
   Wing surface                               |    SHOCK → subsonic wake
                                              Wing surface

  Normal shock (M2 ≈ 1)          Oblique shock (M2 may remain > 1)
       |  |                           /
  ====>|  |====  subsonic             /====>  turned flow
       |  |                         /
   perpendicular                  angled to flow

Normal shock: Shock front perpendicular to flow. Large pressure, density, and temperature rise; velocity drops from supersonic to subsonic in one step. Maximum entropy rise — very high wave drag.

Oblique shock: Inclined at angle $\beta$ to upstream flow. Weaker than a normal shock at the same upstream Mach; downstream flow may remain supersonic (weak oblique shock) or become subsonic (strong oblique shock).

Across any shock:

• Static pressure, temperature, and density increase
• Total pressure decreases (irreversible — energy lost to drag and heating)
• Boundary layer may separate if adverse pressure gradient is severe

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Wave Drag, Centre-of-Pressure Shift & Mach Tuck

The pressure jump across a shock adds a component of wave drag — drag unrelated to skin friction or induced drag. As Mach increases past $M_{crit}$, wave drag rises sharply; the drag divergence Mach is where $\mathrm{d}C_D/\mathrm{d}M$ becomes steep.

Simultaneously, the centre of pressure (CP) on the wing moves aft because suction aft of the shock weakens and the shock-induced pressure rise acts predominantly on the rearward upper surface. This nose-down pitching tendency is called Mach tuck. Transport aircraft employ:

• Mach trim systems (automatic stabiliser or THS input)
• Swept wings and washout
• Limiting $M_{MO}$ in the AFM

If Mach tuck is not trimmed and the aircraft accelerates beyond the approved envelope, dive tendency can intensify — a flight-test and certification concern, not merely academic theory.

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Compressibility Buffet

Compressibility buffet (shock buffet) is an aerodynamic oscillation caused by intermittent shock-induced boundary-layer separation on the wing. The shock position moves forward and aft; the separated wake grows and collapses, producing vibrations felt in the fuselage and often registering on g meters.

Characteristics:

• Onset near buffet onset boundary in the flight envelope — often a few hundredths of Mach below $M_{MO}$
• Worsens at higher altitude (lower Reynolds number, thinner boundary layer)
• Worsens at higher g or angle of attack (higher local suction)
• Distinct from stall buffet (low speed, low Mach, wing-root separation)

Pilots use buffet as a tactile warning; engineers document buffet boundaries during certification. For maintenance, recurring buffet reports at normal cruise may indicate wing contamination (ice, damage, mis-rigged high-lift devices) or AFM exceedance — not something to dismiss as "turbulence."

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Worked Example 5.2.1: Identifying $M_{crit}$ from Description

Problem: Flight test notes state: "At M 0.75, schlieren imaging shows entirely subsonic flow. At M 0.78, a local sonic point appears at 38% chord on the upper surface. At M 0.80, a terminated supersonic region and visible shock are present." What is $M_{crit}$?

Solution: $M_{crit}$ is the lowest freestream Mach where local M = 1 first appears — here M 0.78. At M 0.80 the shock is fully formed, which is above $M_{crit}$.

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Worked Example 5.2.2: Buffet vs Stall

Problem: A B737 at FL 370 experiences moderate airframe rumble at M 0.82 and 1.25g in light turbulence. IAS is 245 kt; stall speed at this weight is 195 kt IAS. Is compressibility buffet plausible?

Solution: IAS is well above stall speed — stall buffet is unlikely. At FL 370, M 0.82 is near typical $M_{MO}$ for this class; high g increases local $C_L$ and lowers local $M_{crit}$. Compressibility buffet is plausible — check AFM Mach/g envelope and whether the aircraft is at or above buffet onset.

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Exam Traps

1. $M_{crit}$ is a freestream value, not the local peak Mach on the surface (which can be > 1 when $M_\infty = M_{crit}$).
2. Shocks always increase static temperature — aerodynamic heating begins here (Section 5.3).
3. Buffet at high altitude/high Mach is not always stall — check Mach and g limits first.
4. Wave drag appears only with shocks, not in purely subsonic flow.
5. Mach tuck is a CP shift, not engine failure or CG movement — though it affects pitch trim loads on the tailplane.