Compressibility, Mach number and shocks

Mach compares speed with a pressure-wave speed

The local speed of sound depends primarily on absolute temperature in the ideal-gas model.

A temperature-based ratio

M = V/a and a = √(γRT). Use absolute temperature in kelvin. In ideal air with constant γ and R, lower temperature means lower speed of sound, so the same TAS corresponds to a higher Mach.

Compressibility effects depend on Mach rather than TAS alone. The local speed over an aerofoil can exceed the free-stream speed, so local Mach can reach 1 while the aircraft free-stream Mach is still subsonic.

Critical Mach number

Critical Mach is the lowest free-stream Mach at which sonic flow first appears locally on the aircraft under the specified condition. It is not the Mach at which every surface point becomes supersonic.

Thickness, camber, CL and sweep affect the local acceleration and therefore the critical condition. A single critical Mach number is not fixed across every loading and configuration.

Keep absolute temperature in the sound-speed calculation

At T = 220 K, a = √(1.4 × 287.05 × 220) ≈ 297.35 m/s. An aircraft at TAS 240 m/s is therefore at M ≈ 0.807. At 288 K, a is about 340.20 m/s and the same TAS is M ≈ 0.705. Changing temperature changes the Mach ratio even when the aircraft’s speed through the air is held fixed.

Using Celsius directly would give the wrong physical result because the square-root relation requires absolute thermodynamic temperature. The specific-heat ratio and gas constant also belong to the stated ideal-air approximation. Atmospheric pressure does not appear independently in this temperature form of the ideal-gas sound-speed expression.

The laboratory holds Mach rather than TAS when you change temperature, so its TAS readout changes. State that control constraint before comparing with the fixed-TAS example above. Then raise Mach toward the supplied critical value and distinguish the first local sonic condition from the free-stream condition M = 1 and from a certified maximum operating Mach.

The shock is a rapid compression

A shock is a thin region with an abrupt change of flow properties, not a solid barrier at M 1.

Across a compression shock

Static pressure, density and temperature increase across a shock. For a normal shock the flow changes from supersonic to subsonic. Total pressure decreases: the process is irreversible.

The pressure rise can make the downstream boundary layer separate. Shock-induced separation increases drag and can produce buffet or control changes.

Wave drag and design

Wave drag can rise rapidly as local supersonic regions and shocks strengthen. The drag-divergence Mach is a practical drag-rise characteristic, distinct from the first local sonic point.

Thinner or suitably shaped sections, sweep and careful area distribution can help control compressibility effects. The laboratory uses an illustrative drag-rise curve and explicitly does not derive a certified MMO.

Explain the drag rise without an equal-energy error

Imagine a local supersonic region over an aerofoil ending in a shock. Downstream static pressure is greater, so the boundary layer must cope with a rapid pressure increase. If it separates, the pressure distribution and drag change further. The shock and the separated layer are related but distinct parts of the flow response.

A higher downstream static temperature does not mean useful propulsive energy has been created. The shock is irreversible and total pressure falls. That loss reduces the flow’s ability to do useful work and accompanies the compressibility drag penalty. Do not apply the reversible, isentropic relations across the shock itself.

Use the laboratory’s drag-rise curve to compare a point below the supplied critical Mach with one above it. The curve does not solve shock position or strength. A proper quantitative shock calculation would need upstream Mach and the shock geometry, while a complete aircraft buffet prediction would also need the wing loading and boundary-layer interaction. Identify those missing inputs before making a stronger claim.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.