Shock Waves - ATPL 081 — Principles of Flight

The previous lesson defined the speed of sound as the speed at which the air ahead is warned. This lesson is about what happens where the warning fails. Over a transonic wing, part of the flow runs faster than sound: inside that region no pressure signal can make headway upstream, so the air arrives at the pressure rise behind the wing's suction region completely unprepared, and the adjustment it could not make gradually, it makes all at once. The wall where that happens is the shock wave, and everything the rest of this module studies (the drag rise, the pitch change, the buffet) begins at one.

What a shock wave is

A shock wave is an extremely thin front (a small fraction of a millimetre) standing in a supersonic flow, across which the flow properties change abruptly: the air is compressed and slowed almost discontinuously. It exists because supersonic air cannot be told in advance. Subsonic flow approaching higher pressure feels that pressure ahead of time and decelerates smoothly over a long distance; supersonic flow outruns its own pressure signals, meets the higher pressure with no warning at all, and must complete its entire deceleration and compression in the thickness of a few molecular collisions. A shock wave is that forced, instantaneous adjustment, held stationary relative to the wing that causes it.

Through a normal shock

The shocks that stand on a transonic wing are normal shock waves, normal in the geometric sense: the front stands essentially perpendicular to the local flow and to the wing surface it rises from. Crossing one, every property jumps in the direction compression demands. The velocity falls abruptly: from supersonic ahead to subsonic behind, and with the air packed together, the static pressure, static temperature and density all rise. Two consequences hide inside the temperature rise, and the exam asks for both. First, the local speed of sound rises behind the shock, since warmer air carries sound faster. The Mach number behind therefore falls for two reasons at once (the flow is slower, and it is measured against a faster sound speed) and lands below 1. Second, although the static pressure jumps up, the total pressure falls: the compression in a shock is violent and irreversible. No energy vanishes; it is degraded: ordered kinetic energy becomes disordered heat, unrecoverable as pressure, so the total pressure falls. That loss is physical, not bookkeeping; it is the origin of wave drag, the next lesson's opening subject.

How the shock system grows with Mach

Now put the shock on the wing and turn the flight Mach number up. At the critical Mach number the fastest point of the upper surface just touches the local speed of sound: nothing dramatic yet. A little beyond it, a pocket of supersonic flow opens over the forward upper surface, and where that pocket must return to subsonic speed a normal shock stands on the upper surface, typically around mid-chord. From there, more Mach means more of everything: the supersonic pocket deepens and lengthens, the shock strengthens and moves aft, and because the lower surface accelerates the flow too, just less fiercely at positive lift, a second supersonic pocket eventually opens underneath, ended by a second shock on the lower surface. As the flight Mach number pushes toward 1 the two shocks march toward the trailing edge, the lower one running aft quickly over the flatter, less-cambered lower surface once its pocket exists, typically arriving at the trailing edge first — until just below Mach 1 both stand at the trailing edge with nearly the whole wing supersonic. What those marching shocks do to lift, drag and pitching moment on the way is the next lesson.

Angle of attack moves the shock

Mach number is not the only control on the system: the angle of attack works it too, at constant Mach. Raising α deepens the suction over the upper surface: the local flow there runs faster, the supersonic pocket ahead of the shock reaches a higher local Mach number, and the shock that ends it must kill a bigger speed difference; its intensity increases. At the same time the harsher pressure recovery behind the strengthened shock presses on the boundary layer, separation creeps in behind the shock, and the shock's position moves forward toward the leading edge. A strengthening, forward-moving shock with separation growing behind it is the onset of shock stall: the buffet boundaries of the stall module begin here, at their aerodynamic root. Notice the practical reading: at high altitude and high Mach, pulling g is a Mach event — a turn or a gust that raises α stresses the shock system exactly as extra Mach would.

What the exam asks

A short, dense lesson, and the property-change list is asked almost verbatim. The overview, following the learning objectives:

Describe the changes across a normal shock: static temperature, static and total pressure, velocity, local speed of sound, Mach number, density

Describe its orientation: perpendicular (normal) to the local flow and the wing surface

Explain the influence of increasing Mach number at positive lift: shock strength, aft movement, the second shock on the lower surface

Explain the influence of angle of attack at constant Mach: intensity up, position forward

What a shock wave is

Through a normal shock

Check you understood

How the shock system grows with Mach

Angle of attack moves the shock

What the exam asks