# Laws of aerodynamics after breaking the sound barrier

my knowledge of physics is not very extensive, so I hope my question isn't too stupid.

I know that when (for instance) a plane breaks trough the sound barrier, the laws of the aerodynamics change.

But I don't know why because the plane is still being carried by the same air, only it's travelling much faster and this creates a state where the air is (in relation to the plane) much more dense. But I can't make out how this would have an effect on these aerodynamic laws.

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It's related to the compressibility of the fluid and the change from laminar flow to turbulent flow.

At high speeds, the air flow around an airplane tends to change from the laminar to turbulent, and the pressure applied is enough to make the air sufficiently compressible.

Read the Laminar vs turbulent flow section of this wikipedia atcile to get a better understanding of laminar and turbulent flow: http://en.wikipedia.org/wiki/Fluid_dynamics

Read the Fluid dynamics section of this wikipedia article and you should get a better understanding of compressibility: http://en.wikipedia.org/wiki/Compressibility

Cheers!

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It has absolutely nothing to do with laminar or turbulent flow. – Peter Kämpf Jan 16 '15 at 22:38

The main thing is that small pressure changes will not race ahead of the airplane once it flies at supersonic speed. Instead of "alerting" the air with a gentle change in pressure, it "surprises" them all of a sudden. This causes rapid pressure changes, called shocks.

The next important effect is that the magnitude of density changes becomes bigger than that of pressure changes in supersonic flow. At very low speed, you will find only pressure changes because the flowing medium behaves like an incompressible gas. At high supersonic speed, however, pressure changes are small and the main flow effects are on the local density of the gas.

## Subsonic flight

In subsonic flow, the oncoming air is first decelerated ahead of the wing, then swiftly accelerated when it flows around the strongly curved nose section of a wing. This acceleration is the consequence of the wing's curvature. See it this way: If the airflow would be along a straight line, it would move away from the surface, creating a local vacuum. In reality, the air settles at a compromise between the straight path and following the contour, creating decreasing pressure along a surface with increasing curvature and increasing pressure along surfaces with decreasing curvature. More precisely, it is always in an equilibrium between inertial, viscous and pressure forces.

This suction not only bends the airflow into following the wing's contour, but also accelerates the air ahead of it. The lower the pressure, the more the air speeds up, such that the total energy of air (the sum of pressure and kinetic energy) stays constant. Therefore, pressure and local speed change in sync.

If the wing moves at high subsonic speed, the curvature-created suction accelerates the flow such that it reaches supersonic speed. Now something odd happens: Supersonic flow accelerates further when subsonic flow would decelerate. This is caused by the change in density which happens at supersonic speed. Now we have a supersonic pocket of air on the upper surface of the wing where speed increases and density decreases downstream, and the surrounding subsonic air sees little change in density.

This cannot last, and at some point this supersonic pocket collapses. This happens instantly in a shock, and in a straight shock density increases suddenly and speed decreases such that the Mach number after the shock is the inverse of the Mach number ahead of the shock. Aft of the shock, you have subsonic flow again.

## Supersonic flight

Once the aircraft accelerates to Mach 1, this shock moves aft to the trailing edge. Now the forward parts of the airplane are fast enough to "surprise" the air they fly into, and the consequence is a straight shock at those parts (mainly the fuselage tip, air intakes and straight leading edges).

If the aircraft accelerates further, the straight shock is bent backwards, because layers of air further away from the fuselage tip or the leading edge will "learn" later of the arrival of the airplane. The result is the Mach cone of a shock, and also the trailing edge shock becomes oblique. Both leading edge and trailing edge shock produce the double-shock system that causes sonic booms, because these shock waves can travel all the way to the ground (if the local speed of sound in the air permits). See the picture above (shamelessly lifted from Wikipedia) which shows how small pressure changes propagate away from the moving aircraft.

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