# What is the highest and lowest air pressure induced by an aircraft at supersonic speeds?

When an aircraft is supersonic, is the greatest pressure at the wing leading edge, below the wing surface or in front of the shock wave, or another location all together.

Also is the lowest pressure at the upper wing surface or behind the shock wave or another location all together?

Is there a pressure range for these values just to give a point of reference?

When an airplane goes supersonic, it creates a shock wave in front of it. The shock wave compresses the air and slows it down so the speed component orthogonal to the shock front becomes subsonic. See it this way: The airplane sort of creates it's own cocoon of denser and less voluminous air to fly in.

As in subsonic flow, the highest pressure is found behind the tip of the shock wave, in a stagnation point, a point where the speed is reduced to zero, like on the leading edge. The lowest pressure and density is usually found before the shock wave, this is the normal atmospheric pressure. Differently to subsonic flow, in supersonic flow every change in flow speed comes with a large change in density.

There are 2 types of shock waves:

• the normal shock wave:
They have nice tables where you can see the speed, pressure and density behind the wave. This shock wave mostly occurs in pipes, like a pitot intake.
• Oblique shock waves:
These shock waves are called strong when the mach number after the wave is below 1, and weak when the speed after the wave is still supersonic.

NASA has some nice programs to show how different types of shock waves are formed and how they interact, you can find them here.

The highest pressure is found at the stagnation point of a part which directly faces the oncoming flow. This is the stagnation pressure and it rises with the square of the flow's Mach number. Since a supersonic wing is usually swept, its leading edge will not reach the full stagnation pressure because the flow's speed component orthogonal to the leading edge is not changed.

The lowest pressure is normally found on the upper side of the fuselage. Air is so rarefied there that the vertical tail surface becomes increasingly ineffective at higher Mach numbers. The inclination of the local surface away from the direction of movement can be used with the Prandtl-Meyer expansion calculation to give you a rough idea how low this pressure can drop.

• After a compression shock, subsonic speed is only reached normal to the shock front, so speed past an oblique shock is normally still supersonic. Only the component of flow perpendicular to the shock front will become subsonic. Commented Feb 10, 2022 at 13:18
• That is correct. Not sure how I can correct my answer to correct that, my knowledge has faded a few bits. Commented Feb 10, 2022 at 13:51
• Should I give it a try? Commented Feb 10, 2022 at 15:35
• @PeterKämpf: You are very welcome to edit as you please. Commented Feb 14, 2022 at 13:36
• As an addition to the range of pressures (Approximations for aircraft design): For the static pressure range the lowest pressure can be calculated with c_p,min = 0.8 * c_p,vac where the vacuum pressure is calculated by c_p,vac = -2/(k*Ma^2) with k the Heat capacity ratio and Ma the Mach number of the outer flow. cp = (2*alpha) / sqrt(Ma^2-1). Both are approximations, but can give a first approximation. further reading: There is a good book tackling hypersonic aerodynamics. It is by E.H. Hirschel "Selected Aerothermodynamic Design Problems of Hypersonic Flight Vehicles". Commented Feb 14, 2022 at 19:38