What is the pressure distribution around a supersonic wing?

Question

In subsonic flight the lift manifests itself at 25% of chord, but shifts to 50% of chord when the airplane goes supersonic.

Wondering about that made me think that the reason might be that there is high-pressure in front of the wing´s top-point like there is at the bottom in front of the low-point, and low pressure behind the low-point of the wing like there is behind the top-point.

Assuming a symmetrical biconvex wing profile, that would put the centre of lift the 50% of chord.

A symmetrical biconvex wing going straight forward would produce no lift, so it has to be put at an angle to compensate for the weight of the airplane and the Mach-tuck, but still the lift would manifest itself at 50% of chord "seen my way" - and that gets more and more the faster the plane goes as the AoA gets closer to 0.

A couple of extra questions: at what AoA is a fighter (F-16/18/22/35/Rafaele/Typhoon/Gripen) flying with in low (M 1.3) and high (M 1.8) supersonic flight?

Do fighters have symmetrical biconvex wings or do their wings have a camber?

Answer 1

Normally, supersonic fighter wings for which airfoil information is published use a very thin NACA 6-digit section with very little camber, such as

Aircraft                root airfoil      tip airfoil
McDonnell Douglas F-15  NACA 64A006.6     NACA 64A203
General Dynamics F-16   NACA 64A204       NACA 64A204
Lockheed-Martin F-22    NACA 64A?05.92    NACA 64A?04.29

This information is from The Incomplete Guide to Airfoil Usage by Dave Lednicer. As you can see, the F-16 uses camber throughout, indicated by the 0.2 design lift coefficient of the airfoil, while the F-15 uses an uncambered root airfoil.

Those airfoils are chosen because flow around them at supersonic flight speed is still heavily influenced by subsonic flow characteristics as long as wing sweep allows for a subsonic leading edge. This produces nose suction, and flow around the wingtips disturbes the pure supersonic flow characteristics even when the leading edge is supersonic.

How the idealised flow around a supersonic airfoil looks is explained in this answer.

The angle of attack in supersonic flight depends on air density and load factor, but generally is only a few degrees because drag increases with the square of angle of attack. In other words, if the plane flies at high angle of attack, it decelerates to subsonic speed quickly.

The angle of attack in straight flight depends on altitude, wing loading and aspect ratio and grows with decreasing air density. Normally, at low level the maximum dynamic pressure limit and engine thrust will only allow very low supersonic speeds around Mach 1.1 to 1.3. Only above 20.000 ft will the envelope expend enough to make flight at Mach 1.8 possible.

For a typical wing loading of $\frac{m}{S}$ = 300 kg/m² and Mach 1.3 at 10.000 ft (air density $\rho$ = 0.9 kg/m³, speed of sound $a$ = 330 m/s) the angle of attack is $$\alpha = \frac{2\cdot m\cdot g}{\rho\cdot (Mach\cdot a)^2\cdot S\cdot c_{L\alpha}} \approx 0.5°$$ with a typical lift curve slope of a supersonic wing of $c_{L\alpha}$ = 4.

Answer 2

In general, the combat aircraft do have cambered wings. Most of the combat aircraft use NACA 6-series was designed for low-drag at transonic speeds, as this is where they spend most of their flight.

Take the wing of the F-15 Eagle for example. The wing root is symmetrical, while it becomes cambered going outwards. According to the report on CAP-TSD Analysis of the F-15 Aircraft:

The wing root is a 6 percent thick symmetric airfoil. The wing decreases in thickness towards the tip, which is a 3 percent highly cambered airfoil. The F-15 wing has conical camber outboard of he 20 percent semi-span location.

F-15 wing airfoil shape; image from CAP-TSD Analysis of the F-15 Aircraft

There are a number of reasons for using camber- most of their flight is in subsonic speeds anyway and having a cambered airfoil helps keep the aircraft more or less level, as the angle of attack is only a few degrees anyway; any further increase will incur a drag penalty due to the speeds involved.