April 06, 2018, ©. Leeham News: In the last Corner, we discussed the pressure distribution of an aircraft’s wing when producing lift. This was with a conventional airfoil (though of the more laminar flow type).
Now we continue by looking at how a modern airliner wing achieves lift by using a “supercritical” airfoil.
The wing profile we studied in the last Corner works well to about Mach 0.6. At higher speeds, the peaky suction pressure distribution on the top of the wing causes a large speed-up of the flow into a supersonic flow. As the flow goes back to subsonic flow on the back of the profile, it will be through the strong normal shock wave we discussed in aircraft drag reduction Corners.
To fly at the cruise speeds of today’s airliners (M0.75-0.85) we need wing profiles which speed up the air less on the topside of the airfoil. Such airfoils are called “supercritical” airfoils as they keep the speed of the air on the top side close to the critical Mach for supersonic flow (still supersonic flow, but not as deep supersonic as on a conventional airfoil).
Figure 2 shows such an airfoil which was developed by Embraer for its first Jet airliner, the Emb145.
The blue wing profile and pressure curves are for a conventional NACA 23012 airfoil flying at M0.75 and the red the airfoil developed by Embraer for the ERJ145.
As we learned in the first Corner on lift, the pressure around a wing and its airflow speeds are related. Low pressure = high airflow speed. This is true also for compressible flow, tough Bernoulli’s theorem, which defines the mathematical relationship between the pressure and the speed, is not exact at these speeds.
As in the last Corner, the pressure scale (Cp) is inverse. The top of the scale is high suction (Cp is – 1.4), lifting the wing’s top surface and the bottom (Cp 0.8) a high static pressure, pushing on the wing’s bottom surface.
For the conventional wing, the higher blue curve is how the pressure changes on the wing’s top side. At first, the flow is slowed down when it hits the wing’s nose (slowing flow means the pressure goes higher than the surrounding air. It’s at Cp=0.5 at first).
The flow starts curving around the top of the nose, and as it’s curving around a convex surface the flow’s speed increases. The pressure drops all the way to -1.1. This suction peak creates a lot of lift but also a fast supersonic flow (Past Cp = -0.6 the flow is supersonic).
At 40% of the wing profile, the flow returns to subsonic through a strong direct shock. As we learned in the drag Corners, this increases the pressure and the strong shock causes boundary layer separation. We have high transonic drag.
This is what happened to the P-51 Mustang during WW2. It has a wing profile of the type we discussed in the last Corner. When diving to increase speed, the Mustang gets strong Supersonic flow on the wing’s top side and the increased drag keeps it from flying faster.
As we discussed in the drag Corners, the fully conventional airfoils of the Spitfire and Messerschmitt were even worse. The laminar flow airfoil of the Mustang didn’t create a lot of laminar flow, but its form kept the suction peak on the top side lower and by it the transonic drag lower than the other WW2 fighters.
To come to an even better wing profile than the Mustang’s, Richard Withcomb of NASA experimented with wing profiles with a lower suction peak. He could achieve this if he formed the airfoil with a less curved top side (the red airfoil in Figure 2. The form now resembles a whale, my comment).
The top red pressure curve for the wing’s top side now passes lightly into a supersonic flow (Cp = -0.6) and passes back to subsonic flow at 70% of the profile through a weak shock, which keeps the boundary layer intact.
The problem was, the lower transonic drag didn’t come for free. The lower suction meant lower lift of the airfoil for the same forward speed of the aircraft. To regain lift, the bottom of the airfoil was given a concave finish, slowing the airflow and pushing it down. This increased the bottom pressure of the wing (bottom red curve past 70% of the profile), by it increasing lift.
The flat top suction pressure and the high rear pressure on the bottom surface of the wing, have given these airfoils the nicknames “flat rooftop” or “back-loaded” airfoils.
The early methods of designing airfoils were based on shaping airfoils and measuring their lift, drag and tipping moment in wind tunnels. With the introduction of Computerized CFD (Computational Fluid Dynamics), one could do it the other way.
The designer decided a desired pressure distribution (and by it the airflow speeds around the airfoil). The computer would then calculate the airfoil shape which would produce this pressure profile.
This is the way the Embraer designers developed the Emb145 airfoil and wing. In the next Corner, we shall look at how we master the desire of the wing to tip over backward.