Bjorn’s Corner: New aircraft technologies. Part 19. Supersonic drag

By Bjorn Fehrm

June 30, 2023, ©. Leeham News: In our discussions about the drag of an airliner, we now cover the most complex drag type, Wave drag, or the drag created when the air goes from subsonic to supersonic flow.

We will focus on the physical understanding of what’s happening as the math behind the drag calculation is complex.

Figure 1. The Concord is designed for low Wave drag. Source: BAC and Aerospatiale.

Supersonic drag

In subsonic aerodynamics, the air molecules can move out of the way of an approaching object as they are warned by the pressure wave leading the object.

When the object travels at or over the speed of the air’s pressure wave, i.e., at supersonic speed, the air molecules can’t move out of the way anymore, as the pressure wave that shall warn them is no longer able to propagate faster than the object’s forward speed.

We get a violent collision with the object’s leading surfaces, much like when a curling stone hits another, and the air molecules change their direction instantly. They are bounced to the side as they are light, and the object is heavy if it’s an aircraft.

We are now experiencing an additional drag caused by violent collisions. I think of it as “bounce aerodynamics.” The name of the drag is “Wave drag.”

The amount of Wave drag that is created depends on the shape of the objects leading edges that run into the air molecules. If the object has a blunt nose with a large diameter (like a subsonic airliner), there will be a lot of molecule bouncing and much momentum loss for the object. The Wave drag will be high.

If the object instead has a sharply pointed nose, the collisions will be at a shallow angle and less energy-consuming. The change of direction for the air molecules is only slight and the momentum loss for the supersonic object will be less. The Wave drag will be low.

An example of aircraft designed for low Wave drag is the Concorde, Figure 1. The Concord shows that if you want to fly a certain volume through the air at supersonic speed, you shall package it with a small frontal area with a pointed nose and then let the volume expand backward. All volumes shall have a low frontal-area-to-length ratio.

Wave drag for subsonic airliners

For subsonic airliners flying at M0.78 (single-aisle) to M0.85 (the fastest widebodies), you have pockets of supersonic flow where the curving of the air around the top of the wings increases its speed to over Mach 1, Figure 2.

Figure 2. The pressure distribution, and by it, the local airspeed on a Boeing 787 (low pressure = high airspeed). Source: Boeing.

The transition to supersonic speed doesn’t create all the drag; the major drag from these pockets is created by the transition back to subsonic airspeed that rips up the sensitive wing boundary layer, Figure 3.

Figure 3. The flow around an airliner wing as it passes into the transonic speed range. Source: Wikipedia.

The Mach cruise limit of an airliner is typically put at the Mach where the Wave drag equals 20 drag counts (a single-aisle has about 280 counts of drag at cruise).

Long-range cruise is set so there are no pockets of supersonic flow on the aircraft, i.e., there is no Wave drag added to the Parasitic and Induced drag of the airliner.

7 Comments on “Bjorn’s Corner: New aircraft technologies. Part 19. Supersonic drag

  1. The engine fan also have supersonic areas where the speed vector if air sucked into the intake meets the rotating fan blade tips. It can be heard sometimes as a buzz saw sound during climb.

  2. The shocks that form around the wing surfaces tend to be more oblique than normal, until the airspeed is sufficient for the shocks to advance to the leading edge, at which point they merge and become normal.

    • Hi Rob,

      I’m not understanding the point you’re trying to make here.

      The supersonic regions on an airfoil in subsonic free stream flow decelerate by shocking back down to subsonic. The shocks in these cases are always very close to normal to the flow direction, as shown in Fig. 3. As the free stream Mach number increases, those normal (mostly) shocks in Fig. 3 move toward the trailing edge and the onset of supersonic flow moves toward the leading edge. Once the free stream Mach number slightly greater than one, an unattached normal shock develops close to the stagnation point at the blunt nose of the airfoil, but loses strength quickly because it curves back into an oblique shock further away from the airfoil. At this point the entire surfaces of the airfoil are in supersonic flow, except for the region right at/near the bunt nose. There is a small region of subsonic flow here because it is getting shocked down to subsonic by the normal shock. Meanwhile, the shocks in Fig. 3, have moved back entirely to the trailing edge, and will be slightly oblique because the flow along the top and bottom will meet at the trailing edge and force each other to change direction slightly but suddenly. In supersonic flow, a sudden direction change is always accompanied by an oblique shock.

      As the free stream Mach number increases beyond one, both the leading edge shocks and the trailing edge shocks will get more oblique.

      The flow field around airfoils in the transonic regime are complicated. What I’ve said here is my understanding of it, at least what I remember of it because it’s been a while. I welcome any input here, especially for the parts that could need correction.

  3. Björn, 20cts is the old definition. The more up to date one is, to put it where the dCdc/dM increases beyond 0.1.

  4. Bjorn:

    You did it again, very good mental pictures of it all.

  5. Bjorn, I always enjoy reading your blog and find it very informative. However, here I feel I need to object to the last paragraph. Modern airliners (and business jets) are in fact purposely designed to have some supersonic flow and, hence, some wave drag on the wing. The employ so-called super-critical wing designs, that make use of the high velocities in a limited supersonic flow region to generate some extra lift. And the optimum lift-to-drag ratio is typically achieved with a few drag counts of wave drag.

  6. One point Bjorn:

    “Concorde also acquired an unusual nomenclature for an aircraft. In common usage in the United Kingdom, the type is known as “Concorde” without an article, rather than “the Concorde” or “a Concorde”.

    I’m not sure how the French refer to it, does anyone know?

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