Bjorn’s Corner: Aircraft drag reduction, Part 16

By Bjorn Fehrm

February 9, 2018, ©. Leeham Co: In the last Corner, we discussed some further aspects of supersonic flow. Now it’s time to talk about the drag created by supersonic flow on an aircraft.

We will start with the full supersonic case this week, followed by the transonic case next week.

Supersonic wave drag

In addition to the drags we discussed before, an aircraft flying supersonically will have two added drag components: supersonic wave drag due to the volume of the aircraft and wave drag due to lift.

As both these drag components are coming from the pressure distribution over the aircraft when flying supersonically, they are separate from the drag due to air friction and drag due to air’s circulation in the spanwise direction, induced drag. We, therefore, have to add them to the other drag components when passing the sound barrier.

Supersonic volume wave drag

Volume wave drag is created by the compression and then the expansion of the air when an aircraft or an object passes through the air (with no angle of attack). In Figure 2, we have a slender body passing through the air at supersonic speed.

Figure 2. Slender body flying at supersonic speed through the air. Source: Stinton. The Anatomy of the Airplane.

As it’s flying supersonically, the air in our imagined cylinder ahead of the Mach cone has no idea of an object coming. Inside the Mach cone, the air is compressed by the body volume forcing the air to the side. At the body midpoint, the compression stops. From the midpoint to the finish of the object, the air expands and the pressure drops. As the air reaches the end of the body, it readjusts the pressure to the ambient pressure through a shock wave.

If we now think how the created pressures affect the body, we can see the compression will have a compression force against the movement in the first half, followed by a suction pressure force in the same direction after the body’s midpoint (there are also forces perpendicular to the direction of flight, but as it’s a circular body, these cancel out).

We have a pressure drag from these two components, which is related to how much the body is forcing the air to compress and expand. The volume wave drag force is strongly dependent on this compression and decompression of the air and how violent these movements are.

The volume drag of a needle body, like in the picture, is proportional to the inverse square of the body length divided by its diameter. The body length divided by the diameter is called the fineness ratio of the body.

So, the higher the finesse of the body, the lower the drag. A normal airliner fuselage has a finesse of around 10. So, the volume wave drag is some factor of 1/100. In fact a drag coefficient of around 0.1, which is high. The total subsonic drag coefficient of this fuselage is around 0.025, so the volume wave drag component adds four times as much drag again.

Concorde had a fuselage finesse of around 20. The volume drag coefficient component of its fuselage would then be ~0.025. This is four times lower than for a normal airliner fuselage.

Supersonic lift wave drag

Wave drag caused by aircraft lift is also created by the compression and then the expansion of the air when a wing passes. This time the body has an angle of attack to the air. In Figure 3 we have a slender wing passing through the air.

Figure 3. Supersonic wing flying through the air with an angle of attack. Source: Stinton. The Anatomy of the Airplane.

The angle of attack has the top leading edge of the wing at the same angle as the airflow, so we have no compression there. After the leading edge, the top surface falls away and we have expansion fans with lower static pressure over the length of the wing. At the end we have a shock, returning the pressure to ambient level.

On the bottom surface, we have compression and therefore an oblique shock at the leading edge, followed by gradually lower pressure due to expansion fans.

The pressure distributions, taken together, create lift in the vertical direction and drag in the direction of flight.

The wave drag from the lift is dependent on the Mach and lift divided by the wings cord, all factors squared. Once again, a long and slender wing is important for low drag. We have violent compressions and expansions, the gentler, the better.

A normal wing would have a wave lift drag coefficient component beyond 0.1 at supersonic speed. At the high speed, the induced drag due to lift would be a fraction of this drag. Concorde had a lift wave drag coefficient of around 0.001 and induced drag coefficient of around 0.004 at M2.0.

In the next Corner, we discuss Transonic compressibility drag.

7 Comments on “Bjorn’s Corner: Aircraft drag reduction, Part 16

  1. For a body with wings and a jet Engine you have a mix of supersonic and subsonic flow in different regions even flying supersonically. It can get quite tricky around M=1 where both areas are quite big and effect rudders and center of lift on all surfaces.
    For some reason is the change in cross sectional area important factor for transonic drag and from the Starfighter an later often one can see the body cross section and placement of tails and elevators designed not to change the total cross section to abruptly, like on the F18, F22, F35, T-50 but totally neglected on the Chungdu J-20 and somewhat neglected on the European Delta wing fighters.

    • don’t the canards work as shock bodies?

      some time before Whitcomb “reobserved” what he then called “area rule” wind tunnel tests were run with engine mounted
      just ahead of the wing.

  2. @Bjorn – in low speed subsonic (particularly automotive) aerodynamics there are a number of features frequently seen that I don’t see on aircraft, notably so called kamm backs (which “fool the air” into believing the car has a long tail) and gurney/fowler flaps which increase lift at a lower drag penalty than a higher camber wing.

    I would be interested to understand some of why this is not used in an aircraft context. in particular, I would think a “kamm back” on the tail end of the fuselage tube would allow a longer passenger compartment in a given fuselage length, reduce weight and dead volume in the tail as well as improving apparent fineness ratio.

    clearly, some of the “abrupt” features can have positive benefits at transonic speeds as seen by the “trailing edge wedge” McD added to the MD-11 to fix drag related fuel burn issues.

    • Hi bilbo,

      the Camm back is used on cars as vehicle length is important. It’s then efficient to cut the back so a clear break occurs to wake turbulent flow. It’s a high drag end but a slow taper back would give less baggage space with little drag improvement (the forced taper creates a lot of form drag from boundary layer separations).

      Aircraft have no tail length restrictions when flying. Only wetted area and weight trades determine how long you make the tail. Therefore Camm tails are not used on aircraft, you get better aircraft efficiency with a nicely tapered tail.

      Gurney flaps are quite different. It’s used on racing cars to increase downforce from highly cambered wings. These wings have boundary layer separation of the last part of wing+flap. The Gurney stops these separations by inducing clean up vortices, look it up in Wikipedia for details.

      Lift to drag ratio for racing car aero is very different to aircraft. Airliners seek L/D of over 15, racing cars are content with 4-6. You accept almost any drag to increase your downforce. It makes for a faster lap time through higher corner speeds, despite lower speeds on the straights.

  3. Keeping the fuselage small seems to be very important, as explained. The Lockheed 2000 mock-up for the SST had 266 passengers at 5 a breast!

  4. As usual Bjorn, your article is GREAT. I am an Aeronautical Engineer with a Commerical Pilot Rating with ~60 years of flying experience; flew B-47’s in the Air Force, F-86H’s in the Mass ANG, worked at Pratt & Whitney for ~40 years, mentor with youngsters and ‘oldsters’ about ALL kinds of ‘Aviation’ topics, and member of EAA chapter 26 here in Seattle, WA ‘made-up’ of men and women that range in age from late 20’s to over 90…many still flying, and share ALL kinds of flying experiences, etc

    • Thanks Joel,

      it’s nice to get feedback. Keep up the good mentoring work. With the B-47 you were flying high where you were boxed between stall and transonic drag rise, the subject for our next Corner.

Leave a Reply

Your email address will not be published. Required fields are marked *