Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Series

Drag budget — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. A wing's two drags, and the lift at which they are equal. Friction drag and induced drag plotted against lift coefficient, with their sum above them. Friction is flat, because a surface costs the same whatever the wing is doing; induced drag rises as the square of the lift. The total is least where the two are equal, and that is also the point of best glide.

    The two drags a wing pays

    A wing pays for having a surface, and it pays for making lift with a finite span. One of those bills falls as it flies faster and the other rises, so there is a speed at which the total is least — and the condition for it turns out to be that the two are equal.

    part 1 · viscous
  2. The speed for least drag is not the speed for least power. Drag and power against airspeed, in units of the speed at which drag is least. Power is drag times speed, so its minimum sits slower — at the fourth root of a third of the least-drag speed, which is 0.76 of it. Flying for range and flying for endurance are therefore different speeds, and the difference is not a rule of thumb.

    The cheapest way to stay up

    There is a speed at which an aircraft's drag is least, and a different, slower speed at which its power is least. The ratio between them is the fourth root of a third — a number that does not depend on the aircraft, the altitude, or anything else about the flight.

    part 2 · viscous
  3. Two drag laws, one derived and one fitted. Flat-plate drag coefficient against Reynolds number, laminar and turbulent, on log axes. The laminar curve is Blasius' similarity solution, solved by shooting; the turbulent one is the 1/7-power correlation, which was fitted to experiment and is drawn dashed-in-kind to keep the difference visible. Their slopes differ — −1/2 against −1/5 — so the gap between them widens rather than staying put.

    The cost of going turbulent

    A turbulent boundary layer costs several times the friction of a laminar one, and the multiple is not a constant — it rises with Reynolds number, because the two laws have different exponents. That is why laminar flow is worth more on a long fast surface than on a short slow one.

    part 3 · viscous

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