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

Leading edge suction — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Why a flat plate has no drag, drawn as a triangle. A flat plate at incidence with the three forces that must balance. Pressure can only act along the plate's normal, so the pressure force is the arrow perpendicular to the plate. Kutta–Joukowski says the resultant is perpendicular to the free stream. The difference between the two directions is the suction force at the leading edge, which acts forwards along the plate and is exactly L sin α. Without it the plate would have a drag of L sin α, and an inviscid fluid does not permit one.

    A finite force from an infinite speed

    Pressure on a flat plate can only act along the plate's normal. Kutta–Joukowski says the force is perpendicular to the free stream. Those two directions differ by the angle of attack, and the discrepancy is made up at a single point where the velocity is infinite and the area is zero.

    part 1 · circulation
  2. Losing the leading-edge suction doubles a slender wing's drag due to lift and multiplies a long wing's by about half its aspect ratio. The drag due to lift with no leading-edge suction, Cₗ²/Cₗα, over the induced drag a full suction leaves, Cₗ²/(πAe), against aspect ratio, from a vortex lattice for rectangular, delta and elliptic flat wings; with the closed form 1 + √(1 + A²/4) that Helmbold's lift slope gives an elliptic wing. Rectangular: 2.15 at A = 1, 3.46 at 4, 5.33 at 8, 7.11 at 12; delta: 2.22 at 0.5 and 2.83 at 2. The slender limit is 2.

    A wing that cannot hold its suction gains little from its span

    The leading-edge suction is a small force concentrated at one edge, and on a finite wing it decides what the aspect ratio is worth. With it, the drag due to lift is the induced drag, which falls as the span grows. Without it, the drag due to lift is the lift tilted back by the incidence, and that falls only as fast as the lift slope rises — which stops at the section's 2π. A slender delta that loses its suction pays exactly twice its induced drag; a wing of aspect ratio eight pays more than five times it. Without the suction no span can lift a wing's best lift-to-drag ratio past a ceiling set by the section alone.

    part 2 · circulation

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