№ 39 · engineering

How a wing makes lift

A wing holds an aircraft up by bending the air it meets. The story most of us were told about why gets the argument backwards — and one step is simply false.

What a wing does

Air arrives at a wing travelling level and leaves the trailing edge travelling slightly downward. The wing has redirected a great deal of moving air, and to change anything's motion you must push on it. The air is pushed down, so the wing is pushed up. That push is lift.

Why the usual story is wrong

The familiar version: the top of the wing is curved and longer, air over it must reach the trailing edge at the same moment as air underneath, so it travels faster, and faster air has lower pressure. This is the equal transit time explanation. Air over the top is faster and its pressure is lower. But nothing forces neighbouring parcels of air to reunite at the back. In measurements and in the flow equations, the parcel that goes over the top arrives well before the one underneath. The rule the story relies on does not exist, and it cannot explain why a flat paper aeroplane flies, or why aircraft fly upside down. It survives because an idealised 1750s theory of fluids (D'Alembert, then Euler) predicts equal transit — along with zero lift and zero drag. Engineers patched the theory around 1900 by adding circulation; the schoolbook story kept the unpatched version.

Turning the air

In the interactive below, tilt a flat plate slightly into a steady wind. The angle between the plate and the oncoming air is the angle of attack. Air cannot pass through the plate and leaves no gap behind it: it follows the surface, above and below, and leaves the trailing edge heading where the plate points. The whole stream near the plate is bent downward. A streamline is the path a small parcel of air follows; tilt the plate and every streamline near it deflects down.

Newton's third law does the rest: the plate pushed a mass of air down, so the air pushes the plate up with equal force. Push more air, or push it harder, and lift grows: lift rises with angle of attack, and with the square of airspeed: doubling the speed doubles both how much air passes each second and how fast each parcel is deflected.

InteractiveDrag the angle of attack and the airspeed: watch the streamlines bend down, the lift climb, and the upper parcel (filled dot) beat the lower one to the trailing edge.

The streamlines are the exact solution for a thin flat plate in smooth, non-viscous, two-dimensional flow (potential flow with the Kutta condition, which is what fixes the flow to leave along the trailing edge). Lift uses the standard form L = ½ρV²·S·CL with sea-level air, ρ = 1.225 kg/m³, and one square metre of wing; the exact flat-plate result is CL = 2π·sin α (≈ 2πα for small angles). Simplified: the model has no viscosity, so it cannot stall by itself — the 15° stall marker is borrowed from ordinary rounded wings (a real sharp-edged flat plate separates earlier); past it the lift curve is a sketch of the drop a real wing shows, the streamlines are dimmed, and the grey region marks where the real flow would separate. Transit times are for the two parcels drawn, released side by side 1.5 chords upstream; other release points give other ratios, but the upper parcel always arrives first.

The pressure version is the same event described differently. Bending a stream of air downward takes a pressure difference: the air just above the wing is at lower pressure than the air just below. Lower pressure on top and higher underneath add up to a net upward force on the wing — and the same difference curves the air's path. A wing does not create low pressure and then get lift, or deflect air and then get low pressure. One flow, one force, two vocabularies.

Tilt too far and the air can no longer stay attached to the upper surface; it separates and tumbles, the wing stops turning it cleanly, and lift drops sharply. That is a stall. It begins at roughly fifteen degrees for many ordinary wings, though the exact angle depends on shape and speed and is usually found by wind-tunnel testing.

In short

A wing makes lift by turning the air past it downward. Pushing air down means the air pushes the wing up, and the same act shows up as lower pressure above the wing than below. Air over the top is faster, but not to keep an appointment at the trailing edge — it gets there first; the equal-transit story was never true.

Where this comes from

  1. On the Origins and Relevance of the Equal Transit Time Fallacy to Explain Lift reuse permitted with attribution
    Graham Wild · arXiv:2110.00690 · 2021
    arxiv.org/abs/2110.00690
  2. Bernoulli and Newton — Beginner's Guide to Aeronautics linked only, not reproduced
    NASA Glenn Research Center · 2024
    www1.grc.nasa.gov/beginners-guide-to-aeronautics/bernoulli-and-newton/
  3. What is Lift? — Beginner's Guide to Aeronautics linked only, not reproduced
    NASA Glenn Research Center · 2022
    www1.grc.nasa.gov/beginners-guide-to-aeronautics/what-is-lift/