Planes do not fly because the air travels further over the top

Here is the explanation almost everyone gets, in a classroom or a museum or a documentary:

A wing is curved on top and flatter underneath. Air splitting at the front has further to travel over the curved upper surface, so it must move faster to meet up with the air below at the trailing edge. Faster air has lower pressure — Bernoulli’s principle — so there is less pressure above the wing than below, and the wing is pushed up.

It is neat, it invokes a real principle, and it gets to the right answer. It also contains a step that is simply false, and NASA’s own aerodynamics pages list it explicitly among the incorrect theories of lift.

The false step

Nothing requires the two parcels of air to meet at the trailing edge.

That constraint is invented. It appears in the explanation because it is needed to derive a speed, and there is no physical principle behind it. Air is not paired up at the leading edge, and no rule obliges two parcels that separated to arrive anywhere together.

And when you actually measure it — which people have, in wind tunnels and in simulation — air travelling over the upper surface arrives at the trailing edge considerably earlier than the air underneath. Not simultaneously. It is much faster than the equal-transit story predicts.

So the explanation gets the right conclusion from a premise that is not true, and whose predicted magnitude is wrong.

Three things it cannot explain

The quickest way to see it fail is to point it at ordinary facts:

• Symmetric aerofoils generate lift. Many aerobatic aircraft use wings with identical curvature top and bottom. Equal path lengths, equal transit satisfied trivially, and they fly.
• A flat plate generates lift, tilted into the airflow. No curvature at all.
• Planes fly inverted. Under the curvature story, an upside-down wing should produce firm downward lift, and the aircraft should accelerate into the ground. Air displays suggest otherwise.

What all three have in common is angle of attack — the tilt of the wing relative to the oncoming air. That is the dominant control over lift in practice, it is what the pilot is actually changing, and the equal-transit explanation has no place for it at all.

What is actually happening

Two descriptions, and the important thing is that they are not rivals.

The momentum description. A wing deflects air downwards. It does this both by the underside pushing air down and — larger — by the flow over the upper surface following the curve and leaving the trailing edge angled downwards. Air leaves the wing with downward momentum it did not arrive with. Something had to push it down, so by Newton’s third law the air pushes the wing up. Lift is the rate at which the wing throws air downwards.

The pressure description. Integrate the pressure over the whole surface of the wing and you get the same force. Pressure really is lower over the upper surface, and the flow really is faster there, and Bernoulli’s principle really does relate the two.

Note carefully what this means: Bernoulli was never the problem. The relationship between speed and pressure is sound. What was wrong was the reason offered for the speed difference — the equal-transit story — not the physics it was feeding into.

The actual reason the flow is faster over the top is circulation: a net rotational component of the flow around the aerofoil, whose magnitude is set by the requirement that air leaves the sharp trailing edge smoothly rather than whipping around it. That condition, plus the shape and the angle of attack, determines the circulation, and circulation multiplied by air density and airspeed gives the lift. This is the result the whole field is built on, and it is why lift rises with angle of attack until the flow separates and the wing stalls.

Pressure or momentum?

You will find arguments online insisting lift is “really” Newtonian or “really” Bernoullian. That argument is a category error.

There is one flow field. You can account for the force by adding up pressures on the surface, or by measuring the momentum given to the air. Both are complete, both give the same number, and neither is more fundamental — they are two ways of totalling the same thing, like measuring a company’s value from its assets or from its cash flows.

Why the wrong version survives

It is short, it fits in one paragraph, it names a principle the audience has heard of, and it arrives at the correct conclusion. Almost nobody who repeats it is in a position to check it, and it is printed in enough textbooks to look settled.

The irony is that the correct explanation is easier. “The wing throws air downwards, so the air pushes the wing up” needs no invented constraint, no appeal to a named principle, and it immediately predicts the things equal transit cannot — why tilt matters, why flat plates work, and why aircraft can fly upside down.