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Flying seems so everyday that we rarely stop to ask why a giant metal tube can glide across continents with ease. In physics classes, many people are taught a simple story about the theory behind flight. Since the upper surface of a wing is curved, air flowing over the top must go farther and therefore faster than the air on the bottom. By Bernoulli’s principle, faster flow means lower pressure, so the pressure difference produces lift. The air streamlines are assumed to meet again at the trailing edge, an idea sometimes called “equal transit time.” It’s an appealing story and it appears in many sources, but it’s wrong.

The fallacy

A review in Advances in Aerodynamics shows that equal transit time isn’t supported by experiment. Flow visualisations of dye or smoke lines demonstrate that the two parts of a marker line separated at the leading edge do not meet at the trailing edge; the segment moving over the wing travels much faster and reaches the end much earlier. A symmetric flat plate at an angle of attack or a paper airplane can generate lift despite having identical top and bottom lengths.

NASA also explained that the lift predicted by the equal-transit theory is much smaller than observed, because it produces a velocity difference that is too small to produce lift. In reality, the velocity over the top of a lifting airfoil is much faster than necessary to meet the bottom flow at the trailing edge. Even early aerodynamic literature acknowledged that no physical law requires equal transit.

So why does this myth persist? One reason is the temptation to use Bernoulli’s equation in isolation. Bernoulli tells us that, along a streamline, faster velocity corresponds to lower static pressure, but it does not tell us why the velocity differs in the first place. The equal-transit story supplies a convenient mechanism that wrongly suggests that different path lengths produce different speeds. But still, Bernoulli’s equation alone cannot answer the question of why the flow over the wing accelerates.

That question is answered by considering the full Navier-Stokes equations, boundary layers and vorticity.

Momentum, deflection and circulation

A more physically grounded way to understand lift is through momentum change. The wing acts like a vane that turns the incoming stream downward. According to Newton’s second and third laws, if a wing deflects the air downward, the air must exert an upward force on the wing. Flow visualisations show that the wake behind a wing is indeed deflected downward. The immediate intuition is that pushing air down makes the wing go up… a view sometimes called the Newtonian or momentum explanation.

However, momentum transfer alone also does not explain why the flow adheres to the wing and turns downward on the top surface. The Coanda effect is often invoked (the tendency of a jet to stick to a nearby surface) but the Advances in Aerodynamics review warns that applying the Coanda effect here is also problematic. There is no jet, and using different mechanisms for the upper and lower surface fails to give a unified explanation.

So what is it really?

The proper explanation lies in circulation. When an airfoil starts moving, viscous effects at the sharp trailing edge cause a starting vortex to be shed. By the conservation of vorticity, an opposite circulation develops around the wing. This circulation modifies the potential flow around the wing so that streamlines are curved, velocities differ on the two surfaces and pressure differences arise. The Kutta condition (that flow leaves smoothly at the trailing edge) selects a unique circulation value. Classical potential-flow theory then gives lift via the Kutta-Joukowski theorem, which states that the lift per unit span is proportional to the product of circulation, freestream velocity and fluid density. Crucially, viscous effects are required to establish the circulation; in an ideal inviscid flow no lift is generated at all, which is the conclusion demonstrated in a 2023 paper titled “Can lift be generated in a steady inviscid flow?”

Viscous flow near the surface is also responsible for the boundary layer (a thin region where friction and shear stress are significant). Within this layer, the flow is slowed and a pressure gradient forms from the stagnation point to the suction peak over the wing’s upper surface. The combination of viscosity and the wing’s shape ensures that streamlines accelerate over the top surface and decelerate along the bottom, resulting the required pressure difference. The AIAA review stresses that the critical role of viscosity in lift generation has been under-emphasised in many textbooks. Without viscosity, the idealised Euler equations predict no lift at all!

So Bernoulli made a mistake?

No. Because once the velocity field around the wing is determined, Bernoulli’s equation can be used to compute the pressure distribution. The acceleration of the flow around the wing, which is determined by viscous and circulatory effects, leads to lower pressure on the upper surface and higher pressure on the lower surface. Integrating this pressure difference over the surface gives the lift force! The lift also generates an induced drag because the wing produces downwash, hence there is also a component of the aerodynamic force that opposes the motion of the object (or airplane in this case).

How then, should we explain flight to curious minds? The modern, unified picture combines the momentum and pressure point of views. A wing generates lift because it accelerates air downwards and imparts momentum to the flow. This acceleration is achieved through a pattern of curved streamlines and circulation around the wing, which arises due to the wing’s shape, its angle of attack, and the fluid’s viscosity. The resulting velocity field leads to a pressure distribution, i.e., low pressure on top, high pressure underneath. Bernoulli’s principle can relate velocity to pressure after the velocity field is known, but it cannot determine the velocity field by itself. Newton’s third law ensures that the momentum imparted to the air produces an equal and opposite force on the wing, but without considering how viscosity and circulation shape the flow, we cannot predict the magnitude of that force, or in other words, we cannot say that it’s the sole reason behind an object’s ability to fly.

Landing

For the science enthusiast like me, knowing why airplanes fly is surprisingly humbling. You come to a realisation that a lot of our everyday experiences are often governed by subtle, interconnected micro processes. As physicist Richard Feynman liked to remind us, “the imagination of nature is far greater than the imagination of man.” So the next time you watch a jet take off, remember that its ability to soar into the sky is not due to a simplistic dual-stream model, but to the combination of vortices, viscous layers and Newtonian mechanics working hand-in-hand to produce lift.

Don’t forget to look up,

Krish

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