The cushion that is not there

Every pilot has felt it: an aircraft in the last few feet of a landing — at an angle rather than a speed — stops wanting to come down. The usual explanation is a cushion — air trapped between the wing and the runway, compressed by the wing’s descent, holding it up.

The explanation has the merit of predicting the right sign, and it is worth taking seriously enough to compute, because the computation says something more interesting than wrong. It says the story describes a real regime that aeroplanes do not fly in, and that it leaves out the larger half of what the ground actually gives.

What the air under the wing is actually doing #

If the air is trapped and compressed, it is nearly stationary, and nearly stationary air under a wing has a pressure coefficient approaching one — the stagnation value. If it is not trapped, it flows through, and its pressure coefficient is somewhere well below that.

Both quantities are computable, and both were computed on this site’s own thin-aerofoil solver with a mirrored row of vortices supplying the ground:

The last column is the one that settles it. It is the mass flux through the gap under the wing, as a fraction of what would pass through the same gap if the wing were not there.

At the heights an aircraft flies at, four fifths of the air goes through. A large airliner in the flare has its wing about four tenths of a chord above the runway; the air under it is moving at most of flight speed, its pressure coefficient is a third of the stagnation value, and describing it as trapped is describing something else.

Where the extra lift actually comes from #

The mechanism is the image system, and it is the same one that makes a wall push back and a wind tunnel flatter its models.

A ground plane is a plane of symmetry: the boundary condition no flow through it is satisfied identically by a mirror-image wing below, flying upside down. That image’s circulation induces an upwash at the real wing. Less downwash means less induced angle, which means the same geometric incidence produces more lift and less induced drag.

So the extra lift is a circulation effect, and it is a consequence of the same image system that produces the far bigger effect the cushion story omits entirely.

The half the story leaves out #

Ask a pilot what ground effect does and the answer is lift. Ask the arithmetic and the answer is drag.

Halving the induced drag is a very large thing. For a transport aircraft in the flare, at high lift coefficient and low speed, induced drag is most of the total drag — so a wing at a tenth of a span above the runway is in a substantially cleaner aircraft than the one that was in the circuit ten seconds earlier. That is why an aeroplane in ground effect floats: not because something is pushing up harder, but because much less is holding it back, and it therefore fails to slow down.

The distinction is testable in the cockpit. A cushion would resist descent; a drag saving would resist deceleration. What pilots actually report — an aircraft that will not slow down and consequently will not settle — is the second.

The cushion is real somewhere, and it is not here #

At a tenth of a chord the numbers change character. The pressure coefficient under the wing reaches 0.96 out of 1.0, the flux through the gap falls to a fifth, and the air under the wing genuinely is nearly stagnant. The cushion story is a correct description of that regime.

It is the regime of ground-effect vehicles — the Soviet ekranoplans, hovercraft skirts, racing cars’ underbodies — where the gap is a small fraction of the chord and where holding air is the design intent rather than an accident of altitude. It is not the regime of aeroplanes, whose wings are metres above the runway at touchdown and whose chords are metres long.

So the verdict is not false. It is that a picture drawn for one limit has been carried into a regime where the numbers are entirely different, and where the mechanism that dominates is one the picture does not contain.

Where the reaction goes, since something must carry it #

If the wing is not resting on trapped air, the runway still has to take the weight — and it does, as pressure, spread out.

Integrating the pressure on the ground under the wing gives exactly the extra lift the wing is making, which is the momentum theorem applied to a control volume with the runway as one of its faces. At four tenths of a chord the peak pressure coefficient on the ground is about a third, spread over a footprint several chords long; at a tenth of a chord it is nearly one, concentrated under the wing.

So the ground does feel the aircraft, in both regimes. What differs between the cushion story and the computation is not whether the runway is pushed on — it is whether the air doing the pushing is the same air from moment to moment. In the cushion picture it is a captive parcel; in the computation it is a stream passing through at four fifths of flight speed, and the pressure is a consequence of its being turned rather than of its being held.

Two consequences that are not obvious #

Ground effect makes an aeroplane less stable in pitch, not more. The image system’s upwash is stronger at the tail than at the wing when the tail is lower, and the wing’s downwash at the tail is reduced — both of which change the tail’s effective incidence, usually nose-down, which is why aircraft entering ground effect often need a trim change and why the flare is a moving target.

And a low wing gets more of it than a high wing on the same aircraft. Everything above scales with height in chords or in spans, so an aircraft whose wing is under the fuselage is measurably deeper into ground effect at the same wheel height than one whose wing is on top — which is why some high-wing transports are described as landing “firmly” and some low-wing types as impossible to make touch down.

What the image system does to the wake, which outlives the aeroplane #

The same mirror that raises the lift and lowers the drag also decides what happens to the two vortices the wing leaves behind, and that is the part of ground effect that matters to somebody who is not in the aircraft.

In free air a trailing pair descends: each vortex sits in the other’s field and is carried down at $\Gamma/2\pi b'$, with $b'$ the spacing between them. Bring a ground plane into it and there are four vortices — the real pair and its mirror image, an upside-down pair below the surface. The images induce an outward velocity on the real vortices, growing as they get lower, so the pair descends, spreads apart, and slows its descent. The inviscid answer is a pair that never lands: it approaches the surface asymptotically while running sideways along it, tracing a curve that is the image system’s own hyperbola.

That is the model behind every wake-separation rule at an airport, and it predicts something useful and something wrong. The useful part is the lateral spread — vortices from a landing aircraft do not stay on the centreline, they walk outwards at a few metres a second, which is why a light crosswind can hold one of them stationary over the runway and why the dangerous case is not calm air but a crosswind of exactly the wrong strength. The wrong part is that real vortices rebound, climbing back up ten or twenty per cent of their initial height before decaying.

The rebound is not in the image system, and the reason is the same absence this essay has already listed. The image argument treats the ground as a plane of symmetry with no fluid property of its own. A real ground has a boundary layer, the vortex running along it drives an adverse pressure gradient beneath itself, that layer separates, and the separated sheet rolls into a secondary vortex of opposite sign which then orbits the primary and lifts it. Nothing made of images can produce that, because an image carries no vorticity of its own into the flow — it is a bookkeeping device for a boundary condition, and the boundary in question has stopped satisfying it.

The other thing the arithmetic warns about #

The table at the top of this essay has an operational reading that no cushion story supplies, and it is a warning rather than a curiosity.

At four tenths of a chord the wing carries 1.25 times the lift it would carry in free air at the same incidence and speed, and it pays substantially less induced drag. Climb out to one chord and both of those are nearly gone. So there is a band of speeds at which an aircraft can be flown off the runway and cannot climb away from it: the lift that got it airborne was borrowed from the image system, and leaving the image system behind means giving it back at exactly the moment the aircraft is asked to accept more drag.

The failure mode is a settling one rather than a stalling one. The aircraft lifts off, accelerates poorly because it is now dragging more than it did a second ago, and either descends back onto the surface or stays trapped a few feet up. Overloaded aircraft on hot days do this, and it is consistently misreported as a loss of the cushion — which gets the sensation right and the mechanism exactly backwards. Nothing was holding the aeroplane up and has now escaped. An image wing beneath the runway was cancelling part of the downwash, the real wing climbed out of range of it, and the induced drag it had been saving came back.

What the picture cannot show #

All of this is ideal flow. There is no boundary layer on the wing and none on the runway, and the runway’s own layer is not thin at the scales involved — a real ground plane under a moving aircraft has air already in motion near it, and the mirror-image argument assumes it does not.

The ground is flat, level, solid and stationary relative to the air. Wind shear near the surface means the wing at ten feet is in a different flow from the wing at a hundred, and that gradient is not in this calculation. A wind-tunnel ground plane has the same problem, which is why moving-belt rigs exist.

The aircraft is not descending. Everything here is steady. A wing coming down towards a surface is an unsteady problem with an added-mass term in it, and that term is the closest thing in the real physics to the cushion the story describes — a body approaching a wall does feel a force from the fluid it has to displace, and it is not the mechanism that holds an aeroplane up in the flare.

And the lift numbers are two-dimensional while the drag numbers are three-dimensional. They are different calculations with different length scales, quoted here side by side because the aeroplane experiences both at once.

What a pilot should take from the arithmetic #

Three practical statements follow from the numbers, and they are more useful than the picture the cushion story supplies.

The effect starts higher than it feels. The induced-drag saving is measured in spans and is already ten per cent at half a span above the runway — which for a large aircraft is thirty metres, well before the flare. The lift effect is measured in chords and arrives much later. So an approach is already in ground effect, aerodynamically, at a height where nothing has yet been noticed.

What is felt is the failure to decelerate. With induced drag cut by a third to a half at approach lift coefficients, an aircraft in the last few metres is much cleaner than it was, and an approach flown at the usual speed arrives with more energy to dispose of. The float is a drag phenomenon.

And the trim changes. The image system alters the downwash at the tail as well as at the wing, generally reducing it, which is a nose-down change at the moment when a pilot is raising the nose. Every type has its own version of that and every type’s handbook mentions it.

None of those three is predicted by a cushion. All three follow from an image wing flying upside down beneath the real one, which is the same picture that gives a wind tunnel its wall correction and a box wing its saving.

Where the idea came from #

The cushion picture is old and it comes from hovercraft, which are cushion vehicles: a fan blows air into a plenum under a skirt, the pressure there really does reach a substantial fraction of stagnation, and the vehicle really is riding on trapped air. The word was borrowed for the aeroplane case, where the mechanism is not the same, and it stuck because it is memorable and gets the sign right.

The honest version is barely longer and has more in it. The ground is a boundary condition. It makes the flow symmetric, the symmetry means an image wing, and the image reduces the downwash — which raises the lift a little and lowers the induced drag a great deal. That sentence covers everything a pilot notices, predicts the two length scales, and does not require anything to be held.

What the two length scales mean in a cockpit #

The clearest test of the two mechanisms is that they arrive at different heights, and a pilot meets both on every landing.

Drag first, measured in spans. For an airliner with a sixty-metre span, a tenth of a span is six metres — around the height at which the aircraft crosses the threshold. From there down, the induced drag is falling through the largest change it will make, which is why the aircraft’s tendency to float begins well before the flare rather than in it.

Lift second, measured in chords. The same aircraft has a wing chord of five or six metres near the root, so four tenths of a chord is about two metres — the height of the wheels at touchdown. The lift increment is arriving at the very end, in the last second or two, and it arrives as a change in the slope of what the aircraft is doing rather than as a step.

The two together explain the sequence a pilot describes without any air being trapped: an approach that will not slow down, then a flare in which the aircraft seems to want to fly on, then a trim change as the tail’s incidence shifts. Three effects, one image system, and two lengths that differ by a factor of ten because a span and a chord are different lengths.

Where the ladder goes next #

The rung above is the unsteady case: a wing descending towards a plane, where the added-mass term appears and where the cushion becomes a genuine part of the physics rather than a metaphor for it. That is the calculation a helicopter’s ground effect actually needs, since a rotor in the hover has no forward speed for the steady argument to work with.

The one beside it is the same image system with the wall further away and all round, which is a wind tunnel — and where the sign of the interference reverses if the boundary is an open jet rather than a solid wall, which is as clean a demonstration as the subject offers that the effect belongs to the boundary condition rather than to the air.