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

Ground effect — where it appears

The change in a wing's forces near a surface, produced by the image system the surface implies. The lift rises and the induced drag falls, because the ground reduces the downwash the wing induces on itself.

Named by 6 essays across 3 fields — each of them below, with the objects they name alongside it.

Flow net — a free vortex. Two families of curves drawn over the same flow: the streamlines, along which the streamfunction is constant, and the equipotentials, along which the velocity potential is constant. They cross at right angles at every point, because they are the two parts of a single analytic function of position.

A wall made by reflection

Imposing a boundary condition on a plane is work. Putting a mirrored copy of everything on the far side of where the plane would be is not, and the plane then appears on its own — as a consequence of the symmetry rather than as a condition anybody enforced.

inviscid · Images A wing at h/c = 0.4. A wing close to the ground, with the mirrored vortex row that makes the ground a streamline drawn faintly beneath it. The air between wing and ground is squeezed through a narrowing gap, and the wing carries more lift than it would in free air.

The wall that pushes back

A wing near the ground carries more lift than the same wing in free air, and the usual explanation — a cushion of compressed air underneath — is not what the equations say. The ground is a mirror, and what changes is not the pressure under the wing but the circulation the wing is forced to carry.

circulation · Images What the ground actually gives a wing. Induced drag near the ground as a fraction of the same wing's in free air, against height in spans, at constant lift. The ground is a plane of symmetry, so the wake is joined by a mirrored wake of opposite circulation below it, and the upwash from that image is what takes the drag away. At a tenth of a span the wing keeps 0.516 of its induced drag — a saving of 48 per cent — and by a span and a half the effect is 1.3 per cent and going. The lift is held fixed all the way along this curve: what the ground gives here is not more lift, it is the same lift for less drag, and the two are different claims about a landing aeroplane.

The cushion that is not there

Ground effect is usually explained as air trapped under the wing and compressed into a cushion. At the heights an aeroplane actually flies at, the air under the wing is moving at four fifths of flight speed and most of what the ground gives is a drag saving the story never mentions.

misconceptions · Ground cushion The one term in ground effect that really is about carried air. The added mass of a plate approaching a plane, as a multiple of its free-air value. In free air a plate borrows ρπc²/4 per unit span — exactly 0.79 for a unit chord in unit density, which is the mass of the circle its chord spans. Near a wall the fluid in the gap must leave sideways through a narrowing passage, so it moves faster than it would in the open and carries more energy: the borrowed mass grows as the inverse of the gap and diverges as the gap closes. At half a chord it is 1.21 times, at a tenth 2.06, at a twentieth 3.12. This is a cushion in the ordinary sense — fluid that has to be got out of the way and resists being — and it is the term the steady argument has none of.

The cushion that is there after all

A wing near the ground makes more lift for reasons that have no cushion in them, and that account cannot reach two cases — a wing descending, and a rotor in the hover, where there is no steady flight for the image-vortex account to be about. Those cases have a term that really is about carried air, and it grows without limit as the gap closes.

misconceptions · Ground cushion The cushion changes its physics 0.36 mm from the ground. The two forces on a plate 10 cm across closing on a plane at 1 m/s in air at 20 °C, per metre of span, against the gap on logarithmic axes. The viscous squeeze film, Reynolds' lubrication result μVc³/h³, rises as the cube of the closeness; the inertial one, ρV²c³/24h² from the potential flow's added mass, as the square. They are equal where the gap Reynolds number ρVh/μ is exactly 24, at 0.361 mm, where each is 3.84e+2 N/m. Above that gap the cushion is the fluid's inertia and below it the fluid's viscosity — and at the crossover neither formula is accurate, since it is where one limit hands over to the other rather than a solution of the flow between them.

A cushion that changes its physics

A plate closing on a plane is resisted by the fluid it has to squeeze out, and the resistance is two different forces with two different laws — one from the fluid's inertia and one from its viscosity. They hand over at a gap of twenty-four kinematic viscosities per unit of closing speed, which for a wing in air is a third of a millimetre, and the two films disagree about whether the plate ever lands at all.

misconceptions · Ground cushion The same plate borrows more near a wall and less near a free surface. The added mass of a plate closing broadside on a boundary, as a multiple of its free-air value, against the gap in chords on a logarithmic axis, for a solid wall and for a boundary held at constant pressure — a free surface struck quickly, or the edge of an open jet. At a tenth of a chord the wall gives 1.966 and the free boundary 0.677; at 0.035 chords 3.97 and 0.584. The wall's value grows without limit as the gap closes, because the fluid in the gap has to be squeezed out. The free boundary's falls towards exactly one half, because a plate lying on a free surface sets in motion only the half-space below it. Same plate, same fluid, same speed — the boundary decides the sign, through the one thing it is allowed to tell the flow.

The borrowed mass the boundary decides

A body accelerating near a solid wall has to squeeze out the fluid between them, and borrows more mass than it would in the open. The same body accelerating near a free surface, or inside an open-jet wind tunnel, borrows less. The fluid, the body and the speed are identical, and what reverses the answer is the one thing each boundary is allowed to tell the flow.

misconceptions · Ground cushion

Named alongside it

The objects these essays reach for when they reach for this one.

Boundary conditionMisconceptionAdded massImage systemMethod of imagesModel limitPotential flowCirculationLift coefficientLubricationSymmetryWall interference

All concepts