Flight

A Wing Throws Air Down

Watch the air a wing has passed through, and it is moving down. A wing meets the air tilted up a little, and curved, and it turns the passing air downward. Turning the air takes a push, and by the third law of motion the air pushes back on the wing just as hard. That push back, upward, is lift.

The books balance exactly. A force is the rate at which momentum changes, so each second the wing hands the air as much downward momentum as its lift. Behind the wing the air sinks, rolled at the wing’s tips into two long swirls that trail far behind it and go on turning after it has gone.

The two accounts of lift, Bernoulli’s pressure and Newton’s push, are often set up as rivals. They are one event, counted at its two ends. The difference in pressure over the wing’s skin is how the wing pushes on the air, and the air turned down is what that push does to it. Add up the pressures on the wing, or the momentum given to the air, and you get the same number.

The air does not keep that momentum. The sinking air presses on the air below it, and that on the air below it, until the push reaches the ground. So the weight of a plane ends up on the surface of the earth, spread over a wide patch of slightly raised pressure, far too slight to feel. The push can be weighed all the same. Small parrots have been flown inside a closed box that stands on force sensors, and every downstroke of a bird’s wings presses on the box, through the air, with up to twice the bird’s weight.

The Sharp Back Edge Decides

Now the question the old story got wrong: why is the air over the top so fast? The answer is at the back of the wing, where it narrows to a sharp edge.

Set a tilted wing moving through a perfect fluid, with no stickiness at all, and it would get no lift. The flow from underneath would swing up round the sharp back edge and leave from the top, and the wing would turn no air down at all. Real air cannot take so sharp a corner. When a wing sets off, the air whipping round its back edge rolls up into a swirl, which the wing leaves behind where it started. Tow a wing through water with aluminum powder sprinkled on the surface, and the swirl can be photographed.

Air at rest never starts swirling one way without swirling just as much the other way somewhere else. So while the swirl is left behind, the air round the wing takes up an equal swirl the other way: backward over the top, forward underneath. Added to the oncoming air, it makes the air over the top faster and the air underneath slower. The swirl left behind is not what pushes the air round the wing. It is the other half of the account. Stop the wing, and the swirl round it is let go too: it rolls off the back edge as a second swirl, turning the other way, as strong as the first.

How much swirl? Just enough for the air from above and below to leave the sharp edge together, smoothly, instead of one of them whipping round it. That one condition sets the lift. On each meter of any wing, the lift is the density of the air, times its speed, times the strength of the swirl round the wing. Tilt the wing further and the air needs more swirl to leave the edge smoothly, so the wing gets more lift. This is where the theory of wings begins.

So the air’s slight stickiness does its work for lift at one place above all, the sharp back edge. That is why wings have one.

The Angle, and the Stall

The angle at which a wing meets the air, its angle of attack, is how a pilot controls lift. At small angles the lift grows almost in step with the angle, by much the same amount whatever the wing’s curve. The curve adds a little, as if the wing were tilted a couple of degrees more. That is why a flat sheet glides, why a stunt plane can fly upside down with its nose held up, and why a plane coming in to land raises its nose: at the lower speed, a bigger angle makes the same lift.

Why does the air follow the curved top at all? Nothing has to pull it. A stream of air follows a smooth surface as long as the thin, slowed skin of air next to the surface keeps going. Where the stream bends to follow the wing, the pressure next to the surface falls, and the lower pressure is what bends it: the bend and the low pressure hold each other up. The clinging is sometimes put down to the Coanda effect, the way a jet of air hugs a curved surface beside it. Aerodynamicists object that a jet clings by dragging the still air round it along, and a wing sits in a stream with no jet in it. Nor does the air’s stickiness pull it round the curve.

That slowed skin is also where a wing fails. Past the low pressure near the front of the top, the air has to slow down again and push its way back up to the higher pressure at the back edge. Tilt the wing further and that climb gets steeper. Somewhere around fifteen degrees for a typical wing, the slowed skin no longer has the speed to make it. It stops, turns back, and the flow peels away from the top. The wing has stalled. The air over the top churns, the lift falls, and the drag climbs steeply.

So a stall is an angle, not a speed. Pilots are taught exactly that: a stall comes from too great an angle of attack, not from too little airspeed, and a wing can stall at any speed. In a level turn banked at 60 degrees, the lift is tilted toward the turn and its upward part is only half of it, so the wing must make twice the plane’s weight in lift. The plane then stalls at a speed 41 percent higher than in straight flight. Pulled round so hard that the wing must lift four times the plane’s weight, it stalls at twice its usual stalling speed. The cure is to lower the nose and so the angle, and it feels wrong when the ground is near.

Air France flight 447, an airliner crossing the Atlantic at night, lost its speed readings when ice crystals blocked the probes that measure its speed. It climbed to about 38,000 feet, nearly 12 kilometers, and stalled. The crew never recognized the stall, and the pilot at the controls kept making mostly nose-up inputs. For three and a half minutes the plane came down with its nose high and its engines running, its wings meeting the air at more than 35 degrees, until it struck the sea. All 228 people on board died.

What Lift Costs

Throwing air down is not free. The air left sinking and swirling behind a wing carries energy, and that energy comes from the engines. It is a drag that exists only because the wing is holding the plane up.

How much depends on how the push is given. Momentum is mass times speed, but the energy of motion grows with the speed squared. So the same downward momentum, handed to twice as much air at half the speed, leaves only half the energy behind. The cheap way to hold something up is to move a lot of air gently.

That is the case for long wings. A wing twice as long, holding up the same weight at the same speed, sets air moving over a region twice as wide and twice as deep. Its swirls are half as strong and twice as far apart, the air between them sinks at a quarter of the speed, and a quarter of the energy is left behind. Put as a rule: for a given weight and speed, the drag of holding a plane up falls with the square of its span.

The cost falls with speed too, because a faster wing meets more air each second and needs to turn it less. Ordinary drag does the opposite, so every plane has a speed in between at which its total drag is least. Hovering is the costly extreme, with no oncoming air at all: a helicopter must make its own downward stream, which is why its blades are long, since the power to hover falls as the rotor grows.

So the wings that fly farthest on the least are long and slender. A wandering albatross, its wings up to three and a half meters across, takes its energy from the sea wind and travels thousands of kilometers flapping little more than to take off. Many airliners would have longer wings if airports allowed them. Boeing’s 777-9 folds the last three and a half meters of each wing up on the ground, so that a span of nearly 72 meters fits a gate built for 65.

The swirls have an upside, too. Just outside each one the air rises, and a bird flying there gets some of its lift for free. Northern bald ibises tracked flying in a V hold that spot beside the bird ahead, and time their wingbeats to stay in it. In a test, two airliners flown three kilometers apart, the second in the rising air beside the first one’s wake, saved more than six tonnes of carbon dioxide on one crossing. No airline flies that way yet.

Where the Steady Wing Stops

There is an old joke that science proves a bumblebee cannot fly. It is usually traced to a zoologist who wrote that he and a mathematician had applied the rules for aircraft wings to insects, and found that their flight was impossible. He added at once that insects plainly do fly, and that what was missing was knowledge of how their wings work.

i An artist's impression: a swirl rides each wing's front edge ×

He was right that something was missing. Many hovering insects need two or three times the lift their wings could give in a steady stream. The answer came from big, slow models. One was a robot hawkmoth ten times life size, flapped in air laced with smoke. Another was a pair of wings cut to the shape of a fruit fly’s, 25 centimeters long, flapped in a tank of mineral oil, each beat taking seven seconds. Both showed a swirl riding along the front edge of the wing through each stroke, keeping the air attached at angles where a fixed wing would stall at once. The wing also gains from twisting sharply at each end of the stroke, and from meeting the wake of the stroke before. Smoke over bumblebees in free flight shows such a swirl on each wing. The bee still throws air down. It does it with a stall held off by a swirl.

The Part Still Hard to Compute

Every few years a headline announces that no one can explain why planes fly. The physics is not in doubt. The equations of a sticky fluid, known for nearly two centuries, predict lift. While the air holds on, computers solve them, with the turbulence averaged out, for a whole airliner well enough to design it. What is missing is a short explanation without the equations that every expert accepts, and a reliable calculation of the stall.

The stall is the hard part. At a recent workshop, 47 teams computed the same model airliner close to its greatest lift. The usual methods, which average out the turbulence of the air, disagreed widely. Methods that compute its larger eddies directly came closest to the wind tunnel, at a far higher cost, though they still differed among themselves in places. What would settle it is a method that follows the turbulent skin of a whole wing, eddy by eddy, at full size and speed, and gets the stall right before the wind tunnel does. The most promising are still far too costly for everyday use. Until then, the stall of a new airliner is found the old way, by flying it.