Lift Comes in Many Forms

NBC accompanied its coverage of the ski jumping events at the Winter Olympics with a graphic showing, in profile view, a schematic ski jumper prone over their skis, with a row of bold arrows marching along a curved path above them and a second row passing in a straight line below.

It was the classic explanation of an airfoil—curved top, flat bottom, air goes faster over the top, Bernoulli, etc. It might have been cribbed from a high school physics textbook. 

I must protest.

That explanation at least bears a resemblance to the truth when applied to airplane wings—applied to ski jumpers, it’s nonsense. The reason is wingspan, or rather the lack of it. A normal wing has enough span that spillage around the tips does not greatly affect flow over most of the wing.

If you take a vertical slice through the airflow near the middle of a wing, it looks like those textbook pictures of flow over airfoils, and whatever conclusions you would draw from them would be more or less correct. That kind of flow is called “two-dimensional.” Only out near the wingtips does the flow add a sideways dimension—outward along the undersurface, inward on top—and curl up into a whirling vortex that spills from the tip. Out there, the flow is three-dimensional, combining a spanwise component with the vertical and the chordwise.

If you reduce the span of a wing until it becomes a small fraction of the chord, the flow loses its two-dimensional character. That’s the case with ski jumpers—they’re all tip and no wing. Yet they still manage to produce some lift, as evidenced by the fact that they travel farther than they would on a purely ballistic trajectory. How do they do it?

That question has been the subject of a great deal of study, using both computer simulations and wind tunnel tests in hopes of gaining tiny advantages in competition. Because the landing zone slopes quite steeply downward to nearly match the trajectory of the arriving jumper, even small gains in lift or reductions in drag can add yards to the flight distance.  

Still, the spontaneous innovations of the jumpers themselves have contributed more to jumping distances than science has. At first, early in the 19th century, ski jumpers just stood on their skis. Later they leaned over with their arms pointing forward like Superman’s. Through a series of innovations, often resisted by conservative “style” judges, competitive jumpers arrived at the stance that is nearly universal today—leaning steeply forward, arms away from the body with hands serving as ailerons, and skis held in a V shape. Distance flown has doubled.

The effect of their lift is to slow their descent. Ordinarily, a falling object, even one initially launched upward, accelerates downward at a rate determined by the force of gravity. If part of the pull of gravity is counteracted by aerodynamic lift or drag, that downward acceleration is proportionately reduced.  

The bodies of ski jumpers are nothing like wings. Flow on an unstalled wing remains attached to the surface, minimizing the turbulent wake. An airfoil magnifies the force exerted by the air at a right angle to the flow while minimizing the force acting parallel to the flow, with the result that it produces lots of lift and little drag.

But flow on a prone body or a ski does not follow the profile of the object the way air follows the surface of an airfoil. Instead, it spills diagonally upward around the sides before separating and leaving a large turbulent wake above. The lift produced actually looks a lot like drag, and, in fact, the lift and the drag of a ski jumper are about equal.

Despite the generally unfavorable aerodynamics of wingless bodies, evolution has managed to produce flying lizards, flying frogs, and even a flying snake. Most of these have more in common with parachutes than with gliders. Flying frogs use their disproportionately large webbed feet as parachutes, while the Asian paradise snake flattens its body into a semblance of an airfoil while gliding. The word “gliding” is used figuratively here—what they do is more like falling at an angle.

On the other hand, the draco lizard, found in India, has a retractable wing that really is a wing. Consisting, like the wing of a bat, of a thin membrane stretched between bones, the so-called patagium is normally held folded against the sides of the body. When the lizard jumps, the patagium extends to form a well-shaped cambered wing with an aspect ratio of two and an approximately elliptical area distribution to reduce induced drag.

In flight the lizard uses its front legs to grasp the leading edge of the patagium, holding it open, providing it with a large, stall-resistant leading edge radius, and enabling the draco to maneuver and flare and even climb briefly for landing. Draco lizards can achieve an L/D ratio of around 3.5, which corresponds to a glide angle of 18 degrees. In practice, however, they have to dive initially to gain speed, and so their actual gliding distance is shorter than that glide angle would suggest.

The flying squirrel, to us the most familiar wingless flyer because it is native to North America, also relies on aerodynamics approaching those of an airplane or bird wing. With an aspect ratio of 1 and a square wing, it must experience large tip losses, but it seems to use its hands as vortex generators that effectively increase its span. Nevertheless, its glide ratio is on the border between gliding and parachuting. The performance of its human counterpart, the wingsuit jumper, is similar, with glide ratios of 3:1, maybe a little more.

The lesson from all this is that what we call lift comes in many forms. The classic Bernoulli pressure-velocity relationship explains only one of them—the case of an airfoil immersed in a generally two-dimensional flow. But there are at least two other kinds of lift. One involves an upper-surface flow that separates but reattaches, forming a “bubble” that in effect makes the wing thicker. That’s how delta wings lift, with a vortex that curls off the leading edge and forms a captured vortex on the upper surface. 

And then there is the lift of the ski jumper, in which the body is supported mainly by impact pressure on its underside while the flow breaks away from the upper surface. The skis, which are more similar to wings and thanks to the V position have a large effective span, make a significant contribution. 

I wonder, however, whether ski jumpers’ drag might not be as important as their lift. Flight time may possibly be more affected by the rate at which the skiers slow down than by the rate at which they lose height.

But then, what do I know? I can’t even ski.

This column first appeared in the April Issue 969 of the FLYING print edition.