Aerofoil

In 1944, a pilot and writer named Wolfgang Langewiesche published the first edition of his flying manual–Stick and Rudder. It was highly controversial because his description of the way wings produce lift was at odds with the popular theory of the time. Langewiesche encouraged his readers to forget nearly everything they learned in flight school about airfoils and focus on a simplified, useful theory. Even though the complete story of airfoil lift is much more complicated, his explanation gradually became accepted as the correct one, and as the most effective way to teach the idea to pilots.

Strangely, though, the old theory that Langeweische debunked in 1944 persists to this day in high school textbooks and even in some flight manuals. The popular writer David Macaulay even presented it in his 1988 book, The Way Things Work. Why is this happening? Some have suggested that it’s entirely possible to learn the incorrect theory as a child, grow up to be an accomplished pilot in spite of your misunderstanding, and then write your own book from a position of authority. Another possibility is that one correct, but very complicated, mathematical explanation of lift is based on the same equation as the incorrect explanation, and so the two theories are given equal credence by some amateur scientists.

Bernoulli’s equation is correct, but it’s being used the wrong way here. The lift force that it predicts is not strong enough to explain flight: a Cessna 152, relying entirely on the lift predicted by the Bernoulli equation, would need to fly more than 300 miles an hour to stay aloft instead of 55. And the principle of equal transit times has been proven wrong, far beyond any doubt, in wind tunnel experiments. Air goes over the top of a wing so much faster that the neighboring molecules split apart at the leading edge never see each other again. Here are a few more problems with the popular explanation:

• Airplanes and gliders can fly upside down and still generate lift.
• A wing with a very concave underside, like a single surface hang glider, should produce very little lift according to this theory, but in the real world it produces a lot of lift.
• Some airplanes use a symmetrical airfoil, or even one that is longer on the bottom than the top.
• Paper airplanes (and vintage hang gliders) have no airfoil, yet they seem to fly just fine.

As Langeweische says, you’d do well to forget about Bernoulli-the 18th Century mathematician you should be concerned with is Isaac Newton. Newton’s famous Third Law states that for every action there is an equal and opposite reaction, and explains how rockets work, why a pistol recoils, and what would happen if you used a fire extinguisher while standing on a skateboard. Applying it to flying, we find that a wing goes up because it forces air down.

It’s all about angle of attack. That’s basically the vertical angle between the wing and the oncoming air, but you can also see it as the degree to which the back of the wing is tilted down. Figure 2 shows a more accurate picture of the airflow: it encounters the leading edge at the angle of attack (roughly the angle between the dashed line and the air stream lines on the left, exaggerated for clarity), splits apart at some point, and, most importantly, is forced downward by the tilt of the wing. The air going under the bottom is deflected downward, too, and adds something to the effort, but the heavy lifting is done by the flow over the top.

What makes the air stick to the top so it can be shot downward is a curious thing called the Coanda effect. This effect causes a moving fluid to adhere to a nearby surface, as long as the surface is smooth enough and doesn’t curve away from the flow too sharply. You can see the Coanda effect in person by holding a spoon under the kitchen faucet like I did in the picture. The water stream is pulled sideways by the back of the spoon, the spoon is pushed in the opposite direction by the water stream, and Isaac Newton is happy. Rotate the picture until it reminds you of an airplane wing, and you’ve got one of the most important concepts in aerody namics.

Changing your thinking about wings is more than just an academic exercise-it can also help you understand some things about flying hang gliders and paragliders. Here are a few examples:

WAKE TURBULENCE AND TIP VORTICES

When you see that a wing keeps itself up by shoving air down, it’s easy to visualize where and how strong the wake from another glider is going to be. It’s going to be below and behind the trailing edge from the point of view of that glider’s pilot, or anyone flying next to it. Since a more massive craft needs to displace a bigger mass of air to stay up, heavier gliders will produce bigger wakes. It’s never smart to fly directly below and behind a loaded tandem glider, a hang glider pulling up from a dive, or any glider flying at a high angle of attack.

And the old explanation doesn’t account for tip vortices, the tiny sideways tornadoes that form at your wingtips and sap energy from your wing. When you see that air flows off the top faster than it slides under the bottom, it’s easy to imagine those vortices and then to understand other ideas like ground effect and the influence of aspect ratio.

IMPORTANCE OF THE LEADING EDGE AND TOP SURFACE

Since a large proportion of lift comes from the momentum of the air flowing over the top surface, it’s important not to slow down that flow. Keeping the Mylar leading edge stiffeners in top shape has a big effect on performance, whether they’re on a hang glider or a paraglider. And in the mid 1990s, hang glider manufacturers recognized the importance of a smooth, unobstructed flow over the top surface and found a way to remove the top rigging on their high performance models. This produced a quantum leap in high speed glide efficiency.

WHY A WING STALLS

The phrase “stall speed” is a little misleading because it implies that a wing will stall because of low airspeed. It’s a matter of causality vs. correlation: a high angle of attack is the cause of a stall and of low airspeed, but low airspeed is not the cause of a stall. Stalls happen because of the angle of attack, period. The airflow over the top has to stick close to the wing to make it fly, but air is only so sticky. If the angle of attack is too large, the flow will detach from the wing and won’t be forced downward. The correlation of airspeed to the stall point is useful, though, since airspeed is easier to measure than angle of attack.

The Newton model also explains why your stall speed goes up when flying in thinner air. A particular airfoil will always tend to stall at the same angle; in other words, it can only ever point downward so much and still fly. If the air gets thinner, it will weigh less per cubic foot, and the up-force from the “equal and opposite reaction” will be weaker. Gravity will then pull you down and speed you up until the air flows over the trailing edge fast enough to create a lift force that balances your weight. It’s like shooting a charging rhino with a lot of little, fast bullets instead of one big, slow bullet.

The Newton and Coanda explanation should be enough to satisfy any pilot, but the complete story of wing lift has a much larger cast of characters. There’s the Magnus effect (good for explaining a baseball pitch), the bound vortex theory, boundary layer science, laminar flow theory, the correct application of Bernoulli’s equation, and more. It is possible to describe lift using only the Bernoulli Effect, but you’ll end up using more Greek letters than the Athens phone book. Like many other ideas in physics, the airfoil story can be told in a few ways that look very different, but end up at the same conclusion. The best explanation to follow is one that is not only correct, but also makes intuitive sense and is simple enough to serve as a building block for further study.