# Kite / Hang-Glider Aerodynamic Improvement

A simple improvement can be done to kites, hang-gliders, and ultra-light aircraft, to enhance their aerodynamic lift.

Kites, Hang-Gliders, and Ultra-light aircraft all fly in accordance with the usual physics of flight. There are actually two separate sources of aerodynamic lift. The Bernoulli Effect is the source of some the lift created. The bulged curvature of the topmost surface is central to this. A "reaction left" is the other source, where the (relatively) moving wind "bumps into" the lower surface and is deflected downward. This cause the air to now have a downward momentum. Conservation of momentum means that the device is therefore given an upward momentum of the same quantity.

## Bernoulli Lift

Air passes the object, either because of the wind (for the kite) or due to its own forward motion through the air. As the air passes it, the air that passes over the bulged out top has a longer path because of that upward bulge of that surface. This air must basically meet the other air that went under the wing (or airfoil) surface, which essentially went in a straight line, so it must necessarily go faster over the top.

The Bernoulli Effect says that faster moving air has a lower natural pressure than it would have otherwise had. (Remember that ALL air has continuous atmospheric pressure of about 15 pounds per square inch pressing on it from every direction). Since this means that the pressure pushing DOWNWARD on the top of the airfoil surface is slightly reduced, when compared with the un-reduced pressure pushing UP on the underside of the airfoil. This DIFFERENCE of pressures is the source of the Bernoulli lift that supports the airfoil.

The Bernoulli Lift is easily calculated! The difference in pressure is given by:
P - Po = 1/2 * ρ * (V2 - Vo2)

where is the air density at that temperature and pressure (which can usually be taken as around 1/420) and the V's are the relative air velocities above and below (Vo) the airfoil.

As an example, say a hang-glider has a wing surface area of 100 square feet, the expected relative airspeed will be 20 mph (29 ft/sec) and the shape of the wing is such that they air must go 20% farther over the top than under the bottom. That's all we need!

P - Po = 1/2 * 1/420 * (352 - 292)
P - Po = 1/840 * (1225 - 841) = 384/840 = about 0.46 lb/sq.ft.

This is the Bernoulli lift per square foot, so by multiplying by the wing area, we get the total Bernoulli lift, around 46 pounds.

Since the craft certainly weighs more than this, and adding the weight of a rider makes it heavier still, the Bernoulli lift along is not enough to support this hang-glider at that speed. In other words, if the angle of attack was zero (a level wing) there would not be enough lift to support it in flight. This is why all practical flying craft have their wings tilted, so that the second effect can be added.

## Reaction Lift

If any surface is tilted upward in a moving air stream, an effect of lift is created. This is actually created because the air is getting deflected downward by the impact with the bottom surface of the wing, so it therefore develops a downward momentum. Newton's Laws of motion says that momentum must be conserved, so that means the airfoil must receive an upward momentum of the same amount. The steeper angle of attack, the more this lift increases, up to a point called the stall angle where turbulence, drag and other losses become larger than the lift that is being created, and the airfoil just stops working at all, and the craft tends to drop like a rock. A VERY bad thing! All pilots are very familiar with the stall angle of the craft they are piloting, to make sure to avoid this problem.

Our example again:
This reaction lift, for small angles of attack, is given by:
P = 1/2 * ρ * Vo2 * 2 * π * sin (angle of attack)
P = 1/2 * 1/420 * 292 * 2 * 3.14 * sin(α)
P = 1/840 * 841 * 6.28 * sin(α)
P = 6.28 * sin(α)

If we had, for example, a 30° angle of attack, this would be:
P = 6.28 * 0.500 = 3.14 pounds/sq. ft Our hang-glider would have 3.14 * 100 or 314 pounds of this kind of lift.

Between the two, we would get a total of around 360 pounds of lift, enough to support the total weight of the craft and the rider, and it would be able to fly.

## The Improvement

Each of the objects under consideration normally uses a single thin surface (often made of very thin plastic) to minimize weight. This is in contrast to airplanes, which have a solid structure for their wings, which, of course, makes them much heavier. Airplanes use this solid structure (with a pretty much flat bottom surface) to keep air from going up under the top surface. It is most desirable for the air going UNDER the airfoil to go as straight as possible past the bottom of the airfoil (in order to have the least turbulence and the lowest possible relative air speed). Airplane wings accomplish this by having a solid rather flat surface on the bottom side.

This is not true for kites, hang-gliders, and ultra-light aircraft. As a result, a substantial amount of the air that should go straight past the bottom of the airfoil, can go up into the hollow area above that (but under the actual curved top airfoil surface). This has two bad effects. First of all, it allows a substantial amount of turbulence to occur there, which rapidly gets worse and worse as velocity is increased. That's a primary reason that these objects only work well for rather low relative air speeds. Second, since this air has an undefined path past the bottom of the airfoil, all sorts of random motions can occur in that air (called turbulence) and the air molecules generally travel farther than if they had gone straight past it. This effect means there is less benefit from the Bernoulli Effect, which means there is less lift created by the airfoil surface.

It's probably obvious by now what the improvement is. Stretching a second, very thin, plastic membrane tightly across the underside of the airfoil would create a LOWER, flat surface on the airfoil. This would eliminate the inner turbulence and it would generally greatly increase the overall Bernoulli lift as described above. The weight of the additional thin (Mylar??) plastic would slightly increase the total weight of the airfoil, but the significantly better aerodynamic lift usually easily makes up for that. The result is that the kite, hang-glider, or ultra-light aircraft has cleaner aerodynamics and substantially increased lift. In case it is desired, it will also operate much better at higher speeds.

The improvement is certainly worth considering!

### Update

May 2000

I have been informed that some hang-gliders have been made and sold with such a bottom membrane, for around 20 years. I have been told that the glide ratio of such hang-gliders is 15:1 where single-surface hang-gliders only have 8:1 to 10:1 glide ratios. That represents a significant improvement in performance. With this experimental verification for the benefits of a lower membrane, it's hard to understand why single-membrane hang-gliders are still used. Except that they're simpler and cheaper!

Dacron sailcloth is apparently the preferred material, because it is strong, durable and light. Mylar/Dacron laminates are also used.

In any event, it would be important for the bottom membrane to be stretched rather tightly, to avoid any luffing or vibration resonances in that surface, which would greatly reduce the benefit.

This new information strengthens my thoughts! Now I am even more convinced that all ultra-light aircraft, hang-gliders and even kites might greatly benefit from this second membrane.

This presentation was first put on the Internet in July 1997.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago