John P. Crotty
The same principles that held for actual airplanes also apply to paper airplanes. There are two conditions necessary to make a paper airplane that flies well. It must be able to glide well and it must have good stability. The most important part of a glider is the main wing. It has to support the plane during flight. The shape of the wing’s cross section is called an airfoil. A chord line is a straight line drawn from the leading edge of the wing to the trailing edge of the wing. The angle that the chord line makes with the wind direction is called the angle of attack. The angle of attack changes as the nose of the plane raises or lowers.
When a plane is gliding, wind pressure acts against the wing. This force can be thought of as a vector. It has a vertical component, lift, and a horizontal component, drag. The ratio of these forces is called the lift/drag ratio. A plane that flies well will have a high lift/drag ratio. The glide ratio is the distance a plane will glide divided by its altitude. The glide ratio has the same value as the lift ratio.
A good wing shape is necessary to have a high lift/drag ratio. A good way to do this is to make the wing with a slight bend or camber. The amount of camber should be no more than six percent of the chord length.
It is very important to decrease the drag on the airplane. This can be done by making the surfaces of the plane as smooth as possible. This decreases the amount of air which sticks to the surface of the plane. The plane then has less friction as it passes through the air.
For a glider, a slender wing is preferred. A term that is used when discussing drag on a wing is aspect ratio. The aspect ratio is found by dividing the wing span by the chord length. The more slender the wing the higher the aspect ratio will be. On a paper airplane, however, the body of the plane is small, the weight is light and the speed is slow. Therefore, according to Dr. Ninomiya, it is not necessary to build the wing too slender. It is more important to build a light and sturdy main wing with an aspect ratio of about five or six.
The lift/drag ratio changes with the glider’s angle of attack. For paper airplanes, a 5 degree or 6 degree angle of attack is best.
The weight of the whole plane divided by the surface area of the main wing is called the wing loading. A heavy plane with small wings will have a large wing load. Planes with high wing loads glide faster so that their rate of descent is high.
Today’s actual glider’s have glide ratios exceeding forty. That is it can fly more than forty meters horizontally for each meter of altitude it falls. This allows skilled pilots to take advantage of updrafts and stay in the air almost indefinitely. The record for distance covered in a straight line is 1,461 kilometers and the record for altitude is 14,102 meters.
For paper airplanes if you want a flight of long duration, you want to have a low wing load. You can do this by making a large wing area with a body as light as possible. Examine the winning plane in the duration aloft category from the 1st International Paper Airplane Contest. The plane is essentially a sheet of paper which is folded in half. The fold serves as the fuselage. It would be hard to get a wing load much lower. The actual construction is: Take a sheet of paper 3 3/4” by 8 1/2”. Fold the paper in half so that the new dimensions are 1 7/8” by 8 1/2”. Open the paper. Fold one side in half. Open the paper. Fold one of the new folds in half again. Fold over again. Tape. Camber edges. Crease the folded section at the center point. Launch with a gentle horizontal motion.
A plane’s gliding speed and rate of descent depend a lot on the wing loading. You must decide what you are designing your plane for when you choose the amount of wing area you want your plane to have. If you want a long time-aloft flight, design your plane with a large wing area. If you want a long distance flight, make your plane with a small wing area.
The first airplane contest had an interesting story about thin versus thick wings. It seemed that every entrant also submitted a letter. Frederick Hooven, the winner in the professional duration aloft category, wrote one of the most interesting letters. It turns out that when he was a boy in the 1910’s, he became friendly with Orville Wright. One of the topics they discussed was thin versus thick wings. The National Advisory Committee for Aeronautics was reporting that thick wings were better. However, in their wind tunnel, the Wrights had demonstrated the superiority of thin wings. Orville Wright, Wilbur had already died, helped Hooven with his experiments. Sure enough, thin wings tested better.
Years later, Hooven learned that air viscosity plays a negligible part in low speed airflow around a small object. The flow will be more laminar than turbulent. Thus, according to the models, thin wings have a much better ratio of drag to lift. When the models and speeds are brought up to normal size, the effects of air viscosity must be accounted for. The thick wing then becomes more efficient. However, in supersonic flight, thin wings again become superior. Hooven concludes by saying how paper airplanes conform to early aerodynamic theory.
The shape of the wing or wing planform is very important in determining flight characteristics. Aspect ratio is the primary factor in determining the lift/drag ratio of a wing, where aspect ratio is the ratio of wing span to wing chord. An increase in aspect ratio will decrease the drag; a decrease in aspect ratio will increase the drag. It should be noted in actual aircraft an increase in the aspect ratio because of an increase in the wing span will also increase the weight of the wing. This increase in weight negates part of the gain.
You can choose the wing shape you want from a variety of shapes. For a good flying plane, try to avoid odd shaped wings. The elliptical wing is an ideal shape. It provides a minimum of induced drag for a given aspect ratio. However, it is difficult to construct. A rectangular wing does not provide as much lift; however, it stalls less. On a rectangular wing, air turbulence affects the central part of the wing. A sweptback wing will stall at low speeds. Air turbulence affects the wing tip which sends the plane into a tip stall which causes a sudden loss of lift.
Then there’s the Kline-Fogleman airfoil which doesn’t seem to stall. This airfoil was created and patented by Richard Kline, an advertising executive who liked flying paper airplanes, and Floyd Fogleman, a weekend pilot. Their airfoil is flat on the top and notched, partially hollowed out, on the bottom. This seems to be opposite of Bernoulli’s principle which would want air to travel farther and therefore faster on the top. Dan Santich, the chief designed for Top Flite, a company in Chicago that manufactures model-airplane kits, has done tests on the airfoil. He hypothesizes that the cutout creates a vortex within the cavity of the airfoil. This vortex produces a forward and an upward push. Thus, the vortex acts as a lifting force within the shape of the airfoil. The area seems to expand and contract according to the speed and the angle of attack. The vortex acts as a parasite boundary layer which helps prevent the separation of air molecules.
On page 47 of
The Ultimate Paper Airplane
is a picture of the flow around the airfoil in a smoke tunnel. There is a smooth flow of air over and under the airfoil. Because of this laminar flow, I believe the hypothesis.
In tests at Notre Dame, the airfoil developed better lift/drag ratios with the step on top. The wing’s lift improved by 44 percent and its lift/drag ratio improved by 30 percent. Kline-Fogleman was patented with the step on the bottom for supersonic flight. As alluded above, the effects reverse themselves in supersonic flight.
There are two theories why this airfoil has not been embraced. One is that the design is too close to the Whitcomb supercritical wing which was patented by NASA in 1976. The cavity in the Whitcomb wing is not as pronounced as in the Kline-Fogleman, but it could be close enough.
The other reason could be that early tests on the Kline-Fogleman airfoil showed a poor lift/drag ratio. Kline defends this by saying that they patented a concept, not an exact shape. The drawings for the patent show a sharp leading edge. If a more aerodynamic leading edge is used, the lift/drag ratio will improve.
They also feel that the wind tunnel tests don’t take into account the lift that is generated from thrust. In the previous section, I simplified the forces that act on an airplane by pairing lift as the opposite of weight. Lift is actually the sum of all forces in the upward direction. Thrust is a force which has a horizontal and vertical component. Kline-Fogleman contend that wind tunnel tests didn’t calculate accurately the lift that is generated by thrust.
They also contend that the vortex the airfoil traps produces added thrust. They backup their claims by tests that have been done with radio-control models. In 1974, sixteen-year-old Richard Foch entered the Kline-Fogleman concept in the International Science and Engineering Fair. He designed a flying wing that did not need a stabilizer. In 1976, fifteen-year-old Gregory Tyler demonstrated that the airfoil was safer than the conventional Clark “Y” airfoil.
Again, the importance of this airfoil is safety; it doesn’t seem to stall. Stalling is one of the principal causes of airplane accidents. The plane turns at too great an angle to the wind, loses its lift and crashes to the ground. Kline’s little paper plane simply refused to stall. I’ll be curious to see if anything more comes of this paper plane. The next section offers us another novel idea in flight, aerobies.
