Ever since I can remember, airplanes have always captured my attention. Even today, whenever an airplane flies over my house, my neighbors can still see me run out to get a good look at it. As a kid, I made all kinds of paper airplanes – and obviously, I still do. Besides the satisfaction in making a flat sheet of paper fly, I find a certain degree of therapy in them. When I have a problem to solve that involves some serious thinking, I usually can be found designing and folding a paper airplane while I mull over the issue.
30 Plans for the Paper Pilot was written to provide proven, wind tunnel developed paper airplane designs that, along with innovative folding and launching techniques, allow one to fly these designs where the “pilot” wants them to go. Having grown up with a few proven designs as a kid, in 1974 I started an effort to expand my designs. This page contains a brief excerpt from the book and provides some insight on how to make paper airplanes.
In order to help you understand why the paper airplane designs in this book fly so well, I should touch on the laws of aerodynamics. Understanding these laws will help you to build your airplane with greater precision and better performance. Generally, there are four forces acting on an airplane at all phases of its flight:
Thrust: The first is thrust, the forward motion of the plane through the air. Paper airplanes are gliders, converting altitude, or height, into forward motion.
Lift: The second is lift, which the wings produce as a result of the forward motion.
Drag: The third force – air resistance, is also known as drag, which is always trying to slow the airplane down.
Gravity: The fourth force affecting a plane’s flight is gravity – which is always pulling toward the ground. Some aeronautical engineers include a fifth force known as either tail lift, or tail down force – depending upon the type of airplane design. This “fifth” force is critical for stabilized flight.
Whether it is a quarter-ounce paper airplane, or an 803,000 pound Boeing 747 jumbo airliner – all aircraft function with these same principles to achieve flight.
An airplane must also be properly balanced in order to fly properly. This is known as having a proper center of gravity, or in pilot lingo – CG. Every object has a center of gravity; that is, the point at which it will remain level if balanced. If for example, you horizontally balance a pencil across your finger, the balance point is the pencil’s center of gravity. The same holds true for airplanes. However, there has to be a proper relationship between the CG and the center of lift or CL, which is produced by the wings. To obtain this correct relationship, many of the airplanes in this book require the addition of paper clips to the airplane’s nose.
Wing size vs. its weight will affect its flight characteristics. Having more weight with a smaller wing increases the wing loading – or the amount of weight the wings must carry. For example, if two airplanes weigh the same, but airplane A has half the wing area of airplane B, then airplane A has a higher wing loading as the wings must carry more weight. This will generally give airplane A more stability because it is less affected by wind or turbulence. But, airplane A will also have a higher stall speed, which means that it will not be able to fly as slowly or be able to glide as far as airplane B (this will be covered in more detail later).
The shape of a plane’s airfoil (a cross-section of the wing), combined with thrust, is what gives a plane its lift. The best analogy of how an airfoil produces lift is to look at a stream of water as it is coming out of a faucet. When the faucet is on low, you’ll notice how the water stream is the same diameter of the spout as it leaves the faucet. But as the water stream nears the sink, notice how the stream thins out. This is because the water is accelerating as gravity pulls it away from the faucet, thereby thinning it out. With this in mind, picture a “block” of air as it meets the leading edge of the airplane’s wing, or airfoil, as depicted in the sketch below. As the “block” of air hits the leading edge of the wing, it separates, with half going over the top of the wing, while the other half goes under.
This “block” of air must meet together at the trailing edge of the wing. However, due to the upper curved surface of the airfoil, the airflow on the upper surface has a greater distance to travel, and it must therefore speed up to arrive at the same time as the lower half. This results in the air on the top of the wing thinning out, or becoming less dense, much in the same way the water thins out from the faucet. The airflow under the bottom of the wing remains the same pressure as it was prior to the wing slicing into it. Thus, the air flow on the upper surface is less dense and “thinner” weighs less. The result is that the airfoil creates lift by being “sucked” up.
Airfoils also achieve lift due to Angle of Attack. Angle of Attack is best described by the following example: A water skier skims along the surface of the water through forward motion. Upon releasing the tow rope, he or she starts to slow down. As the speed slows, the front of the skis must be raised in order to keep him or her on top surface of the water, thereby increasing the angle of attack of the skis. The more the speed slows, the more the skis must be raised to remain on the surface of the water. The skier can remain upon the surface by increasing the angle of attack of the skies.
However, as the skier raises the tip of the skis, more drag is created, due to the angle of the skis going through the water. This creates drag and it exponentially slows him or her down. As the drag is increased, the skier slows more and again to compensate, more angle of attack is required, etc. This cycle increases until the speed is so slow that the skis will no longer maintain the skier’s weight. The same basic principal holds true for an airplane wing.
When the angle of attack of an airfoil gets too high for its speed, the airflow cannot adhere to the upper surface of the wing. The airflow burbles, killing most of the lift, resulting in a Stall. Using the previous mentioned principal, the slower the wing speed, the greater the angle of attack is required to maintain the same amount of lift, until the angle becomes too great and a stall occurs. Some airfoils behave well in this realm – others do not.
All of my paper airplane designs utilize full-sized aircraft high lift devices known as, Slats, Flaps and Winglets. Incorporating these full-sized lift devices on these paper airplane designs allows the wing to generate more lift over a wider speed range, than typical designs. This results in a paper airplane with a flatter, longer glide angles, and better behavior in windy conditions.
The leading edge of the wing is drooped down. This acts much like a shovel, scooping the air stream up and over the wing by creating a camber of the wing, forcing the airflow to thin out or become less dense, as it covers the greater distance over the upper surface of the wing. This generates lift on thise paper airplane designs – just as full sized aircraft do.
Flaps are trailing edge devices, which also increase the camber of the airfoil. These designs incorporate two types of flaps; Hinged, where the trailing edge is folded down, and Split, where the design allows the lower layer of paper to be bent down, as shown in the sketch below.
Both types work well, with the split type providing a higher measure of drag over the hinged version.
Winglets are “end caps” for the wing. When a wing is generating lift, the higher pressure airflow that exists under the airfoil, wants to spiral around the wing tip to flow into the lower or less dense airflow that exists on the upper surface of the wing. This generates “vortices” which could be thought of as horizontal tornadoes that trail behind every wingtip that is generating lift. The winglets act as a dam to reduce this, thus providing more lift.
To prove this effect, make a paper airplane of any design, and fly the airplane through the middle of a cloud of cigar smoke. You will notice how the smoke swirls around the wing tips, creating horizontal “twisters” or vortices. Again, this occurs because the higher pressure air that is under the wing is swirling around the wingtip to the lower pressure air on the top of the wing.
Different types of airfoils have different flying characteristics. Generally, a thicker one will generally develop more lift, and is better for slower speeds, but at the cost of higher drag. A thinner airfoil has less lift, less drag and is designed for a higher speed, but at the cost that it cannot fly as slowly as a thicker one.
Most of the designs in this book incorporate a differential stall wing – also referred to as “wash-out” or “wing twist”. A wing incorporating wash out, has less angle of attack toward the wing’s tip, which allows the wing tip to continue to provide lift, while the inboard sections of the wing are stalled at high angles of attack (or at slow speeds), thereby creating a “mushy” stall that is predictable. We can create this airfoil aerodynamically in the same way that a commercial airliner can modify its wings, to compensate for different flight requirements, by folding a slat into its leading edge. And by increasing the amount of this slat toward the tip, it will aerodynamically produce wash out of the wing tip. This allows the paper airplane to fly much better in changing wind conditions.
Vertical Fins and Rudders
Many of these designs employ inverted twin rudders, which are located at the rear of the aircraft. These act in the same fashion as a rudder on a boat or fins on an arrow. On these designs, please note that the fins are turned a few degrees inward to ensure stability. On a Delta Wing, the inverted twin rudders also act much like a winglet, helping to increase lift, while also providing yaw stability.
This is something that is all too often overlooked on a paper airplane. The dihedral angle is the angle at which the left and right wings meet at the center of the airplane, and is paramount for stability. Most airplane wings are bent slightly upward at the wing tips, as can be seen on any airplane of today. This upward sweep of the wings enables the aircraft to straighten itself out when deflected or rolled by wind, or with our paper airplanes, by launching technique. When the airplane is deflected from level flight, the upper wing loses lift due to its shorter lifting surface, while the lower wing increases in lifting surface – this returns the airplane to level flight. This is illustrated in the sketch below:
Trim and Trim Tabs
Trim is probably the most important facet of an airplane in flight. Due to the lift characteristics of the airfoil while in flight, the plane has a tendency to nose down, or dive. The faster the airfoil goes through the air, the more nose down tendency becomes. This happens to any airfoil whether it is a full sized airplane or any of the designs in this book. To counter this in paper airplanes, the airplanes need elevator trim tabs. These tabs aerodynamically push the tail down and thereby the nose up, to provide a positive angle of attack on the airfoil. If you will notice in all of the photographs of the more conventional airplanes in this book, there are tabs at the rear of the airplane, which have a slight upward bend to them. How much bending of the trim tab you add, will depend on trial and error. The more the trim tabs are raised, the higher the nose will want to be, thus creating a higher angle of attack on the wing, which in turn produces more lift. The airplane climbs, and as it climbs it slows down (much like a car coasting up hill). As the airplane climbs, it slows down and as a result the wing produces less lift, causing the nose to drop and the airplane will pick up speed again. On a properly designed airplane, this results in a series of climbs and dives that will dampen out within a few cycles. When you find the “sweet spot” of the proper amount, your airplane will have a slight nose up attitude and will fly in a flat glide.
Flaps provide more lift and allow the airplane to fly at a slower speed, examples of which can be seen in the photographs of the designs. These are optional, but if you add flaps to the aircraft (especially split flaps if the design permits), some incredibly slow air speeds can be attained. Flaps also have a speed limiting effect to them, keeping the airplane’s speed in check. These can be beneficial if you have a design that you want to launch from a “high apartment window”, bridge, or rooftop. While providing lift, they also help keep the airplane in its more efficient speed range, providing a longer flight.