# What is useful with paper airplanes

3.1 The physics of the paper airplane

A plane - no matter which one - is exposed to 4 forces. We got to know lift and drag in the previous chapter. In order for the buoyancy to be effective, however, a certain minimum speed is required. Only when the suction effect is greater than the weight of the aircraft does the aircraft begin to take off. The weight is caused by gravity. Unfortunately we have no influence on gravity, but we can build the plane more easily. All bodies fall at the same speed to the center of the earth, but this only applies if we neglect air resistance. In aerodynamics, we have to take air resistance or weight into account. If a plane is lighter, you can get by with less lift - but a lighter plane usually also means less stability.

The lift counteracts the force of gravity, and the thrust is weakened by the drag. Conversely, the lift is dependent on the speed (caused by the thrust) of the air.

The following principles apply:

1) The thrust (caused by the thrust) must be greater or greater than or equal to the air resistance.
2) The buoyancy must be greater than the weight (caused by gravity).

In the beginning, the plane gets its acceleration from the force of the limb. However, the air resistance slows the aircraft down and the nose tips forward - the aircraft now has the characteristic speed. Now it becomes clear whether a paper airplane can really fly and has aerodynamic properties or whether it simply crashes. If the lift caused by the characteristic speed is in equilibrium with the weight, then the aircraft glides in a straight line and does not lose any height. Due to the air resistance, the speed decreases, the lift decreases and the paper plane hovers towards the ground.

If the nose is tilting down slightly and gravity is pulling the plane down and there is sufficient speed, then the plane should begin gliding. The speed and the angle of inclination then no longer change. If the plane has enough lift then it glides over a nice long distance until it lands at rest. If the lift of the characteristic speed is no longer sufficient during the flight, the aircraft will crash.

During the sliding phase, all 4 forces are in equilibrium. The buoyancy that counteracts the weight is determined by the characteristic speed. The weight pulls the plane to the ground and the speed would increase again if it were not slowed down by air resistance. The speed is controlled by air resistance and weight. Since the weight force and also the air resistance can be viewed as constant in these areas, a characteristic speed results. The characteristic speed results from the air resistance and the position of the center of gravity. If the plane's center of gravity is right up front, the plane will inevitably crash. If it is right at the back, the plane rears up, there are vortices in the air and it also falls. The center of gravity should be just in front of the point of lift. The lift point is defined by the fact that the lift acts there. Unfortunately it is not always easy that the point of lift and the center of gravity coincide simply because of the folds of the paper airplane. You can still improve a lot by tuning the plane.

When folding a paper airplane, an airfoil is always created, which produces lift. This is a little more complicated with paper planes, because a wing consists of two parts: the part that creates the lift and structural components.

If you look at the arrow flier (from building instructions 1), you can see the difference. The fact that the paper is not folded perfectly (you shouldn't fold it too hard) creates a pocket. This bag has an aerodynamic profile that forms the actual wing. From an aerodynamic point of view, the structural components would not be needed, but they are important for the overall stability of the aircraft.

Practically every paper airplane has these pockets, but sometimes they are on the underside of the wing. When a plane doesn't glide properly, the pockets have usually been squeezed too tightly. You can help a little if you slide your fingers into the pockets and bend them open - this usually helps.

There are no pockets on the planar plane and some exotic paper planes. Here the aerodynamic profile is created in a different way.

The rollers made of paper create a large obstacle for the air flowing around them - see Bernouilli's theorem. If the rollers are folded well, you get an excellent wing profile - unfortunately, the air resistance is also correspondingly high.

3.2 Crash - when the dream of flying turns into a nightmare

Sometimes paper planes just crash. There are also physical reasons for this. If the symmetry or other parameters of the aircraft are poorly adjusted, the greatest lift is of no use. There are a few simple tricks that can be used to improve the flight stability of a paper airplane. To do this, however, it is necessary to know how a paper plane crashes or how a plane moves in space.

To do this, some technical terms must be explained.

Roll: The plane rotates around its longitudinal axis. Pendulum motion can also occur - but no complete rotation is performed. If a plane has this property, then the plane does not crash immediately, but staggers through the room.

Nod: Your nose rises or falls when you nod. If the nose tilts too much towards the ground, the plane will crash. Conversely, the nose can also tilt upwards too much. This can be due to excessive buoyancy. Unfortunately, the air resistance also increases, which can affect the distance of the flight. If the plane straightens up too much, then it loses its lift and it also falls. The most important thing in building paper planes is to get a grip on nodding.

Yaw: The plane flies in a circle. Sometimes you want a long straight flight and yaw is a hindrance.

How can a flight look like?
The four possible trajectories are shown in the graphic below. After the plane is thrown away (throwing phase), it goes into the gliding phase. The plane can crash - red or purple trajectory, or glide for a very long time - green trajectory. The fourth trajectory is something between a crash and a glide phase. By making various changes to the plane, you can get (almost) every plane to move on a beautiful (green) glide path. But even if the plane is already gliding nicely, it is usually possible to increase the distance. The optimal glide angle g should be 11 °. This is a fairly small angle - but it results in great widths. For example, the world record for the distance for a tuned A4 paper plane is 64 meters (in a closed room!).

The stability of a paper airplane is given by three conditions:
1) Slope stability
2) Course stability
3) Fall stability

The inclination stability is responsible for ensuring that the bow is not tilted too much upwards or downwards. The plane nods. Correct trim is important for flight. The weight of the nose of the fuselage or the center of gravity of the paper airplane is important for the stability of the flight. With a good paper airplane, the folding results in an optimal position of the center of gravity in relation to the lift point. The plane no longer needs to be adjusted - but this is rarely the case.

If an aircraft is not well balanced, there are a few little tricks that can be used. Some planes fall on a trajectory parabola (red trajectory) towards the ground. By slightly bending up the rear corners of the structural components (left graphic), the inclination changes and with it the lift. But be careful: if the lift is too strong, it will lead to a crash again - purple trajectory that covers the plane. The lift is then so great that it rises vertically upwards. The speed decreases rapidly - the lift decreases and the plane crashes. At the rear corners of the paper plane, the paper should not be kinked under any circumstances, but should only be bent very slightly. In practice, you shouldn't be able to see the bend with the naked eye. One is always surprised what a great influence such small bends can have. The paper must be bent equally on both sides. It takes some practice to do this correctly. You start with a slight bend, test the plane and bend further if necessary. You should always start with the smallest changes as it is very difficult to undo them. Of course, you can also bend the paper down if the aircraft's lift is too strong. If the plane slides to the right, then the corner at the right rear end has to be bent up a little or at the left corner bent downwards. This is where the arduous work of a professional paper airplane manufacturer begins - but the effort is worth it.

With some aircraft it is not possible to change the structural components on the sides. By bending up the rear fuselage segment, you can change the inclination of the paper airplane in flight. You bend a triangle (lower graphic on the left) into the trunk - you should be able to move the triangle in both directions. Then you fold the trunk slightly and press the tip of the triangle slightly upwards.

An additional element is created that changes the angle of inclination and thus the lift of the aircraft via the air resistance. At what angle should the triangle be folded? Unfortunately there is no answer to this question. It takes a lot of practice to know the exact angle. But you don't have to tune every plane into a record-breaking plane. One should not forget that with this method the speed is strongly reduced by the increased air resistance.

Another way to stop the aviator from nodding is to use a simple paper clip.This is particularly useful if the trajectory is marked by alternating ascent and descent (blue trajectory). The paper clip is attached in the front third. This shifts the center of gravity - the plane can no longer climb as much. This is where the real work of the paper airplane builder begins. It takes some time to find the right position for the paper clip, but the results are impressive.

Unfortunately, paper planes don't always follow a straight line. The course is not stable. Some planes are designed as gliders, other planes as aerobatics. The aerobatic pilots can fly impressive loops and turns - but this is not absolutely desirable with a glider. Sometimes a plane should just fly straight ahead. Unfortunately, it's not always easy to fold fliers that are really symmetrical. One wing has a little more lift or a slightly different drag than the other wing. The plane will fly in turns. So the plane needs a rudder. For most aviators, this is the fuselage. The larger the fuselage, the more stable the aircraft will fly.

If the fuselage is small, then the wings are large - there is a lot of lift and the plane will stay in the air for a long time, but possibly turn in turns (top left figure). If you fold the fuselage and the wings in a delta shape, the fuselage becomes larger and the aircraft remains stable on its flight path, but it has less lift. Caution: the wing must not be too small!

Additional stability can be achieved with an additional elevator. You fold a small triangle of the structural component at the top. It is very important that the folding is parallel to the fuselage (straight line in the lower graphic), otherwise the aircraft will lie down even more in the curve (dashed line in the lower graphic). Unfortunately, this increases the air resistance, or the aerodynamic part of the wing may become a little smaller, which is at the expense of lift.

The crash stability can be fixed by a simple trick. A plane can crash in many ways. A crash-stable flyer begins to fly ever tighter turns and moves faster and faster towards the ground in ever tighter circles. This happens when a small breeze of air throws the plane off balance and the plane begins to taxi in one direction. A good-natured aviator then begins to taxi in the opposite direction and he recovers from this breeze. This does not apply to a crash-stable flyer. This is due to a typical mistake beginners make.

The wings can be folded in three different ways. The wings can point upwards (Y-position), be straight (T-position), or point downwards (negative Y-position). When folding paper planes, the wings have to be properly unfolded. Most beginners don't pay enough attention to this and the paper plane crashes. The Y position is essential. The wings must be folded up as a whole.

Why should the wings be folded up so much? Let us consider a plane with a T-section that we hold with our fingers. Let us not forget that the paper folds up easily in flight - no longer held by the fingers. This causes the fuselage to widen and the wings to point down. This is one of the reasons the wings should be folded up.

The wings have to be folded up even more for another reason.

A stable flight attitude is given by the balance between weight and lift. This equilibrium is disturbed by a lateral blast of air.
The Y-position ensures a strong flight stability and in the event of disturbances it restores the balance. If a small puff of air from the side throws the plane off balance, the plane compensates for the disturbance with a small rolling motion. The aircraft then rolls back to its original position. If the airplane were in an inverted Y-position, then there would be this small roll motion as well, but the roll motion is now increased further. This leads to a tailspin and the plane crashes.

3.3 The correct release

Building a paper airplane is one thing - making it fly is another. Most mistakes do not happen when folding - most people pay attention to the exact instructions - it is important to drop them correctly. Unfortunately, it is not easy to explain the speed at which you throw a plane. The most important tip is the old wisdom: Practice makes perfect. Try different speeds when you drop it. Some planes are more suitable for low drop speeds, while other planes have to be thrown into space with the full force of the arm. One must not forget that the lift of a plane depends very much on the speed, that means you should try different launch speeds.

There is hardly anyone who does not have to work on his throwing technique!

Paper planes with a blunt nose are more suitable for slow flight, although considerable distances can be achieved. These fliers should be thrown down slightly.
For gliders with a blunt nose, an angle of inclination of 11 ° would be optimal. The release should be gentle but firm.

Fliers with a pointed nose should be thrown upwards at a slight angle with a lot of force. But you shouldn't overdo it with the inclination. If you throw the plane too steeply into the sky, it will rise nicely, but then it cannot slide into a glide phase and it will crash.

The take-off speed depends heavily on the design. In the case of stable structures, the take-off speed can be selected to be correspondingly high - as long as the wings do not bend. The paper plane should not lose its shape, otherwise the buoyancy will suffer.

In principle one can say that every flyer has an optimal launch speed and an optimal launch angle - you have to try it out.

3.4 Working with paper

There are many types of paper, but only one distinction is important: suitable and unsuitable paper. Suitable paper is resistant to creasing, i.e. the folds are retained. So you shouldn't use newspaper or paper towels.

Cardboard or heavy paper should also be avoided. It is difficult to fold and it has no resilience. This means that the folds are very rigid and not springy. The aviator cannot adapt to the air.

In fact, almost any 80g / m2 paper is suitable. Copy paper is the cheapest and meets all the important conditions. A little tip on the side: Paper that has already been copied is a bit better - it becomes stiffer and stronger when copied. The paper can vary in texture, weight, tint and thickness. For special origami models, 40g / m2 paper is ideal - the wings actually start to flutter when they fly. Unfortunately, this effect only works a few times as the folds then lose their elasticity. If you want to get beautiful, colorful models, you can use wrapping paper - it is crease-resistant and inexpensive. Unfortunately you still have to cut it to size (the A4 format is important). But you can also build beautiful planes from the most unusual papers: tickets, brochures or menus.

When folding paper, one should be very careful. A typical beginner's mistake is to fold the paper too much. A simple fold with a ruler or just a thumbnail is sufficient. If you abuse the paper too much, the fold will lose its strength and the plane will lose its stability. A few more points should be noted:

1) You should only work on a solid surface. The folds become more precise and stable.
2) You should only touch the paper when you are working with it. Everyone sweats and this liquid causes the paper to curl.
3) You should definitely pay attention to the corners. If they are slightly bent, it is better to use a new sheet of paper. Bends at the corners also serve as stabilizers - but only if they are made deliberately.

What is the best way to store the paper planes? Actually not at all, because when the air humidity rises a little, the paper begins to lose the properties that it acquired from the folding. Special models or models that are very difficult to fold can be put in plastic sleeves - the kinks are well preserved. Of course there are other options, but the most important is that the paper should be stored as flat as possible in a dry environment.

3.5 Problems with the plane

Beginners like to forget about the Y position. This is one of the most common mistakes made. Check the airplane for its symmetry (Y-position and trim).

Some planes are built 10 times and only one of them flies. This suggests a problem with the drop technique. Don't be frustrated if it doesn't work the first time. Rather, think about why the plane crashes, rolls to the side or flies in curves. Most of the time it can be changed. But there is also the case that you simply cannot get the plane to fly. This doesn't matter either - a new sheet of paper and a new plane is built in a few minutes.

With some planes, the folds create curvatures. These bulges should be smoothed out with the palm of your hand. If the plane doesn't glide nicely, it can do a lot to restore these arches - gently.

Make experiments with paper yourself - and if it doesn't work out, just throw it in the waste paper and start with a new plane. It is seldom possible to carry out such beautiful aesthetic experiments with nature that are so cheap and simple at the same time. Paper planes are quick to make and you can fly them anywhere.