The science behind paper airplanes is based on the principles of aerodynamics, which is the study of how air moves around objects. The following factors determine how far a paper airplane can fly:
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Aerodynamics: The ease with which an airplane moves through the air is the first consideration in making an airplane fly for a long distance. The aerodynamics of a paper airplane will determine the distance and ease at which it flies. Planes that push a lot of air, like your hand did when it was facing the side, are said to have a lot of "drag," or resistance, to moving through the air. If you want your plane to fly as far as possible, you want a plane with as little drag as possible.
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Weight: The weight of the paper airplane should be kept to a minimum to help fight against gravitys pull to the ground.
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Thrust: The initial thrust comes from the muscles of the "pilot" as the paper airplane is launched. After this, paper airplanes are really gliders, converting altitude to forward motion. Thrust is the forward movement of the plane.
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Lift: As the plane moves forward, its wings cut through the air to generate a small amount of lift. As the air rapidly flows over and under the paper wing, a tiny vacuum is formed over the top of the wing to hold the plane aloft. As the forward motion diminishes, the airflow over the paper wing slows and the lift is reduced. A properly designed paper airplane should glide to a safe landing.
The design of the paper airplane plays a vital role in its performance. The builder folds the sheet of paper to provide maximum wingspan to support the plane for prolonged flight. The construction material (type of paper), angle of lift-off (how you push it off), and even the atmospheric conditions (the weather) also determine how far and high your paper airplane will go.
In summary, a paper airplane can fly far if it has good aerodynamics, is lightweight, has enough thrust, and generates enough lift to stay aloft.