Paper airplanes are like real airplanes in their basic physics. To make a simple model for a game, you might want to start with a simple constant gravity force, a drag force proportional to the square of the velocity, and a lift force also proportional to the square of velocity (which comes from here), and then play around with the parameters until you find something pleasing to your eye. Modeling something like an airplane accurately is mostly the domain of expertise of aeronautical engineers. The basic physical ideas are those of fluid dynamics and the basic equation involved is the Navier-Stokes equation. For example, by constructing the plane slightly differently, you can make it fly faster, slower, further, curve left or right, or bob up and down. The nature of the force between the air and the plane can be quite complicated, and requires an extremely detailed analysis for accurate simulation. The plane is acted on by a constant gravitational force and by contact forces with the air, especially drag and lift. These laws apply to both the airplane and the air it travels through. The physics of a paper airplane is described by Newton's laws of motion. There is no simple equation for how a paper airplane flies like there is for a simple projectile because the airplane can interact with the air in complicated ways.
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