# What is the optimal design for a paper airplane? (Or, at least, how can you approach it?)

Having only really known two designs for paper airplanes since my days as a child, one which flies about eight feet and another which flies about ten feet, I have always wondered how people manage to come up with designs that are able to fly much, much further than that. Clearly, these have no propulsion after their initial burst of energy (from being thrown); after that it's all about gliding.

So what design considerations should I make in order to create a plane that has the maximum flight time and distance? What are general best practices in this endeavor, and what are the physical bases for these choices?

I'm not looking for specific designs necessarily, but what qualities makes up a good paper airplane that can fly for a very long distance?

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The physics of a gliding airplane are simple. There is potential energy, proportional to height above the ground. There is also kinetic energy, proportional to speed squared.

First, understand the speed. If the plane isn't slightly nose-heavy, it will fly a scalloped up-down cycle. If it does that, add a little weight to the nose, or distribute the wing area more toward the rear. Assuming you've done that, you control the speed by turning up the trailing edges. The more they are turned up, increasing the angle of attack, the slower it flies. (Up to a maximum angle of attack, at which the wings stop working, or "stall".)

Back to energy. If there were no drag, the plane would never come down. Since there is drag, the drag tends to slow the plane down, decreasing its kinetic energy. Countering that is the plane's tendency to maintain constant speed and kinetic energy, so it descends, turning potential energy into kinetic energy, just like a ball rolling down a slope. So the more drag, the more quickly it descends, the less drag, the more slowly it descends.

A way to minimize drag is to minimize speed, because drag force is proportional to speed squared. (Therefore the sink rate is roughly proportional to speed squared.)

So the speed you trim it for depends on what you want to maximize:

• To maximize gliding range, you trim for a speed which is slow enough to have low drag, but not so slow that you don't cover much ground.

• To maximize time aloft, you trim for an even slower speed which has even lower drag, thus minimizing the sink rate. This speed is roughly half way between the speed for maximum range and the even slower stall speed $V_S$.

Check these links: V-speeds, and Gliding flight.

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Think about the forces that act on a real life plane.

Forces that help flight:

Going forwards, you have thrust (from the engines)

Going up, you have lift (from the aerofoil) and a force opposing the weight (air resistance)

Along the line of movement, you have a rotational force which affects stability

Forces that hinder flight:

Going back, you have drag (air resistance etc)

Going down, you have weight

Along the line of the wingspan, you have a rotational force that affects stability

A paper airplane has no thrust, and unless you're REALLY GOOD at origami, no lift force.

So you have to consider:

Air resistance in the vertical plane (which you want to be high)

Air resistance in the horizontal plane (which you want to be low)

Weight (which you want to be low)

Stability around the direction of movement

Stability around the line of the wingspan

Therfore, the optimum shape would have infinite area when seen from above, zero area when viewed from in front, zero weight, a vertical stabliser to stop rotation around the direction of movement, and good balance to prevent rotation around the line of the wingspan

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