Differentiate, set equal to zero, yields Cl=sqrt(3*Cdo*pi*e*AR) and therefor v=sqrt(2*wt/(rho*S*sqrt(3*Cdo*pi*e*AR))) Paper airplane gliding performance is not usually very important. We usually want a plane that does a good job of flying across the room, and aren't too concerned if another paper airplane design (which would be more difficult to build) could have made the same flight more gracefully. Notice that for my world record paper airplane gliding performance is extremely important, but a low aspect ratio wing is needed to withstand the high launch speed (more on the specifics of the world record plane later). In short, very well! My son is slightly older than the target age group (he’s 11), but he enjoyed making the various different designs and seeing how they flew differently according to how hard you throw them. The default seemed to be ‘I’m going to hold this like a javelin and hurl it as hard as I can’, but he soon got the idea that doesn’t always work. The goal for gliding flight is to descend vertically as slowly as possible. This represents the lowest rate of change of potential energy(power) which is the minimum product of drag times velocity. Generally the minimum sink rate for gliders is just above stall, and that's true for paper airplanes as well. For those interested in the details and math, finding the minimum power required involves taking the equation for powered required, differentiating with respect to velocity, and setting this equal to zero (standard calculus procedure for finding the minimum or maximum of a function. Starting with the basic parabolic drag curve;

This wasn't going to be easy. If successful, it would be my forth time at setting the record. Each time was the absolute I could achieve, with improvements resulting from improving my planes and from working on a faster throw. My best unofficial time, 20.88 seconds, was the product of months of working out and well over 100 airplanes constructed. And I have another enemy sneaking up on me as well - time. I am 35 years old, and soon I know my arm speed is likely to decrease. Substituting the minimum sink results into the power equation, and knowing that vertical velocity is power/weight, gives the following:

Success!

There are many skills fathers should pass on to their children: how to ride a bike, how to skip a stone, and of course, how to make a paper airplane. When it’s time to show your kids how to fold a humble piece of paper into a soaring jet,don’t stumble around andhastily construct one from the poor memory of your youth — one that takes a disappointing nosedive as soon as it leaves yourfingertips.Instead, teach them the art of making a plane that can truly go the distance. Instructions for folding “Suzanne,” the plane that shatteredthe previous world record by flying an unprecedented 226 feet,10 inches, and garnered more than three million views on YouTube

Instructions for folding “Suzanne,” the plane that shattered the previous world record by flying an unprecedented 226 feet, 10 inches, and garnered more than three million views on YouTube

Multibuys

The airfoil of the plane also affects the launch. I have tried using highly cambered airfoils optimized for slow gliding, but they tend to degrade the ascent. I wrote a computer program to reproduce the flight of the world record paper airplane to learn what parameters were most important for a long flight. One of the most important things I learned was that Cdo, zero lift wing drag, is more important in the ascent than it is in the descent. The airfoil optimized for slow gliding is not optimized for zero lift, and produces extra drag during the ascent. What is needed is an airfoil which produces low drag during slow, high lift flight, but more importantly has low drag during the ascent. I believe a nearly flat, uncambered airfoil does this. Certainly a flat airfoil is ideal for low drag at zero lift, but it can work at higher lift coefficients also. The flat wing at high lift results in a steep pressure gradient near the front of the wing on the upper surface, which likely aids transition to a turbulent boundary layer which is needed for low drag at high lift. I plan to do more airfoil tests during the spring of '97 to help find the best airfoil for long flight. I have also tried a version of the world record plane which does not have a fuselage, it is a flying wing with no dihedral, but uses the wingtips canted up and out at an angle for the dihedral effect. The idea is to eliminate the "V" shape of the fuselage and use that part of the paper to maximize the wing span to reduce the sink rate. Unfortunately I have not been able to achieve good ascents, with low launch heights as a result. This modification noticeably affects the flexibility which allows good launches.