My approach is very different from the way that everyone else seems to try this! Everyone tries to use Engineering refinements to try to make a paper airplane stay up a little bit longer. My College Degree was in Theoretical Physics, so I have a rather different approach!
I CONCEDE that the paper has unavoidable WEIGHT, and that GRAVITY will eventually win! So the idea of trying to use THINNER paper or some lighter material is attractive but destined to have minimal benefit.
Instead, I have watched eagles and other large (and heavy) birds manage to fly for more than half an hour, CIRCLING, where they rarely ever even flap their wings once! They do that because they know that certain areas have climatic effects which create UPDRAFTS or what are also called THERMALS. While still in College, I was intrigued by this! Near some mountains, there are prevailing winds which tend to rise. In farming areas, during hot, sunny days, black soil gets very warm where nearby lighter color sand or rock stays cooler. This causes a Convection Cell to form where warm air nearly constantly rises over the black soil. The birds slowly CIRCLE over and over, rising a little higher after each lap. No wing motion is required, and it is really just solar heat and Convection air circulation that causes the birds to rise. Once they are high enough, they can move out of the convection cell to slowly sink while flying miles away! Virtually no work at flapping the wings is needed!
You may see individual birds or groups of birds CIRCLING over such black fields on a sunny day, or also over a black asphalt parking lot. This is standard knowledge to most birds!
By the way, also while in College, I learned how to sail in a small sailboat. I neglected learning an important detail until one day in Long Island Sound near New York! We had taken the two small Sunfish sailboats out toward the Sound, and we both complained that we seemed to take forever to get very far out. We did not then know that on a hot sunny day, the buildings and pavement of the City of New York heated up far faster than the water out in the Ocean or the Sound. That was causing a large Convection Cell where air was rising over the city and therefore sinking out over the Sound. So we continuously confronted 'prevailing inland winds' that were toward the shore and the city, in other words, winds that we constantly had to overcome to sail outward. We decided that we LIKED that as we would then have onshore breezes HELPING us when we later turned around and sailed back in!
It turns out that we were uninformed about that! So as it got near sunset and we expected to ZOOM in to the dock, we were really quite a few miles out at that time. So we turned around and headed back. But what we did not know was that the City was no longer heating up but actually starting to cool off, as it would continue to do through the night until the dawn. This actually REVERSED the Convection Cell which we had fought all afternoon! As of sunset, the prevailing winds changed to being OFFSHORE, and we wound up AGAIN having to fight prevailing winds to get back! Where we had expected to zoom back in in half an hour, before dusk, we wound up having to tack back and forth for many hours, and we were VERY tired as we got back in a little before midnight!
This IS a lesson which I learned for the rest of my life! As part of it, I realized that right around sunrise and again at sunset, most winds tend to briefly become CALM for a few minutes, while the Convection Cells are in the process of reversing themselves.
This actually was related to this Paper Airplane project. Since I really needed DEAD CALM air, my first thought was to try to fly the paper airplane near Dawn or Sunrise, when there are rarely any significant winds. But that was a non-starter as I also needed the asphalt pavement to have gotten rather hot due to the sunlight, which required me to do these experiments on a sunny afternoon!
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The black asphalt acted like the black soil, in absorbing solar heat to make the asphalt very hot, which then causes pretty consistent updrafts in a large Convection Cell.
I chose to try to do my flights during sunny afternoons when the asphalt was especially warm. Unfortunately, weather is such that there are generally winds that also exist then, so I wound up having to wait patiently for about 30 days before I had a day that there was DEAD CALM on such a sunny afternoon.
I made a rather conventional paper airplane out of a single folded sheet of typing paper. I carefully made it as symmetric as I could, so that it naturally tried to fly very straignt. I then used a conventional stapler and added ONE STAPLE near the outside end of one of the wings. This very slight additional weight made my paper airplane fly 'slightly crooked'. It then flew with a very slight sideways tilt, in order to cause it to CIRCLE.
You need to tweak this to enhance how it performs, but I will leave that up to you.
But on that DEAD CALM DAY on that very hot asphalt parking lot, I would SLOWLY launch my various paper airplanes. When I built it right, my paper airplanes would gradually circle. I found that planning it to circle in about a 50-foot diameter circle seemed best. Each time my paper airplane went past me, it was about two or five feet higher! The rate of rise depended on just how hot the asphalt parking lot was.
In principle, my paper airplane might have circled for hours, going higher and higher and higher! Each lap took about 25 seconds. But eventually, a VERY slight wind existed which caused my circles to drift slightly downwind, and eventually, it was no longer over the hot asphalt parking lot (which had been powering it!).
I found this works for nearly all paper airplane designs. However, the 'jet' types tended to fly rather fast, and I think they needed more power for that, so getting a 'jet' paper airplane to stay up very long was not easy. Wide-winged designs fly at much slower airspeed, and so they create less turbulence and need less power supply, and so they seemed to be easier to keep flying longer.
By the way, when organized Paper Airplane Contests are had, the organizers ALWAYS have them INSIDE some big building. They do that to avoid winds affecting one competitor's effort any more than another, so I understand WHY they do it indoors. But MY approach would not work well indoors! In fact, copying birds, my approach REQUIRES repetitive circling over and over to get much altitude.
I did NOT consider this to be any major project, so once I had one of my paper airplanes fly for around ten minutes, I was satisfied! But if there are others who are more fanatical, and who are more patient for finding a sunny afternoon with absolutely DEAD CALM wind conditions, I suspect having a paper airplane fly for a half hour or more would not have been that hard to do. However, there IS a complication! Even in just ten minutes, the paper airplane has circled about 25 times and so it would get up to around 60 or 70 feet (and occasionally over 100 feet) up! A little paper airplane is NOT THAT OBVIOUS when it is that high up! I probably should have painted my paper airplanes some bright color, but I also did not want to add the weight of a lot of paint!
On one of my test days, a Mall Security Guard came up to find out what I was doing in their parking lot! I pointed up at the tiny dot in the sky and it took him a moment to see the paper airplane up there! He watched for a minute or two, probably trying to figure out if I was committing any crime! But he walked away smiling!
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