Intro: A Non-Spinning Circular Wing Paper Glider
This is a paper glider I learned to make long ago (roughly 1970); unlike other circular wing paper gliders, this one requires only a single sheet of square paper (I'll show you how to make regular printer paper square, too), no glue, tape, or staples, no adjustment, and no special launching technique to impart stabilizing spin.
Step 1: Start Here
The folding starts with a square sheet of paper, but unless you're an origami aficionado, you probably only have the ordinary rectangular sort around. No problem; you can easily make any sheet of paper into a square sheet accurately enough for this build. This works best with 8 1/2" x 11" or A4 printer paper, but I've made these gliders out of note pad sheets as small as 4" square (after squaring up) and as large as tabloid (11" x 17" or A1); the smaller ones don't glide as well (too heavy, because the paper thickness doesn't scale with the sheet size) and the larger ones are fragile (again, paper thickness doesn't scale, so you wind up with thinner paper relative to the forces of handling and flight), but with care, they do work.
To demonstrate squaring the paper, I've started with a common letter size sheet.
Step 2: Squaring Up
Since the fold needs to start with a square sheet, we need to make the sheet square. The easiest way to do this (and one of the most accurate) is to fold one corner of the paper down to meet the opposite side, carefully matching the top edge to the side before forming the crease.
Step 3: Cutting to Square
Once the first fold is creased in, we need to cut off the excess paper -- the bottom of the fold marks the square sheet we want to keep, and the part that isn't overlapped needs to go. I used a paper cutter, since I have one handy, but scissors, a razor knife or hobby blade will work -- years ago in school, I used to fold this tab over the squared piece, crease heavily, and tear carefully along the crease, with good results. I would usually arrange the later folds so the torn edge wound up inside the leading edge, but that isn't very critical, and if you cut even fairly straight, it doesn't matter at all.
Step 4: More Folding
Now that we have a square sheet, we can continue folding. Open out the sheet with the original squaring fold as a "valley", and fold on the opposite diagonal -- that is, bring the ends of the existing crease together and crease between the two remaining corners. You want to wind up with this second fold also a "valley".
Once this is done, open the sheet out again, and flip it over so both creases are "mountain" folds, then pick any corner (one of the ones on the torn side, if you had to tear the sheet to square it up), fold it into the center where the creases cross, and crease in. Now take the fold you just made and bring it to the center fold, matching the creases at the center point, and crease in. Repeat this fold in once more, giving a narrow folded strip eight layers thick at the center (which contributes both nose weight and stiffness, as well as a thickened leading edge, in the finished glider).
Now, fold the entire folded-in strip over the crease, so you have a triangle with the leading edge fold strip at the long edge.
Step 5: Roll and Close
All that remains now is to convert the triangular weighted sheet into a circular wing. Pick up the sheet and start to curl the leading edge, with the folded strip on the inside. Curl evenly and keep the folded strip tight, until you can slip one tip inside the fold of the other; on letter size paper, I overlap about a half to three quarters of an inch (for A4, 10 to 20 millimeters is close enough). Once that's done, even out the curve, and the glider is ready to fly.
The mountain fold that runs out to the tail automatically supplies the elevator incidence needed to perfectly balance the weight of the folded strip, the friction and tension of the fold will hold the ring closed without any glue or tape, and the combination of more weight in the center and the upward curve strongly stabilizes the glider with the longest part at the bottom and the joined tips at the top. Launch by holding gently, either at the leading edge ring or by the tail point, and sliding forward and a little down, speed as if throwing a paper wad to hit a basket a yard or two distant. The glider should glide between fifteen and twenty feet from head height with this launch. If you can arrange to throw one out of a high window, off an observation deck, etc., this design can glide several blocks, and will usually fly straight if there isn't much wind to disturb the glide.
Have fun -- but don't litter!