Over at Pitchpull, just before going on vacation, Greybeard was lamenting public ignorance of autorotation: the procedure by which a helicopter pilot can safely land a helicopter in the event of an engine failure. I have to admit that before I started training to be a pilot, I thought that without the engine, a helicopter took on the aerodynamic properties of a brick.
But now I have a little paper model helicopter I can build to show people how a helicopter fails to plummet, and I'm going to try to share it with you, even though I don't have a camera.
Start with a regular piece of letter paper: 8 1/2 x 11 for the North Americans, or A4 for the Europeans. Cut it in half lengthwise, so you have two pieces of paper. Put one piece aside, so you can use it if you mess up the first one, or if someone you show it to likes it so much they want their own. The piece of paper you have left is now considered your entire piece of paper.
Take your scissors and cut the paper as if you were going to cut it in half again lengthwise, but only cut about an inch less than halfway through. Stop cutting before you get to the halfway point. You now have a strip of paper with a slit at one end. The end with the slit I will call the top. Your next cut will be a short snip from the side. Start halfway down the side of the paper, that is, start about an inch below where the first slit ends. Snip in about a quarter to a third of the way through. Do the same from the opposite side, so the two side slits are opposite each other, with the centre half to a third of the width of the paper uncut. Now take the sides of the paper below the side slits and fold them in towards the centre, one side overlapping the other. Crease them so they stay, and fold up the bottom inch of the bottom to help hold everything together.
Now you should have something that vaguely resembles Binky from Life in Hell. Fold one ear down along the line one inch above the halfway point. Turn it over and fold the other ear down the opposite side.
That's your helicopter. Pick it up just under the rotors and drop it. It should stay right side up and twirl slowly down. Adjust the folding if necessary. If it keeps flipping upside-down, there's not enough weight underneath. You could try adding a paperclip. If it goes down too quickly, you may have too much weight underneath and can trim some. If it plummets without twirling, be sure you creased the rotors so they stick out properly. You can even experiment with folding little winglets into the ends of the rotors.
It's not true origami, because it involves cutting, but it's a neat model. I made it to show a corporate vice president once, and I remember him picking up and dropping the helicopter three or four times in fascination, then asking, "can I keep this?" Someone even sent me a video of someone dropping one of these from the twenty-fifth floor of a hotel atrium and you can see it twirling almost all the way down.