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My son and I are playing "MAKE" (think "HORSE") and we challenged ourselves to build the slowest falling object using only a sheet of paper. We cannot build anything that falls slower than a plain sheet of paper. Any ideas?

Corey Alix
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  • to make it more interesting, increase the height, add some wind. – Abel Aug 25 '21 at 00:34
  • Try to drop two papers from the height, one 8x11 std. sheet and another one with a size equal to one-fourth of 8x11, then clock the time. Have fun. – r13 Aug 25 '21 at 01:35
  • Be interesting to see if folding edges to form a sort-of parachute will work better than the helicopter answer posted by @kamran . BTW I think this would make a great lab experiment for kids of almost any age to show some of the basics of aerodynamics and fluid flow. – Carl Witthoft Aug 25 '21 at 12:39
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    Unrelated to your getting an answer, but I'm intrigued by your game. Do you just think of things to ....make? Then whoever does "worse" gets the letter? A few more examples would be fun! – BruceWayne Aug 25 '21 at 16:33
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    “HORSE”...? Even thinking it, I'm not sure what you're talking about. (Different countries, different continents, different cultures...) – DaG Aug 25 '21 at 20:17
  • Good luck. I was in a "time aloft" paper-airplane contest, and the winner took a crisp dollar bill and dropped it so it spun along the long axis. Stayed in the air for three times as long as the second-place finisher. – Mark Aug 25 '21 at 22:16
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    @DaG HORSE is a game where players take turns making shots with a basketball. When someone makes it, the other person has to make the same shot or they earn a letter. Whoever gets all the letters first loses and is a HORSE. I assume MAKE is similar to that, but I'm intrigued where OP gets their challenges from – GammaGames Aug 25 '21 at 22:56
  • Fold paper plane. Release. A self-stabilising paper plane that *flies* instead of fluttering will be optimal. A half-assed approximation that is easier to build is a helicopter. A quarter-assed even easier approximation is a self-stabilising wedge/cone shape. Strangely enough, a pure random/turbulent approach is very near optimal, too. (see examples of fluttering dollar bill) – PcMan Aug 26 '21 at 04:38
  • Great, thanks, @GammaGames! – DaG Aug 26 '21 at 07:16
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    One of the winners in the the [Great International Paper Airplane Contest](https://books.google.com/books/about/The_Great_International_Paper_Airplane_B.html?id=_Tg5AQAAIAAJ) (you can see it on the book cover) was a simple folded gyrocopter which worked quite well. – Steve Summit Aug 26 '21 at 14:03
  • @SteveSummit I loved that book! In fact I made one of the planes from it at recess in grade school one morning, threw it, it caught a thermal and started rising as it circled. A friend and I chased it to the edge of the playground and watched it rise over a nearby hill till it was out of sight! – Glen Yates Aug 26 '21 at 22:06
  • OK, take it to the extreme. Take one sheet of paper. Feed it to a liquidizer, then feed the confetti to a coffee grinder. Dropping the powdered sheet, will result in a **much** slower rate of fall. – PcMan Aug 27 '21 at 07:04
  • It depends on what you mean by "fall". I can easily make a paper airplane that would take longer to touch the ground. If the rule is it cannot travel horizontally make a simple paper helicopter – slebetman Aug 27 '21 at 07:28
  • @PcMan: I think it might make sense to have two variations of the rules--one in which the paper must remain intact, and one in which it may be cut but all pieces must remain connected. In the latter case, it would be interesting to see how a narrow string would fare against more rigid designs. Turning the paper into powder would make it too difficult to determine when all of the paper was free of the dropper, and when the first particle touched the ground. – supercat Aug 27 '21 at 16:01
  • https://www.metrofamilymagazine.com/simple-science-experiment-spinning-paper-blimps/ – Steve Aug 27 '21 at 18:36
  • Adding something along these lines to the question would be helpful:- The paper may/may-not be cut || The paper must / need not be in one piece. || A staple / paperclop / pin / glue other may not/ may be used. – Russell McMahon Aug 28 '21 at 04:18

4 Answers4

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For regular paper weight and size A6, roughly a card postal size one can tear from the middle vertically the top half and bend the two flaps 90 degrees in opposite directions like a helicopter's blades and fold the bottom half on itself like a narrow rod to make it act like balast.

This will be a primitive gyro- copter and will descend in a slow controled manner as opposed to a paper swinging laterally and then diving in a possible sharp angle of attack.

After a few prototypes one will find the good cut size.

Larger papers could have trouble holding their geometry unless they are thicker.

kamran
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  • We are trying this and reinforcing the "wings" to prevent them from collapsing (we are using legal paper) but it still descends faster than the sheet of paper from 8 feet. We will continue pursuing this approach because it at least gives a more predictable descent. I'm thinking we want to maximize our wing size without compromising stability or adding too much weight but that is easier said than done! – Corey Alix Aug 25 '21 at 15:03
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    @CoreyAlix - Am I right in assuming you're dropping a piece of paper, which then kind of wavers right/left as it descends to the ground? That's going to be tough to beat IMO, so great question. – BruceWayne Aug 25 '21 at 16:35
  • I joined this site just to point that Nasa created a student project (project [Make a Paper Mars Helicopter](https://www.jpl.nasa.gov/edu/learn/project/make-a-paper-mars-helicopter/)) which, IMHO, is exactly what you're looking for. Instructions on how to build a paper helicopter and clues as how to change the design to make it take even longer to hit the ground. – gmauch Aug 25 '21 at 18:13
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    @BruceWayne, there are falling modes that are even slower than side-to-side motion. For example, a strongly-rectangular piece of paper (eg. a dollar bill) spinning along its long axis, with the axis parallel to the ground. – Mark Aug 25 '21 at 22:19
  • Note, these are called whiligigs or whirlybirds: https://www.scientificamerican.com/article/make-a-whirlybird-from-paper/ (at least in the U.S.) – RBarryYoung Aug 26 '21 at 15:08
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I really love this game idea! I think a flat piece of paper falling face-down is probably the least aerodynamic thing you could possibly drop if it maintained its shape and orientation, but naturally the paper bends and changes angle (edge-down) as it descends, tending towards the path of least resistance.

Therefore, my thought is that your goal should be to keep the paper as close to its original shape as possible while providing rigidity to prevent bending and stability to prevent tipping its edges down.

The solution I came up with was to fold the edges of the paper as shown (roughly) in the image below. The creases in the paper help to prevent it from bending into a more aerodynamic shape, and the flaps act like rudders that cause the paper to spin rather than flip into an edge-down position. I only tested it out a couple of times, but it seemed to work for me.

slow paper fold

JDługosz
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bashtown
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What a fun challenge! We had a good time trying out various designs :)

I did eventually come up with a helicopter-style design that falls about 50% slower quite consistently.

Finished

Build instructions:

  1. Cut diagonally along the red line.
  2. Fold one half in the opposite direction.
  3. Fold up the edges along green lines to add rigidity.
  4. Put a single staple through the sheets at the blue line. This both adds a bit of weight for balance and strengthens the connection.

Bend instructions

Here is a set of videos of testing this against a plain A4 paper. To make the launches more consistent, I'm using two sheets of transparent plastic. A typical drop is significantly slower. But sometimes the rigidity of the center strut fails and it falls faster.

jpa
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Extrapolating from the Gyrocopter idea for A4 paper size, I arrived at following conclusions:

  • Bending (i.e. not creasing a fold) part of the helicopter blade along its length provides ample structural stability at the cost of some air resistance. The result however has a nice wing profile.
  • Structural stability is most important at the blades' root, so you should bend diagonally. You can leave about 1/3 of the length of an A4 paper sheet without such structural reinforcement.
  • Tape these stability bends to the hub (where both blades meet), so the blades don't fold up under load. With the hub straight and the bends diagonal, a short stretch of tape will be left hanging in the air.
  • You can crease the outmost point of the stability bend to reduce air resistance. The wing profile will still extend to the blade tips.
  • Angular momentum (in direction of the height axis) increases drastically with the diameter of the rotor disc (aka blade length). This causes the Gyrocopter to spin very slowly, which decreases its effectiveness at slowing down the fall.
  • Angular momentum (in direction along the blades) is very low and decreases with increasing blade length. This leads to poor stability.

However the poor stability led to a lucky discovery: If the Gyrocopter flips over, it can assume a stable state of continually flying loopings. If optimized for narrow loopings (henceforth Gyrocopter being renamed to Looper) with

  • both stability bends on the same edge
  • a hub of small height (long blades/wings and the rest folded into a triangle about as high as the stability bends)

the Looper seems to achieve additional lift. This may be caused by Magnus effect (circular movement of wing surface around an axis along the wing's length affecting the airflow). The effect can be increased by releasing the Looper in downwards position with a little downwards flick to start the first looping.

My Looper build performs up to 8 loopings, taking about 5 seconds for 2m of height.

PS: I build this yesterday evening after seeing the question, before reading Mark's and PcMan's comments about the fluttering dollar bill.

NoAnswer
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