Pleat Swing Physics?

[george7]

Something to play with.
http://www.custom-logic.com/exp/cloth/cloth.html
http://www.lhup.edu/~dsimanek/scenario/newton.htm

[Bugbear]

Oh no... not the Coriolis Effect myth again.

Anyway, I still think the movement of the pleats has a lot to do with the slight springy-ness of the fabric.

[ronstew]

If you are saying that a strip of fabric, with no weight added to the bottom is a pendulum, then fine.

The pendulum with a string of negligible mass and a high-density bob is called an ideal pendulum. A physical pendulum has mass along its lenth, so moments of inertia must be considered. I am proposing a uniform physical pendulum, which has the same linear density along its length. I am imagining the strip of cloth modeled as rigid, with a pivot at the top.

Consider the old physicist joke:

There is this farmer who is having problems with his chickens. All of the sudden, they are all getting very sick and he doesn't know what is wrong with them. After trying all conventional means, he calls a biologist, a chemist, and a physicist to see if they can figure out what is wrong. So the biologist looks at the chickens, examines them a bit, and says he has no clue what could be wrong with them. Then the chemist takes some tests and makes some measurements, but he can't come to any conclusions either. So the physicist tries. He stands there and looks at the chickens for a long time without touching them or anything. Then all of the sudden he starts scribbling away in a notebook. Finally, after several gruesome calculations, he exclaims, 'I've got it! But it only works for spherical chickens in a vacuum.'

Idea being, if you want to create a physics model of a real, complex system, start with a simplified approximation. Solve it, then add a complication. Solve and repeat.

Anyay, this probably has been done already. Watch Shrek or any computer-animated film with a woman in a flowing skirt. Animation companies pay physicists and mathematicians to create effects like this. Somebody at Industrial Light and Magic, Pixar or Dreamworks probably has a pleated skirt model at the ready.

[ronstew]

Something to play with.
http://www.custom-logic.com/exp/cloth/cloth.html
http://www.lhup.edu/~dsimanek/scenario/newton.htm

Wow. That first one verifies my last point.

[Bugbear]

Yes, I know... the Earth is flat.

[Bugbear]

By the way, the egg was around way, way before the chicken came on the scene.

[ChattanCat]

There are three parts to a pleat. Let's say that we have a kilt that is pleated to the stripe to make my explaination easier. So, lets look at one pleat. A pleat is shaped in a Z. The top of the Z is the stripe. The bottom of the Z is actually the next pleat. It is my hypothesis that the middle section of the Z is the leaf spring. It will bend when pulled on by the upper and lower legs of the Z. With 29 pleats, each pleat will only have to open 0.2" to have a total 6" swing of the outside pleat.

[Bugbear]

Ya, and it would have a bit of a twist across the surfaces because it is steeked near the bottom of the fell... That would mean that the inside edge is moving a different amount... posibly even in the oppizit direction from the outside edge of the pleat.

If that is the case the flexability of the fabric in the bias direction also may play a role in this movement.

The reason I am asking is because I don't think that the same weight fabric in most other materials would swing in the same way as wool. For example, cotton twill doesn't seem to move in the same way as wool in about the same weight range. I don't think it is completely the weight that is causing this swing.

[Bugbear]

All right, I have done an experiment.

I took six strips of medium weight hair canvas, the kind you would put in the front of a suit jacket or need to use two layers of for a kilt, and taped them to the inside surface of six pleats on my acrylic kilt.

The strips are about eight inches long, and a little over an inch wide. Most of them taper to about a half inch, and they are only one layer. Basically scraps.

The stiffness of the hair canvas runs parallel to the folded edge of the pleat.
The edge of each strip is directly against the inside of the fold of the pleat.
The narrow end of the strips are toward the fell with the wide end very close to the bottom of the kilt.
A small piece of masking tape holds the top of the hair canvas strip to the inside of the pleat that is the outside face of the pleat.

All I can tell is that they seem to hang a little better, and have a little better feel to them. I have no good way of knowing if they swing better. I only wanted to see if I could put a slight influence on the outside surface of the fabric, and hair canvas was the only thing other than wool tartan that I had that passed the pinch test. Well... a fiberglass window screen kind of passed the pinch test.

By the way, I tried putting the hair canvas along the bottom edge with the stiffness running horizontally, but the pleat tended to curl outward.

Just something that popped into my mind, and I thought I would try. So for what it's worth...

Now I don't have to think about it anymore, ah.

[The Guy in the Kilt at UC]

Physics Analysis....

For T=(2*pi)*sqrt(Length/g) where g=gravity=-9.8m/s^2

Using the length of my kilt that isn't sewn down as the pendulum, I'll assume length to be 15"

If I wanted to optimize the swing of my kilt, i would take one step every 1.3 seconds.

Voila. You can use that formula to figure out what pace you need to walk to get the maximum swing in your kilt.

(By the way, I'm an Engineering student... so this stuff is still fresh. I bet the Wizard could have gotten this one had he read it first.)

I'm sorry to say that it is not that simple (though it may be very close). The problem is that each pleat is coupled to another on each side. What you will need to do is find (one of) the natural frequencies to find maximum swing. This will depend on the number of pleats. Also it will depend on the size of your seat. Because your curvature will ensure that they are not swinging in the same direction. That is, they will want to swing left & right in back as you look at it straight on, but they will want to swing back & forth on the sides as you look at it straight on (albeit a much smaller swing). I imagine that things such as the weight of the wool will not matter much if you can make a generality.

I think I just found something to procrastinate with today.