Pleat Swing Physics?

[vmac3205]

Maybe it has something to do with sheep having curly hair.
Or maybe it's just that old Harry Lauder song, "The Wig Wig Wig Wig Waggle of the kilt."

[george7]

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.)

[Bugbear]

Oh, I'm sure the Wizard already knows the answers. however, I think the pleats would have to move in more of a wave forme than individual pendulems... like a slinky to some degree.
That is not so important to me at this point; it's that slight tendency toward keeping it's shape while remaining very flexable that I'm pondering...

[george7]

Oh, I'm sure the Wizard already knows the answers. however, I think the pleats would have to move in more of a wave forme than individual pendulems... like a slinky to some degree.
That is not so important to me at this point; it's that slight tendency toward keeping it's shape while remaining very flexable that I'm pondering...

Pleats move as a group of pendulums. If you watch a kilt from the back, they all sway in the same direction at once.

Your slinky perception is the sway in the forward direction of motion. That's due to the fact that the motion of walking isn't quite constant.

[ChattanCat]

Pleats move as a group of pendulums. If you watch a kilt from the back, they all sway in the same direction at once.

Your slinky perception is the sway in the forward direction of motion. That's due to the fact that the motion of walking isn't quite constant.

It is more like one pendulum adds to the next and the last pleat sees the most movement.

[Bugbear]

I don't see how a pleat could swing without bending somewhere, even if it is an arch across the vertical length of the pleat, or perhaps a little of a twist.

How is the pleat bending or deforming when it swings and moves?

[ronstew]

It's not doctoral stuff, but a reasonable model would be a high-end undergraduate problem. Consider thirty uniform physical pendula arranged in a line, each rigidly fixed at the top, linked with a horizontal low-constant spring to the next one midway up. The tops of the pendula are subjected to a sinusoidal horizontal driving force.

We need to add damping.

George - could that be solved without differential equations? I doubt it.

Now, to similate the fore-and-aft motion of the legs, rigidly fix out-of-phase sinusoidal fore-and-aft drivers to the end pendula. These have the same/opposite phase as the top driver. Now we have a real challenge.

[Bugbear]

If you are saying that a strip of fabric, with no weight added to the bottom is a pendulum, then fine.
If you can consider a string hanging from a tack in the ceiling, with no weight at the bottom, to be a pendulum, then fine.
There is a uniform weight per square measurement from the bottom of the fell to the bottom of the pleat; that's not counting a hemmed pleat.

[Dixiecat]

Now, to similate the fore-and-aft motion of the legs, rigidly fix out-of-phase sinusoidal fore-and-aft drivers to the end pendula. These have the same/opposite phase as the top driver

Did you add in the Coriolis Effect? Air Resistance?

[george7]

It's not doctoral stuff, but a reasonable model would be a high-end undergraduate problem. Consider thirty uniform physical pendula arranged in a line, each rigidly fixed at the top, linked with a horizontal low-constant spring to the next one midway up. The tops of the pendula are subjected to a sinusoidal horizontal driving force.

We need to add damping.

George - could that be solved without differential equations? I doubt it.

Now, to similate the fore-and-aft motion of the legs, rigidly fix out-of-phase sinusoidal fore-and-aft drivers to the end pendula. These have the same/opposite phase as the top driver. Now we have a real challenge.

I think you can explain most questions anecdotally, with a few equations here and there. I think you can come up with most of the elements of a kilt's swing without differential equations. If you treat the model as an accordion-like object that forms a semi circle, add in some friction at the pleat contacts... then you really only have to figure out the motion of a few of the pleats, the outer most pleats and a center pleat.

Your example sounds like a newton's cradle with some rubber bands. That still leaves out the whip effect some get with their end pleats... although that might explain a kilt that is out of phase with the wearer's pace.

For that... try swinging your single pendulum (a heavy rope with nothing on the end would be even better), then swing it back the other way just before it's ready to stop.

The kilt is a bit longer than most people's stride, so it is forced back slightly before it's natural rhythm.

Voila, a good Physics I explanation for the kilt whip.