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.)

[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.

[george7]

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.

Connecting the pleats and assuming that they swing in different directions doesn't change the resonance, just the dampening. The period of a pendulum tied to another pendulum of equal length will result in a system of pendulums with the same frequency. If you weave them together, they'll dampen each other, but it won't change the frequency they prefer.

[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.

[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.