Tilt a Whirl Math
July 23, 2017 11:01 AM Subscribe
I'm looking to understand the mathematics of how a Tilt a Whirl chair moves. When I was recently in Seaside, OR, I was watching the Tilt a Whirl that operates in the downtown. The entire machine is a disk-like platform that rotates on an angle.
There are, maybe, a dozen half-moon shaped seats that also spin. But although that larger disk turns at a constant rate, the seats may remain motionless, turn slowly or spin quickly depending (or not) on where they are in space on the larger disk. Does it have to do with wind resistance? Gravity and centrifugal force? A chair spinning at a high point might be stationary when it returns to the same point in the next rotation. Is there any math or any study on what seems like the randomness of their fast/slow movement? If one could plot its movement on a graph, would the waveform look like a amplitude or frequency modulation or something else? A wonky question, I know. But I can't get it out of my head.
There are, maybe, a dozen half-moon shaped seats that also spin. But although that larger disk turns at a constant rate, the seats may remain motionless, turn slowly or spin quickly depending (or not) on where they are in space on the larger disk. Does it have to do with wind resistance? Gravity and centrifugal force? A chair spinning at a high point might be stationary when it returns to the same point in the next rotation. Is there any math or any study on what seems like the randomness of their fast/slow movement? If one could plot its movement on a graph, would the waveform look like a amplitude or frequency modulation or something else? A wonky question, I know. But I can't get it out of my head.
No, that's just the Disney teacup ride, which is similar to TiltaWhirls but with some control by the rider. TiltaWhirls, there's no intentional rider control. Shifting your weight might do something, but I think it's negligible compared to the weight of the cars.
posted by LizardBreath at 11:18 AM on July 23, 2017
posted by LizardBreath at 11:18 AM on July 23, 2017
I'm not sure if I properly remember what a Tilt a Whirl is like, but I wonder if some of the mathematics of epicycles which astronomers used to try to explain the motion of planets in the sky when they still thought the Earth was the center of the solar system, would be applicable to what you're trying to figure out.
posted by XMLicious at 11:24 AM on July 23, 2017
posted by XMLicious at 11:24 AM on July 23, 2017
It has to do with gravity and momentum, though I don't have the math to really lay it out. A car can be swinging around as it hits the uphill part of the disc, where gravity pulls it back (or pushes it further, depending on the direction of rotation) causing it to slow/stop or speed up depending on the strength of each at every point. Rinse and repeat. Please tip your pukebucket attendants.
posted by rhizome at 11:28 AM on July 23, 2017 [1 favorite]
posted by rhizome at 11:28 AM on July 23, 2017 [1 favorite]
As a lifelong fan of the Tilt-a-Whirl, my experience is that the more weight, the more it spins and if you lean back into the seat, it increases the speed. Also, there's some cups that spin more than others, perhaps as a function of their ball bearings.
I can't explain it with science tho.
posted by fiercekitten at 11:31 AM on July 23, 2017 [1 favorite]
I can't explain it with science tho.
posted by fiercekitten at 11:31 AM on July 23, 2017 [1 favorite]
So I think your question may actually be more complicated than you think. The forces involved certainly include all the ones you mention. However, as far as a formula goes I believe that the movement of the tilt-a-whirl cars are fundamentally unpredictable or chaotic, sort of the like the motion of a double pendulum.
I'm actually really intrigued by this question now too, so I searched the literature and found a paper on it by Kautz, et al. from the University of Northern Arizona title 'Chaos at the amusement park: Dynamics of the Tile-A-Whirl' that has all the formula you could ever want. Their conclusion was that at intermediate speeds, where centrifugal/centripetal force is negligible that the motion of the cars is unpredictable. Send me a memail and I can send you a copy of the paper. Most of the math isn't super difficult. It's like first or second year physics level.
posted by runcibleshaw at 11:46 AM on July 23, 2017 [6 favorites]
I'm actually really intrigued by this question now too, so I searched the literature and found a paper on it by Kautz, et al. from the University of Northern Arizona title 'Chaos at the amusement park: Dynamics of the Tile-A-Whirl' that has all the formula you could ever want. Their conclusion was that at intermediate speeds, where centrifugal/centripetal force is negligible that the motion of the cars is unpredictable. Send me a memail and I can send you a copy of the paper. Most of the math isn't super difficult. It's like first or second year physics level.
posted by runcibleshaw at 11:46 AM on July 23, 2017 [6 favorites]
The Tilt a Whirl was invented in Minnesota, and I've spent a lot of time riding it. It sounds like the math part is covered above, but yes, how the cart is loaded, whether the occupants pull back to help make it spin, and the distribution of weight in the cart are all factors.
It's been a lot of years but I think you can kind of time where the cart is when you hit the bumps to encourage/discourage spinning.
So yes riders have some control over the motion.
posted by littlewater at 11:52 AM on July 23, 2017 [4 favorites]
It's been a lot of years but I think you can kind of time where the cart is when you hit the bumps to encourage/discourage spinning.
So yes riders have some control over the motion.
posted by littlewater at 11:52 AM on July 23, 2017 [4 favorites]
I too have made a lifelong study of Tilt A Whirls and my technique is to sit on the right side with my two nieces sitting next to me and then we all lean like mad in the direction of the rotation and scream loudly.
Conclusion: it is the ride operator pushing on the lever that makes us spin faster.
posted by TWinbrook8 at 11:55 AM on July 23, 2017 [3 favorites]
Conclusion: it is the ride operator pushing on the lever that makes us spin faster.
posted by TWinbrook8 at 11:55 AM on July 23, 2017 [3 favorites]
My (quite possibly misinterpreted) understanding of something I read once was that the secret to maximum spinnage is, counter-intuitively, to have the weight balanced perfectly rather than offset. I haven't experienced any luck with this by sitting dead center as a single rider, however.
I keenly remember the Seaside Tilt operator "helping me out" when he saw me shifting my weight around. My favorite memory, though, comes from Knoebels in Pennsylvania, where I swear an operator was coaching riders on when to slide to one side or the other.
By the way, CollectiveMind, I envy you your visit (although I'm relatively close). I'm quite fond of the existence of that Tilt. And the Lusse bumper cars. And Fascination at the arcade.
posted by Carouselle at 2:34 PM on July 24, 2017
I keenly remember the Seaside Tilt operator "helping me out" when he saw me shifting my weight around. My favorite memory, though, comes from Knoebels in Pennsylvania, where I swear an operator was coaching riders on when to slide to one side or the other.
By the way, CollectiveMind, I envy you your visit (although I'm relatively close). I'm quite fond of the existence of that Tilt. And the Lusse bumper cars. And Fascination at the arcade.
posted by Carouselle at 2:34 PM on July 24, 2017
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I'm nowhere near physics-y enough to help answer the question overall (although I love it), but I think that's something that would have to be accounted for.
posted by Ufez Jones at 11:11 AM on July 23, 2017