Scaling

[mmcirvin]

The roller coaster I mentioned in the previous entry seems to be a scaled-down variant of a larger model made by the same company. It's interesting to think about the effect of this.

I was wondering about G-forces, but neglecting air resistance (which admittedly is probably not the right thing to do), if you scale the track layout of a chain-lift-powered roller coaster proportionally in every dimension, acceleration at any moment ought to be unchanged. The speed of the coaster goes as the square root of the overall scale, because the gravitational energy available scales up linearly, and speed goes as the square root of kinetic energy. But the duration of the ride, and of any subset thereof, will also go as the square root, so changes in velocity will happen at an unchanged rate. Brake blocks ought to work OK if you just scale them proportionally, because the energy they need to dissipate scales linearly with the length of the block.

The jerk, on the other hand--which contributes to stuff like head-banging and sprained necks--will, if I'm thinking correctly, go as the inverse square root of the size. So if you scale down the whole coaster down to a smaller model, you'd probably want to make the ease-in and ease-out of curves and loops proportionally gentler to compensate. And I think you can see that on these small models.

Comments

[mmcirvin.livejournal.com]

...And the need for proportionally greater easing (and the engineering limits that come from the fact that you can't scale down the cars) probably also mean that you have to take out some of the ride elements, so in practice these things aren't really scale models.