Questions about roller coaster physics

[Matt Jacques]

Hello, I'v lately been intrigued by roller coasters as of late (notice my prior post about that app)

I havnt been able to find any good websites to explain the physics of roller coasters in detail. I know of-coarse that it works on conservation of energy, that the initial potential energy is converted into kinetic at the bottom of hills and back into potential at tops. But there has got to be more, how does change in the direction (z-plane?) change the physics?

 

[suyver]

I think $$m\vec{a}=\sum_i \vec{F}_i$$ pretty much sums it all up. It's just classical mechanics: write down all the forces and plug it into Newton.

 

[russ_watters]

Originally posted by Matt Jacques
But there has got to be more, how does change in the direction (z-plane?) change the physics?

If you mean the g-forces, It really doesn't. The only thing that affects is friction, which is pretty low anyway (wind is probably the biggest component). So except for friction loss, you can use conservation of energy to calculate the speed of a roller coaster anywhere on the track.

 

[turin]

In the limit of negligible friction, a roller coaster is quite classical. The more detailed questions would be better adressed in an engineering context than a physics context: i.e. what's the best way to get the thing started, where should we put the twists and turns, how often do we need to include repeaters and where...

 

[Matt Jacques]

This is the basic equation to go from a top of a hill to a bottom.

$$\frac{1}{2}mv^2 - f \Delta S = mgh$$

But how would one find the velocity around a loop? It's late and my mind is weak. ;)

 

[chroot]

The velocity of the cart at any distance h below its starting height is

$$\sqrt{2 g h}$$

- Warren

 

[PatAll]

I have a research paper on the the physics behind roller coasters. Can you direct me to any library resources? What level of math would one need to accomplish the construction? How does math created a stable ride?