Calculating G Forces

[mathman]

What are the equations used to calculate g forces produced on amusement park thrill rides?

[Unregistered]

ac = (v^2)/r where ac = centripetal acceleration, m = mass, v = velocity, and r is the distance to the center of the loop. By center, I mean that if you have a giant circle where the car is on the edge and it'd follow the path of the circle, r is to the center of that circle.

# of g's = a/g where g = 9.8m/s^2 or 32ft/s^2

[K^2]

You can generally approximate a small section of any curve as a section of a circle, in which case a=v^2/R will work rather well. The acceleration will point towards the center of the circle.

If you need to be more precise, you have to do more work. If you can get the position of the cart as a vector r(t), then the acceleration at any given time is d²r/dt². Note that this is also gives you a vector.

In the most general way, if you have a parametric curve, c(v), the best way to obtain r(t), and therefore the acceleration, is to use the Lagrangian method, using v(t) as a generalized coordinate, and keeping in mind that r(t)=c(v(t)).