Finding the Angle of a Banked Curve for Roller Coaster Design

AI Thread Summary
To find the angle of a banked curve for roller coaster design, the formula tan(theta) = v^2/(rg) is essential, where v is velocity, r is the radius of the curve, and g is the acceleration due to gravity. Understanding this formula involves recognizing that it is derived from the balance of forces acting on a vehicle moving along a banked curve, specifically the centripetal force required for circular motion. A helpful resource on the forces at work on a banked curve can be found at HyperPhysics, although it includes friction considerations. The rearranged formula for maximum velocity on a banked curve is also noted as v_max = sqrt(rg tan(theta)). This foundational knowledge is crucial for accurately designing roller coasters that utilize banked curves.
newme
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Hey I am doing a assignment on Roller coaster physics and i am to design a Roller coaster taking all the aspects of physics.

I am stuck at my banked curve i don't know what formula to use to find the angle of the curve.
I have seen this formula in the forums
Tan theta=v^2/rg

but the thing is i don't know how that formula was derived so i can't useit in my assigment unless i know how it was made.

So if someone know how to make that formula or another forumula i can use please could you post it. Thanks

ahh you and i for got to say that you can ignore friction.
 
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Welcome to PF, Newme. I can't help you with any math stuff; I'm more of a 'hands on' guy. (No one would get on my rides in Rollercoaster Tycoon. :frown:)
You are definitely in the right place to get the answers, though. Just hang tight and the experts will show up like rock bass on a dead minnow.
 
thanks

Thanks for that!
Ok so know with this formula
Velocity max=sqaure root (rg tan theta)
can be rearanged to tan theta=v^2/rg
thanks for the help on that
 

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