Banked Curve Calculator
The angle that needs no friction at all.
Work out Banked Curve. The angle that needs no friction at all. Says where the formula stops holding.
0 gives the ideal frictionless bank. 0.7 is dry tyre on tarmac.
Ideal banking angle
32.51°
No friction needed at the design speed
tan θ = v²/rg. At the ideal angle the horizontal component of the normal force supplies the whole centripetal force, so the corner can be taken at exactly that speed on sheet ice with no friction at all. Friction then opens a band either side of it — too slow and the car slides down the bank, too fast and it slides up. That is why a banked velodrome or oval has a design speed rather than just a speed limit.
How the Banked Curve Calculator works
Enter a design speed and radius for the ideal banking angle, and add a friction coefficient to get the full range of safe speeds. At the ideal angle the corner works on sheet ice.
Also known as: banking angle calculator · banked turn calculator · ideal banking angle formula · road camber calculator
Frequently asked questions
How do I calculate the banking angle?
tan θ = v²/rg. At that angle the horizontal component of the normal force provides exactly the centripetal force needed, with no friction required.
Why bank a road or track at all?
So the corner does not depend on grip. A properly banked curve can be taken at its design speed with no friction whatsoever, which makes it far safer in rain or ice.
What happens if I go too slow on a banked curve?
You slide down the bank, towards the inside. Too fast and you slide up and out. Friction opens a usable band either side of the design speed, and without friction there is only the one speed.
Why are velodromes banked so steeply?
Because the design speed is high and the radius is small, and tan θ scales with v²/r. Steep banking is what lets riders corner at racing speed in a tight indoor oval.
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