Tilting the road lets a component of normal force supply centripetal force.
On a bank of angle θ without friction, the ideal speed is v=√(rg tanθ). With friction, a range of speeds is safe. Banking is used on highways, railways and velodromes to reduce lateral loads.
A 100 m radius curve banked at 10° has ideal speed of about 13 m/s.
Banked curves let vehicles turn at higher speed with less reliance on friction, which is why motorway and racetrack design uses them.
Tilting the road lets a component of normal force supply centripetal force.
Banked curves let vehicles turn at higher speed with less reliance on friction, which is why motorway and racetrack design uses them.
The ideal angle makes the normal force supply all the centripetal force, so tan theta equals v squared over g r, with no friction needed at that speed.
Friction must act up the slope to stop the vehicle sliding down, so too low a speed may need more friction than the road provides.
Typical applications include setting the superelevation of a highway curve for a design speed, calculating the banking angle of a velodrome track and estimating the maximum safe speed on a slippery banked curve.
Study "Circular motion and centripetal force" first (topic 41 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Normal force component gives centripetal force. Cant on railways. Overturning vs skidding limits.
A 100 m radius curve banked at 10° has ideal speed of about 13 m/s.
The next topic is "Stress", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 42 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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