Savchenko Problem 2.1.65
Physics · thermodynamics
Problem
A skater on an ice track tries to turn as close to the inside edge as possible. A cyclist on a bike track, on the contrary, passes the bend as far as possible from the inner edge. How can we explain this difference in turn passing tactics? The bike track profile gets steeper and steeper as you move away from the inner edge of the track.Intuitive explanation
The key is understanding how banking angle and friction work together differently for each sport. A skater relies on friction to provide the centripetal force needed to turn, so staying near the inside (where the track is flatter) actually works fine—friction alone can handle the curve. A cyclist on a banked track, however, benefits from the track's tilt: moving outward increases the banking angle, which means the normal force has a larger horizontal component pointing toward the center. This lets the cyclist turn faster and more efficiently without relying as heavily on friction, which is limited on a bike. The steeper banking away from the inside essentially does the turning work for you.
Intuitive explanation
The key is understanding how banking angle and friction work together differently for each sport. A skater relies on friction to provide the centripetal force needed to turn, so staying near the inside (where the track is flatter) actually works fine—friction alone can handle the curve. A cyclist on a banked track, however, benefits from the track's tilt: moving outward increases the banking angle, which means the normal force has a larger horizontal component pointing toward the center. This lets the cyclist turn faster and more efficiently without relying as heavily on friction, which is limited on a bike. The steeper banking away from the inside essentially does the turning work for you.