Capstan Static Friction Bound

Compare both directions of a rope’s static tension ratio around a rough cylinder. A flexible rope wrapping around a rough cylindrical post can support a much larger tension on one side than the other without slipping. The static Coulomb coefficient mu and contact angle theta determine an exponential bound on the tension ratio.

Exploring limits with real controls

Investigate how the wrap angle and friction coefficient expand the admissible region.

1. Open the interactive module. Set Friction coefficient to 0.3 and Wrap turns to 0.5.
2. Set Reference tension to 2 and Applied tension to 5. Notice the margin is positive, so it is static admissible.
3. Increase the Wrap turns to 1. The maximum admissible tension jumps up to over 13 N, significantly increasing the log admissibility margin.
4. Swap the tensions by setting Reference tension to 5 and Applied tension to 1. The required mu becomes roughly 0.51, which exceeds the available 0.3, resulting in a Below lower bound violation.
5. Set Wrap turns to 0. The required friction coefficient becomes Unavailable if tensions are unequal. Only equal tensions are permitted.

Open Capstan Static Friction Bound