Physical hitch theory
The only mathematical theory that actually talks about dock line on a spar.
Does not pick a knot
This page does not pick a knot for you. DNA, molecules, quantum braids and vortices stay off Decide.
Watch the mechanism
Why wraps hold — the capstan equation
Hitch theory is the one place where the maths matches the rope. Seeing the tension ratio grow with each wrap is what makes wrap count feel like physics rather than folklore.
- Why held tension climbs exponentially with wrap count and frictionDot Physics · Opens on YouTube
Derivation of the Capstan Equation - Frictional Force due to a String Wrapped Around a Circle
External video from a creator we follow — not produced by us.
Loads only when you press play
What it means
Bayman (1977) and Maddocks & Keller (1987) treat a hitch as rope friction against a rigid object. Wrap count and the friction coefficient can produce a no-slip regime. The prediction is approximately right in tests. There is still no equally successful theory for knots in general. Patil et al. (2020) later showed that simple tangle counts correlate with stability in laboratory rods — a correlation, not a field rating.
What it predicts
- ·Some hitches have a regime where they should not slip if wrap count and friction are high enough.
- ·Remove the object and a hitch is usually topologically trivial — the object is the lock.
- ·Clove, rolling, timber and icicle live in this family. Cleat hitch is the same idea on a purpose-made object.
What it does not predict
- ·It does not rank Palomar against FG.
- ·It does not publish a working-load limit.
- ·It does not survive a wet, iced, or HMPE cover without re-measuring friction.
- ·It does not replace Diagnose when a riding turn or dumped cleat is the actual failure.
Not for
- ·Picking a fishing knot for you
- ·Treating a Jones polynomial as a hitch rating
- Cleat Hitch
Full turn on the far horn, figure-eights across both horns, locking hitch under the last cross.
- Clove HitchDiagram in review
- Rolling HitchDiagram in review
- Round Turn & Two Half Hitches
Working end wraps a spar and tucks under itself so friction holds the load.
- Icicle HitchDiagram in review
- Timber HitchDiagram in review
- Crowell — The physics of knots (Bayman / Maddocks–Keller) — Bayman 1977 hitch theory; Maddocks & Keller 1987 extension. No equally good general theory for all knots.
- Sano et al. — Inner workings of the clove hitch (Extreme Mechanics Letters, 2022) — Elastic rod on a rigid cylinder. Empirical hitch mechanics.
- Patil et al. — Topological mechanics of knots and tangles (Science, 2020) — Lab rods: simple topological counts correlate with stability. Not a field rating table.