For an ideal flexible line in limiting static contact around a fixed surface, the capstan identity is Tload/Thold = exp(μθ). This page treats μ and wrap angle as selected inputs; it does not calculate the holding strength of the half hitches or a safe working load.
Ideal Capstan Contact-Tension Model
Explore ideal static capstan-contact tension ratios for selected friction and wrap angle.
Equation Used
- The line is ideally flexible and in limiting static contact.
- The selected friction coefficient is constant over the entered contact angle.
- Wrap turns convert directly to θ = 2πn.
- Half hitches, dynamics, bending damage, materials, anchors and safety factors are excluded.
The entered MBS comparison is arithmetic only and is not a knot-capacity or working-load decision.
Round turn and ideal contact model
A round turn places the line in extended contact with the support before the working end is secured. The diagram distinguishes the selected loaded-side tension from the ideal holding-side tension given by the capstan identity.
The two half hitches are shown only as topology. Their geometry, tightening, cyclic behavior, jamming, slip and effect on rope strength are not included in the equation.
What the calculator determines
Select two line-tension scenarios, a friction coefficient, wrap turns and a rope MBS reference. The calculator returns exp(μθ), the two ideal holding-side tensions and the peak holding-side tension as a percentage of the entered MBS.
The MBS percentage is arithmetic only. It is not a working-load limit, knot efficiency, safety factor, inspection result or permission to use a rope, knot or anchorage.
Ideal capstan-contact identity
θ = 2πn for n selected turns. Tload/Thold = exp(μθ), so Thold = Tload/exp(μθ). The same selected ratio is applied independently to the two entered tension scenarios.
The identity assumes a flexible line, constant selected μ, known contact angle and limiting static equilibrium. It does not predict dynamic impact, changing friction, rope construction, bending damage or the capacity of the finishing hitches.
Selected-input example
For μ = 0.25 and one turn, θ = 2π and the ideal tension ratio is exp(π/2) ≈ 4.810. Selected loaded-side tensions of 4 kN and 8 kN correspond to ideal holding-side values of about 0.832 kN and 1.663 kN.
With an entered MBS of 32 kN, the latter is 5.20% by arithmetic. That percentage is not a safe working-load conclusion.
Scope and correction boundary
The original capstan arithmetic is retained, but the former page treated selected friction values as universal and used the result to make unsupported claims about knot strength, shock loading, tail length, materials, slip, inspection, safe working load and mooring practice.
Those claims and the fabricated tender example are removed. Real rope work is safety-critical: follow the rope and hardware manufacturers, applicable regulations and a competent rigging or marine authority for the actual application.
Questions
Does the calculator rate the half hitches?
No. They are not included in the capstan equation.
Is friction coefficient predicted?
No. It is a selected input and can change with material, surface, contamination, wetness, speed and pressure.
Is the second load dynamically modeled?
No. It is simply a second entered peak-tension scenario passed through the same static ratio.
Does percent of MBS establish safety?
No. MBS is not a working-load limit, and knots, bends, aging, damage, dynamics, terminations, anchors and required safety factors are outside this model.
Technical references
- OpenStax University Physics, Friction — static-friction concepts and their limits.
- NIST Special Publication 811 — SI units and coherent quantity notation.
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