ONE FORMULA, ONE ANSWER
Capstan limiting rope tension calculator
Find the larger rope tension at impending slip around a cylindrical drum. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Limiting higher tension Tₗ
Enter values and select Calculate.
Tₗ = Tₛ exp(μₛ θ)
Assumptions
Required: a flexible rope with negligible mass and bending stiffness, uniform static friction, and continuous drum contact. θ is the total contact wrap angle and may exceed one revolution. The result is a friction limit. Excluded: rope breaking strength, drum strength, added distributed loads, and groove effects.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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