For a flexible line on a cylindrical pulley at impending slip, the ideal capstan relation is T1/T2 = e^(μθ), with θ in radians. This reference reports that limiting condition, not guaranteed working tension or torque.
Capstan Friction Pulley Ideal Limit Reference
Explore the ideal capstan limiting relation with a continuous tangent belt wrapped around a finite pulley.
Equation Used
- The line is flexible and the pulley surface is cylindrical.
- The selected friction coefficient is constant over the complete wrap.
- The relation represents limiting static equilibrium at impending slip.
- Stiffness, groove effects, speed, creep, wear, materials and allowable loads are excluded.
Wrap angle is converted from degrees to radians before applying the exponential relation.
Continuous line, finite wrap and pulley
The animation keeps a sampled belt centerline tangent to both free spans and on a constant-radius pulley arc through the selected wrap angle. Pulley rotation is illustrative; no slip transient is simulated.
What the calculator determines
Select friction coefficient, wrap angle, slack-side tension and pulley radius. The calculator reports the ideal limiting tension ratio, tight-side tension, net belt pull and corresponding torque reference.
Ideal capstan limit
θ = wrap degrees·π/180; T1/T2 = e^(μθ); T1 = T2e^(μθ); pull = T1−T2; torque reference = (T1−T2)r.
Selected-input arithmetic
At μ = 0.25 and 180° wrap, the ideal limiting tension ratio is e^(0.25π), about 2.19.
Impending-slip idealization only
The relation assumes a flexible line, constant friction coefficient, cylindrical surface and limiting static equilibrium. Belt stiffness, groove shape, centrifugal tension, creep, speed, wear, temperature, contamination, materials, fatigue and allowable load are excluded.
Questions
Is tight-side tension an allowable working load?
No. It is an ideal impending-slip reference derived from the selected slack tension.
Does radius affect tension ratio?
No in the ideal capstan relation; radius affects the displayed torque reference.
Primary and authoritative references
- Removal Forces of a Helical Microwire Structure Electrode — peer-reviewed experimental-method paper stating the capstan limiting relation Tload = Thold exp(mu theta) for a flexible line around a stationary cylinder.
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