A winding drum converts shaft rotation into rope travel. Without slip, one turn takes up a rope length equal to the circumference measured at the rope centre. At a fixed shaft torque, a larger effective diameter gives higher line speed but less ideal rope pull. The calculator shows these relationships at one specified effective diameter.
Drum and Rope Conversion Interactive Calculator
Enter diameter to the rope centre, drum rpm and applied torque. Inspect tangential take-up, line speed, travel per turn and ideal rope pull.
Equation Used
- Diameter is measured to the rope centre at the active wrap.
- Fixed effective diameter, no slip, no stretch and no layer build-up.
- Entered torque and speed are independent magnitudes, not a motor performance model.
- Direct rope take-up without additional reeving.
- Support, front flange omission and partial wrap are explanatory; no attachment design or load rating.
Ideal fixed effective radius, inextensible rope and no slip or losses. Pull is not a component load rating.
The tangent links rotation to rope travel
The end-section view exposes the rope wrapped around the drum and its straight tangent run. The front flange is omitted. As the drum winds in, the visible wrap gets longer and the free run becomes shorter by exactly the same amount. The end marker rises; reversing the drum pays out that rope and lowers the marker.
The demonstration winds a quarter turn, then pays out a quarter turn. Motion within each leg is uniform and shown ten times slower than the entered rpm. The instant reversal is a display convention, not a prediction of acceleration, motor control or transient loading.
Effective diameter is measured to the rope centre at the working wrap. The displayed wrap, anchor and bearing are schematic. They do not specify minimum holding wraps, attachment strength, groove form, flange dimensions or an actual winch construction.
Estimate rope travel and ideal pull
Use the calculator to convert a drum speed into line speed, or to compare the ideal rope pull from an entered shaft torque at different effective diameters. The end marker illustrates direct rope motion without an intervening pulley system.
Real winches may have multiple rope layers and changing effective diameter. WARN’s explanation of pull by layer documents that available pulling capacity decreases on outer layers. Enter the effective diameter of the layer you want to compare; this model does not automatically spool layers or predict a motor’s torque-speed curve.
Arc length and torque balance
Let D be effective diameter in metres, R=D/2, n drum rpm and T applied shaft torque in N·m. The circumference is C=πD and line-speed magnitude is v=πDn/60 m/s. One full turn takes 60/n seconds when n is positive.
With no slip or losses, ideal rope pull is F=T/R=2T/D. Shaft power is P=Tω, with ω=2πn/60. These relations give the same power at the rope: Fv=P.
During a winding angle θ in radians, take-up is s=Rθ. The illustrated quarter turn therefore takes up πD/4. Wrapped length gained equals free length lost throughout the animation.
Zero rpm gives zero speed and power and a stopped full-turn time. The ideal torque-to-pull relation remains visible at zero speed; it does not certify a holding brake, anchor or static load rating.
A 200 mm effective diameter
At D=200 mm and n=60 rpm, the rope travels 0.628 m per full turn, at 0.628 m/s or 37.70 m/min. A quarter turn takes up 157.1 mm.
With 100 N·m shaft torque, ideal rope pull is 1000 N and ideal shaft power is 628.3 W. The same torque and rpm at a 400 mm effective diameter give twice the line speed and half the ideal pull. The power stays the same.
These values are geometric and ideal mechanical results. They are not a rated lifting capacity or a claim that a particular motor maintains the entered torque at the entered speed.
Scope of the winding model
The calculation assumes an inextensible rope, no slip, a fixed effective radius and no mechanical losses. It does not predict rope fatigue, layer packing, crushing, fleet-angle limits, drum width, allowable speed or load ratings.
Actual rope and winch specifications govern attachments, holding wraps, brakes and permissible loads. A winding drum and a traction capstan have different rope arrangements; this animation shows a winding drum, not a traction calculation based on wrap friction.
Rope thickness and support details are schematic. The end-section scale fits the window when diameter changes; the dimension labels and calculated travel carry the actual size.
Drum-and-rope questions
Should I enter bare drum or flange diameter?
Neither automatically. Enter the diameter to the centre of the working rope wrap. Flange diameter is not the winding radius.
Why does a larger diameter reduce ideal pull?
The same torque acts through a larger moment arm, so F=T/R is lower.
Why is power unchanged when diameter changes?
At fixed torque and rpm, line speed rises in the same proportion that ideal pull falls, so their product is constant.
Does the animation simulate multiple layers?
No. It demonstrates one fixed effective diameter. Change that input to compare a different layer.
Is the pull output a safe working load?
No. It is an ideal torque balance without component ratings, losses or brake verification.
References
WARN Industries, Winch Performance Specifications: Pulling Capacity by Layer, explains the effect of outer rope layers on pulling capacity. The calculation uses the arc-length and torque/power identities derived above, rather than a product rating or performance curve.
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