BIZOMAT MAKEOS · Mechanics
Rope Winch Drum and Capstan (Wraps, Holding Pull, Torque, Power)
How many turns of rope around this drum let a small tail pull hold the load, what torque and power does the drum need, and is the rope strong enough?
Check of a rope wrapped around a rotating drum or capstan: the tension ratio e^(μθ) for the turns of rope (as the belt friction tool with no groove), the largest load the tail pull can hold, the turns needed for the load, drum torque from the difference of tensions, drive power at the rope speed with the drive efficiency, and the rope safety factor against its breaking load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load on the rope | kN | Pull on the load side of the rope. |
| Tail (holding) pull | N | Pull applied by hand or a tailing device on the slack side. |
| Rope-to-drum friction coefficient | Friction coefficient between rope and drum (about 0.2–0.3 fibre rope on steel; lower when wet or oily). | |
| Turns of rope on the drum | Number of complete turns around the drum. | |
| Drum diameter (to rope centre) | mm | Diameter of the drum measured to the rope centre. |
| Rope speed | m/min | Speed of the rope. |
| Drive efficiency | % | Efficiency of the gearing and drive. |
| Rope minimum breaking load | kN | Minimum breaking load of the rope. |
| Rope safety factor required | Safety factor on the rope you require (from the lifting or rope standard). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load on the rope
- What it is
- The pull in the rope on the load side, where it leaves the drum towards the load.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 10000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Torque, power and the turns needed rise with it; the rope safety factor falls.
- Get it right
- Enter kN; the tail pull below is entered in N.
What this means: Tail (holding) pull
- What it is
- The pull applied to the slack side of the rope, by hand or by a tailing device, to keep it gripping the drum.
- Units and format
- Enter a number in N: newtons. The form accepts 1 N to 1000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The load that can be held is proportional to the tail pull.
- Get it right
- Enter newtons, not kN.
What this means: Rope-to-drum friction coefficient
- What it is
- The friction coefficient between the rope and the drum surface, from rope or drum maker’s data or a test.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The holding ratio grows exponentially with it.
- Get it right
- Wet, oily or glazed surfaces lower it; check the worst case.
What this means: Turns of rope on the drum
- What it is
- The number of complete turns of rope around the drum or capstan. Each turn adds a full circle of wrap angle.
- Units and format
- Enter a plain number with no unit. The form accepts 0.25 to 50. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The holding ratio grows exponentially with the number of turns.
- Get it right
- Count full turns; half a turn is 0.5.
What this means: Drum diameter (to rope centre)
- What it is
- The diameter of the drum measured to the centre of the rope, which is the drum surface diameter plus one rope diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Drum torque is proportional to it.
- Get it right
- Measure to the rope centre, not the bare drum surface.
What this means: Rope speed
- What it is
- The speed at which the rope is hauled in, used for the drive power.
- Units and format
- Enter a number in m/min: metres per minute. The form accepts 0.000001 m/min to 1000 m/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 m/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Drive power is proportional to it.
- Get it right
- Metres per minute, not metres per second.
What this means: Drive efficiency
- What it is
- The overall efficiency of the gearing and drive between the motor and the drum, from the gearbox or winch maker.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 85% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Drive power is inversely proportional to it.
- Get it right
- Type the percentage itself, for example 85, not 0.85.
What this means: Rope minimum breaking load
- What it is
- The minimum breaking load of the rope, from the rope maker’s certificate or catalogue.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rope safety factor is proportional to it.
- Get it right
- Use the certified minimum breaking load for the actual rope, not the safe working load.
What this means: Rope safety factor required
- What it is
- The rope safety factor you require: minimum breaking load divided by the load. Take it from the applicable lifting or rope standard.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Wrap angle θ = 2π × turns; tension ratio = e^(μθ) (as the belt friction tool with no groove).
- Largest load held = tail pull × ratio; turns needed = ln(load ÷ tail) ÷ (2π μ).
- Drum torque = (load − tail) × D ÷ 2; power = load × speed ÷ efficiency.
- Rope safety factor = breaking load ÷ load.
- Example: 3 turns give a ratio of 111.32; 200 N holds up to 22.264 kN. The drum needs 480 N·m and 0.98039 kW.
Limitations
- Impending slip with constant friction; rope stiffness and drum fleet angle are not included.
- Rope riding up on itself reduces the effective turns.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a capstan or warping drum
- Find how many turns a rope needs on a bollard
- Check the drive of a rope haulage winch
Who it is for
- Design engineers
- Rigging supervisors
- Maintenance engineers
What you get
- Tension ratio and holding capacity
- Turns needed for the load
- Drum torque, drive power and rope safety factor
Interpreting the result
- Each extra turn multiplies the holding capacity: friction rises exponentially with wrap.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 165–168. Topic reference; no source tables or recommended settings are reproduced.
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Open the Rope Winch Drum and Capstan (Wraps, Holding Pull, Torque, Power) calculator