BIZOMAT MAKEOS · Mechanics
Capstan and Bollard Rope Turns Check (Holding Force, Turns Needed, Rope Load)
How many turns of rope around a bollard, capstan or drum let a person hold this load, and is the rope strong enough?
Check of rope turns on a bollard, capstan, winch drum or post: the ratio of tight to slack tension from the friction coefficient and wrap angle (as the belt friction tool, capstan equation), the holding force needed with the turns used, the turns needed for the holding force a person can apply, and the rope working load from its breaking strength and safety factor, against the load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load (tight side tension) | N | Tension on the load side of the rope. |
| Holding force a person can apply | N | Force the person tending the rope can safely hold. |
| Friction coefficient of rope on the post | Friction coefficient between the rope and the post or drum (wet, glazed or rope-on-rope contact is lower). | |
| Turns used | turns | Complete turns of rope around the post (one turn = 360° of wrap). |
| Rope | ||
| Rope minimum breaking load | kN | Minimum breaking load of the rope. |
| Safety factor on the rope | Safety factor applied to the breaking load for the working load. | |
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 (tight side tension)
- What it is
- The tension in the rope on the load side of the post, drum or bollard, the force the turns must hold.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Holding force needed and turns needed both rise with it.
- Get it right
- Enter it in newtons, not kN: multiply kN by 1000.
What this means: Holding force a person can apply
- What it is
- The force the person tending the slack end of the rope can safely hold, compared with the holding force needed.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger holding force reduces the turns needed.
- Get it right
- Take it from your manual handling guidance or a competent assessment; the tool does not suggest one.
What this means: Friction coefficient of rope on the post
- What it is
- The friction coefficient between the rope and the surface of the post, drum or bollard, used in the capstan equation.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 2. 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 tension ratio grows exponentially with it, so small changes matter.
- Get it right
- Take it from rope or equipment data for your rope and surface; wet, glazed or rope-on-rope contact is lower.
What this means: Turns used
- What it is
- The number of complete turns of rope around the post, where one turn is a full 360° of wrap.
- Units and format
- Enter a number in turns: a number of turns. The form accepts 0.25 turns to 100 turns. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 turns as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The tension ratio grows exponentially with the turns, so each extra turn multiplies the holding power.
- Get it right
- Count full turns; half a turn is 0.5, not 180.
Rope
What this means: Rope minimum breaking load
- What it is
- The minimum breaking load of the rope from its maker or certificate, used with the safety factor to get the working load.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The working load limit rises in proportion to it.
- Get it right
- Enter it in kN, not tonnes or N: multiply tonnes-force by 9.81 to get kN.
What this means: Safety factor on the rope
- What it is
- The safety factor the breaking load is divided by to get the rope’s working load limit.
- 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.
- Effect on the result
- A higher factor lowers the working load limit.
- Get it right
- Take it from the lifting or rigging standard that applies to your use.
Method and formulas
- T₁ ÷ T₂ = e^{μθ} with θ = 2π × turns (as the belt friction tool).
- Holding force = T₁ ÷ e^{μθ}; turns needed = ln (T₁ ÷ T₂) ÷ (2π μ).
- Working load = breaking load ÷ safety factor.
- Example: 3 turns give a ratio of 111.32; hold 179.67 N; at least 2.6736 turns are needed.
Limitations
- Rope fully bedded on a round post; rope stiffness and crossing turns change the friction.
- Static holding; surging a rope round a capstan heats and wears it.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the turns needed to snub a load on a post
- Check a capstan winch line pull
- Lower a load by hand round a bollard
Who it is for
- Riggers
- Arborists
- Marine and rescue crews
What you get
- Tension ratio for the turns used
- Holding force needed and turns needed
- Rope working load
Interpreting the result
- Each extra turn multiplies the holding power by the same large factor, which is why a few turns hold a heavy load.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 165–168, 2473–2490. Topic reference; no source tables or recommended settings are reproduced.
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Open the Capstan and Bollard Rope Turns Check (Holding Force, Turns Needed, Rope Load) calculator