## Introduction

Capstans are frequently deployed mooring equipment used on all types of vessels. Capstans are berthing/mooring equipment used to multiply the pulling force on mooring ropes.

Traditionally, Capstans were operated manually but in modern ships, they are operated wither electro-hydraulically or electromechanically.

When Capstans are used in mooring ships, they have to be sufficient in size and number to overcome the forces which the ship experiences in the lateral direction due to environmental forces of wind and current. How do we know what size capstans will be sufficient? We’ll take a detailed look at in this article.

This article is based on DDS-582-1 Calculations for Mooring Systems, Department of the Navy, Naval Sea Systems Command, Washington DC, 20362-5101.

## The Concept

When berthing a vessel, a number of capstans on the vessel may be utilized simultaneously. How do we determine if the capstan size is sufficient?

Thinking in basic terms, the berthing operation of the vessel will impose some forces on the vessel, which are transferred through the berthing lines to the capstans. What forces are these?

At the berth, the two major forces are the wind and current forces that the vessel experiences. Also, since the vessel is mostly berthed sideways, these forces must be calculated on the side of the vessel (not on the front).

The wind and current forces are characterized by the wind and current speed at the berth.

Thus, a simple approach to determine the capstan design will be:

- Calculate the lateral berthing forces (wind and current) on the vessel
- Divide the total lateral berthing force by the number of capstans to get the force per capstan. This will give the required line pull of the capstan
- The capstan power is obtained by dividing the required line pull times the warping speed by the capstan’s efficiency.

## Environmental Forces

The first step is calculating the environmental forces on the vessel. Generally, at berth, wind, and current are the most significant forces, while wave forces can be generally ignored.

When calculating the wind and current forces, the standard physics formula of Force = Pressure x Area shall be used. In the method by DDS-582 (Ref 3), wave forces have not been considered for doing the calculation.

For wind force, the formula is F_{wind} = 1/2 x C_{wind} x ρ_{wind} x V_{wind}^{2 }x A_{wind}, where C_{wind} is the coefficient of wind force, ρ_{wind} is the density of air, V_{wind} is the wind speed, and A_{wind} is the total area of ship and cargo which is exposed to the wind from beam direction (the above-water area)

Similarly, for current force, the formula is F_{current} = 1/2 x C_{current} x ρ_{water} x V_{current}^{2 }x A_{underwater}, where C_{current} is the coefficient of current force, ρ_{water} is the density of water, V_{current} is the current speed, and A_{underwater} is the total __underwater__ area of ship which is exposed to the current from beam direction.

The critical items in the calculations for Wind and Current forces are the force coefficients for wind and current.

These coefficients can be obtained from the coefficient plots provided in DDS-582, and some plots are presented below:

Lateral Current Coefficient (DDS-582)

Lateral Wind Coefficient (DDS-582)

We can see that the lateral current force is dependent on an additional factor: the underkeel clearance which is measured as Water Depth to Draft ratio (WD/T).

At the end of this exercise, we’ll have the following with us:

- Wind Force – transverse
- Current force – transverse

Next exercise is using these forces and calculate the capstan line pull using the environmental forces.

## Capstan Design

Once we have the wind and current lateral forces, we add them up together to give the total lateral force on the vessel.

Total Lateral Force, F_{Y} = F_{YW} + F_{YC}, where

F_{Y} = total lateral force on the vessel

F_{YW} = lateral wind force on the vessel

F_{YC} = lateral current force on the vessel

If the number of capstans is ‘n’, then the line pull per capstan is given by:

P_{CP} = F_{Y}/n

Once the line pull is available, the minimum required Capstan power is determined as follows:

P_{CAPSTAN} = P_{CP} x V_{CP}/η_{CAPSTAN}

Here,

P_{CAPSTAN} = Required minimum capstan power

V_{CP} = Capstan’s warping line speed

η_{CP} = Capstan’s efficiency

The Capstan’s efficiency has the following components:

- Capstan Head Efficiency
- Overall bearing and gear efficiency
- For electro-hydraulic capstans additionally – Efficiency of Hydraulic Pump and Motor

From the above process, we can obtain the minimum required Capstan’s power using which we can select the right capstan, or we can evaluate the suitability of an existing capstan for berthing.

TheNavalArch has its own app for selecting the right capstan. Do check it out from the link below.

## References

- https://en.wikipedia.org/wiki/Capstan_(nautical)
- https://www.brighthubengineering.com/seafaring/51281-what-is-a-capstan-on-a-ship/
- DDS-582-1 Calculations for Mooring Systems, Department of the Navy, Naval Sea Systems Command, Washington DC, 20362-5101

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