Bollard Force

The load and effort force in a rope

Bollards is common on quays in and are used when mooring ships and boats.

The effort force in a rope can be calculated

S = F e^-μα (1)

where

S = effort force in the rope (N)

F = load (N)

e = 2.718..

μ = friction coefficient (aprox. 0.3 - 0.5 is common for a rope around a steel or cast iron bollard)

α = angle where the rope is in contact with the bollard (radians) 

Angle - turns, degrees and radians

• 1/4 turn : 90 degrees => α = 1/2 π
• 1/2 turn : 180 degrees => α = π
• 1 turn : 360 degrees => α = 2π
• 2 turns : 720 degrees => α = 4π

Example - A rope with one turn around the bollard

With a friction coefficient of 0.5 the effort force in the rope can be calculated as

S = F e^{-0.5 2π}

    = 0.043 F (N)

As we can see - one turn around the bollard reduces the required effort force to less than 5% of the load.

Example - Shoring a ship

The retardation (negative acceleration) of a ship arriving at quay with velocity 0.05 m/s and stopped within 2 seconds, can be calculated as

a = dv/dt

= 0.05 (m/s) / 2 (s)

= 0.025 (m/s²)

With a mass of 20000 kg the required force F in the rope from the ship can be calculated as

F = m a

= 20000 (kg) 0.025 (m/s²)

= 500 N

The required effort force with a half turn around a bollard with a friction coefficient of 0.4 can be calculated as

S = F e^{-0.5 2π}

= 500 (N) e^{-0.4 π}

= 142 (N)  

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