Bollard Force
The load and effort force in a rope
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Bollards is common on quays 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 (approximately 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 (2)
= (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 (3)
= (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)
The Effort Force - Load Force ratio for various rope angles are indicate in the chart below:
- friction coefficient 0.5
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