One turn equals to 360 degrees or 2 π radians. With a friction coefficient of 0.5 the effort force in the rope can be calculated as
S = F e -(0.5 2 π)
= 0.043 F (N)
One turn around the bollard reduces the required effort force to less than 5% of the load force.
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 ship mass 20000 kg the required force in the rope from the ship (load) can be calculated as
F = m a (3)
= (20000 kg) (0.025 m/s2)
= 500 N
= 0.5 kN
The required effort force in the rope with a half turn around the bollard ( 180 degrees or π radians) with a friction coefficient of 0.4 can be calculated as
S = (500 N) e -0.4 π
= 142 N
= 0.14 kN
The Effort Force - Load Force ratio for various rope angles are indicated in the chart below:
Download and print Rope Turns around Bollard Effort Force vs. Load Force Chart
This calculator is based on the equation above and can be used to calculate the effort force in ropes turned around poles or bollards. Note that the calculator uses degrees for the turns.
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