Bollard Force

Bollard rope friction - the load and effort force in the rope


bollard quay ship mooring

Bollards are common on quays and used to moore ships and boats.

bollard force

The effort force in a rope around a bollard can be calculated as

S = F e-μα         (1)


S = effort force in the rope (N, lb)

F = load force (N, lb)

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 a Bollard

One turn equals to 360 degrees and radians. 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)

One turn around the bollard reduces the required effort force to less than 5% of the load force.

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 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 (180 degrees and π radians) with a friction coefficient of 0.4 can be calculated as

S = (500 N) e-0.4 π

= 142 (N)  

The Effort Force - Load Force ratio for various rope angles are indicated in the chart below:

bollard rope force when mooring ship chart

  • friction coefficient 0.5

Related Topics

  • Dynamics - Motion - velocity and acceleration, forces and torques
  • Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
  • Statics - Loads - force and torque, beams and columns

Related Documents

Tag Search

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