Bollard Force

Rope friction - load and effort force in a rope

 

bollard quay ship mooring

Bollards are common on quays and are 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)

where

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

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 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 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 indicated in the chart below:

bollard force ship mooring chart

  • friction coefficient 0.5

Related Topics

  • Dynamics - Dynamics Motion - velocity and acceleration
  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
  • Statics - Loads - force and torque

Related Documents

Tag Search

  • en: bollard force rope boat ship
  • es: fuerza bolardo barco barco cuerda
  • de: Poller Kraft Seil Boot Schiff

Search the Engineering ToolBox

- "Search is the most efficient way to navigate the Engineering ToolBox!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!

close