Calculating Berthing Energy 2.a-2.c

1. Kinetic Energy Equation

The equation detailing the variables:

EFender = 1/2 MV2 x Ce x Cm x Cs x Cc

2. Variables

a) Mass-M

One or more of the following weights should be readily available from the facility user:

Displacement Tonnage – DT: this is the weight of the water displaced by the immersed part of the ship.

Dead Weight Tonnage –DWT: this is the weight that the ship can carry when loaded to a specified load draft. (Includes cargo fuel, stores, crew, passengers.)

Gross Tonnage – GT: this is based on the cubic capacity of the ship below the tonnage deck with allowance for cargo compartments above.

When calculating the mass- M, use the loaded displacement tonnage DT. Typically DT is 30% – 40% greater than DWT.

M = DT/g


DT = displacement tonnage (tonnes)
g = Acceleration Due to Gravity = 9.81 M/Sec2

b) Velocity –V

As can be seen from the Kinetic Energy Equation, the energy to be absorbed is a function of the square of the approach velocity. For this reason, DETERMINING THE VELOCITY IS ONE OF THE MOST IMPORTANT DECISIONS IN THE DESIGN.

The choice of design velocity (velocity component normal to the dock) is a judgement based on ship size, site exposure and berthing procedure. Environment aspects such as wind and current forces may be an influence. Consultation with Port Management, ship operators and any other available information should be used when making the judgement.

The following chart is offered as a guide to assist in selecting a design velocity:

Calculating Berthing Energy 2.a-2.c

Navigation Conditions

1. Easy Docking; Sheltered
2. Difficult Docking; Sheltered
3. Easy Docking; Exposed
4. Good Docking; Exposed
5. Difficult Docking; Exposed


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