When designing rubber fenders considering the various effects of use conditions and the environment

Release time:2024-06-08    Click:67


When designing rubber fenders considering the various effects of use conditions and the environment, marine fenders that can absorb more energy than the effective berthing energy must be selected; furthermore, the maximum reaction force should be safe for mooring facilities. The surface pressure towards the vessel hull should be within the allowable hull pressure of the vessel. In addition, the rubber fender, including the peripheral parts, must be designed to function as a safe system under the considered design conditions. 

Design procedure of rubber fender

Since rubber fenders vary in size and performance in terms of those for leisure boats to those for super-tankers, it is necessary to design fenders that are appropriate for a given condition. In particular, the effective berthing energy is initially calculated, and the type and size of rubber fenders are selected accordingly. Next, the factors affecting the performance are considered. To select the appropriate factor pattern, the design conditions of the mooring facilities and the allowable hull pressure, as a representative of the vessel side strength, are compared with the corresponding performance of the rubber fenders. Rubber fenders are selected considering the influence factors, and a detailed design process that accounts for installation, pitch spacing, fender panel, chain, etc. is performed. Below figure shows the design process flow of rubber fenders. 


The classification of factor patterns is described ,below Table , and design examples are presented in the Appendix.


3.Effective berthing energy

The effective berthing energy to be absorbed by the rubber fender can be calculated using equation.


The key variables and coefficients in equation can be described as follows:

(1) Berthing velocity: VB

As given in equation, since the berthing velocity is squared when calculating the effective berthing

energy, it exerts more influence than other coefficients do. The berthing velocity is affected by the type of ship, loading condition, location and structure of mooring facilities, weather and sea conditions, presence/absence of tug boats, etc. Vessels have evolved over time, and the measured data and

standards of berthing velocity have been updated accordingly 1), 2), 3). In actual design, it is desirable to set these parameters appropriately based on local measurement data and the latest statistics along with the above mentioned information.

(2) Eccentricity factor: Ce

As shown in below figure, in most berthing vessels, the hull contacts a fender at berthing angle θ and starts to rotate. As a result, a part of the kinetic energy (berthing energy) is consumed by the rotation. The remaining energy can be determined by performing correction using the eccentricity factor Ce . The eccentricity factor Ce  can be expressed using the equation (below figure for Vessel berthing between fenders ) when the berthing direction is perpendicular to the berth. 




If accurate information is not available, or if only a preliminary review is conducted, the values in below table may be used. 


In above figure, it is assumed that a rubber fender is present at the contact point of the vessel; however, in reality, rubber fenders are attached at a certain interval S; in addition, as shown in figure of Vessel berthing between fenders , there exists a case in which the vessel makes contact between two fenders.

In the Technical Standards and Commentaries of Ports and Harbour Facilities in Japan 2), the eccentricity coefficient Ce  at this instant is obtained by determining Rs , as defined in equation (Vessel berthing between fenders figure. As shown in Vessel berthing between fenders figure, Rs is the distance from the contact point to the centre of gravity of the vessel, and it is measured parallel to the berth line. When the hull of the vessel approaches the berth and contacts two rubber fenders F1 and F2, Rs can be determined using equations . Here, Rs is R1 when k > 0.5 and R2 when k <0.5; when k = 0.5, Rs is assigned the value of either R1 and R2 that corresponds to a larger value of Ce

R1={0.5α e(1-k)}Lpp cosθ

R2={0.5α e kLpp cosθ 


k :A parameter that represents the closest point of the vessel and berth between fenders F1 and F2.

k is 0 <k <1; in general, k is approximately 0.5

R1 :Distance (m) from the berthing point to the centre of gravity (CG) of vessel, measured parallel to the wharf as the vessel contacts fender F1

R2 :Distance (m) from the berthing point to the centre of gravity (CG) of vessel, measured parallel to the wharf as the vessel contacts fender F2

θ :Berthing angle (°)

e :Ratio of fender spacing S measured in the longitudinal direction of the vessel to the length between

perpendiculars Lpp

α :Ratio (parallel coefficient) of the length of parallel line at the berthing position to the length between perpendiculars Lpp

The eccentricity factor Ce is determined by substituting the Rs obtained using the abovementioned process into equation (below figure). 


(3) Virtual mass factor: Cm

Several formulas have been used to determine the virtual mass (added mass coefficient, hydrodynamic mass), and it has been researched extensively. The following two formulas are recommended in the

PIANC Guidelines 4) .

1) Ueda's formula

Ueda's formula was proposed in 1981 and is based on model experiments and field observations. It can be presented as equation.


2) Vasco Costa’s formula

In this formula, it is assumed that a certain amount of water mass (d·d·Lpp) is added at the time of berthing. The total added mass is 2 d·d·Lpp because the phenomenon occurs on both sides of vessel. In addition,the mass of the vessel is Lpp·B·d. Therefore, the virtual mass at the time of berthing can be

obtained using equation by adding the two defined masses. 



Subsequently, the virtual mass factor (Cm) can be calculated using equation (below):



Lpp : Length between perpendiculars (m)

B : Beam of vessel (m)

d : Draught of vessel (m)

This formula is considered to be effective only under the following conditions; Ueda’s equation should

be used in all other cases.

・ The bottom clearance of the vessel is 0.1×d or more.

・ Berthing speed is 0.08 m/s or more.

3) Bow and stern berthing

For bow and stern berthing (roll on roll off), as described in the PIANC Guidelines 4) , a value of 1.1

should be adopted. The British Standard 5) advocates a value of 1.0. Here, the larger value is selected.

                                                  Cm = 1.1: Bow and stern berthing

(4) Berth configuration factor: Cc and softness factor: Cs

The berth configuration factor Cc is thought to be applicable in the case of permeable (such as a

pile-supported pier) and non-permeable structures (a quay); when there is no escape for water, the water acts as a cushion and absorbs a certain amount of energy. The softness factor Cs considers energy absorption by elastic deformation of a vessel hull plate. Although both factors represent rational concepts, presently, the value of 1.0 is adopted because no research has yet demonstrated empirical evidence for the determination of numerical values.