Eccentricity Coefficient in Berthing Energy Calculations

The purpose of the eccentricity coefficient in berthing energy calculations is to estimate the portion of the ship’s kinetic energy that fenders must absorb in side-berthing scenarios where angular motion of the ship results from the initial fender contact. Analytical derivations of the eccentricity coefficient were initially introduced to the industry in the 1950s and 1960s. Several analytical solutions were proposed at the time, derived by adopting sets of varying assumptions. More notably, solutions formulated by Vasco Costa and Saurin gained popularity and were eventually introduced into marine design guidelines where they remain relatively unchanged to this day. These guidelines also introduced the notion that berthing velocities of ships approaching under tug-assist should be taken as normal to the berth face, and as such, guidance provided to practitioners on velocity selection for side-berthing scenarios apply only to this approach condition. Standard methods for fender performance rating were also developed based on this assumption, with the energy absorption capacity measurements obtained by compressing the fenders in a direction normal to their base. Authors like Vasco Costa did not necessarily adhere to this simplified approach in their derivation and proposed application of the eccentricity coefficient. Consequently, when ship berthing schematics based on Vasco Costa’s work were introduced in the design guidelines, they portrayed a general solution to side-berthing in which the velocity vector contained a notable longitudinal component. These schematics were seldom updated to reflect the simplified normal direction of the berthing velocity assumed in the guidelines. Since the velocity and berthing approach angles depicted in these general solutions are often used as direct input in the eccentricity coefficient formulae, finding diverse interpretations in fender selection calculations is a common occurrence in cases where practitioners believe special consideration of potential longitudinal velocity may exist because of water currents or due to particular berthing practices. It is also common to find poor and contradictory statements in the definition of these and other input variables in codes and standards, leading to further confusion and misuse of these equations, even when applied to simpler berthing scenarios. A re-derivation of the commonly used eccentricity coefficient solutions provides clarity around the basic assumptions, term definitions, and appropriate application in marine guidelines such as PIANC, MOTEMS, and BS 6349, in a manner that is consistent with the velocity vector assumptions and standard fender performance rating procedures. This paper provides recommendations for existing guidelines that include the adoption of new ship berthing schematics that depict clearly the normal-velocity condition assumed by the standards; clarification that, with very few exceptions, the longitudinal component of the kinetic energy in side-berthing scenarios is assumed to be conserved as longitudinal motion and not absorbed by the fenders; and lastly, clarification that given the stated assumptions, the eccentricity coefficient in side-berthing scenarios only modifies the normal component of the total kinetic energy and therefore the input values used in the eccentricity coefficient equations must reflect the condition in which the velocity vector is normal to the fender base.