Examples covering the calculation of berthing energy for fender system design.

A general cargo ship with a displacement mass ($M_v$) of 35,000 metric tons ($3.5 \times 10^7$ kg) approaches a continuous quay wall. The design approach velocity ($V$) is 0.15 m/s. For this preliminary calculation, the product of all modification coefficients ($C = C_m \cdot C_e \cdot C_c \cdot C_s$) is assumed to be 0.70. Calculate the kinetic berthing energy ($E$) that the fender system must absorb.

A VLCC (Very Large Crude Carrier) with a mass ($M_v$) of 250,000 metric tons approaches a mooring dolphin. The approach velocity ($V$) is 0.10 m/s. The detailed modification coefficients are: Hydrodynamic mass coefficient ($C_m = 1.6$), Eccentricity coefficient ($C_e = 0.5$), Berth configuration coefficient ($C_c = 0.9$ due to open piling), and Softness coefficient ($C_s = 1.0$). Calculate the total berthing energy ($E$).

A RoRo ferry requires a new fender system on an existing quay wall. The calculated design berthing energy ($E$) is 450 kN·m. However, the aging concrete quay wall can only withstand a maximum reaction force ($R$) of 800 kN per fender without sustaining structural damage. Evaluating manufacturer specifications, Fender Type A absorbs 500 kN·m with a reaction force of 950 kN, and Fender Type B absorbs 480 kN·m with a reaction force of 750 kN. Determine the appropriate fender.