Tow Forces for Emergency Towing of Containerships

For a series of five containerships of differing capacities (707, 3400, 5300, 14,000, and 18,000 TEU), systematic computations were performed to estimate the tow force required in an emergency. Time-average ship positions with respect to the given waves, wind, and current directions and the corresponding time-average forces were considered. Current speed was considered to include also towing speed. Directionally aligned as well as not aligned wind and waves were investigated. Wave height, wind speed, and wave and wind direction relative to current direction were systematically varied. Wind speeds based on the Beaufort wind force scale corresponded to significant wave heights for a fully arisen sea. Waves were assumed to be irregular short-crested seaways described by a Joint North Sea Wave Observation Project (JONSWAP) spectrum with peak parameter 3.3 and cosine squared directional spreading. For each combination of current speed, wave direction, significant wave height, and peak wave period, the required tow force and the associated drift angle were calculated. Tow force calculations were based on the solution of equilibrium equations in the horizontal plane. A Reynolds-Averaged Navier–Stokes (RANS) solver obtained current and wind forces and moments; and a Rankine source-patch method, drift forces and moments in waves. Tow forces accounted for steady (calm-water) hydrodynamic forces and moments, constant wind forces and moments, and time-average wave drift forces and moments. Rudder and propeller forces and towline forces were neglected.