MOMENT-CONSTRAINED SIDE-FORCE ALLOCATION FOR WIND-ASSISTED MERCHANT SHIPS: HYDRODYNAMIC PERFORMANCE OF RETRACTABLE ANTI-LEEWAY FINS AND FLAP RUDDERS

Abstract

Wind-assisted propulsion generates an aerodynamic side force and yaw moment that must be balanced hydrodynamically through leeway, helm and appendage loading. Retractable anti-leeway fins with adjustable incidence and flap rudders are being introduced for this purpose, but their benefit for large merchant ships has not been quantified with a method that resolves the coupled side-force and yaw-moment allocation. This paper develops a moment-constrained side-force allocation framework and applies it to the KVLCC2 tanker fitted with four wing sails. The framework couples (i) captive-test-based manoeuvring (MMG) coefficients for hull, propeller and rudder, (ii) a low-aspect-ratio lifting-surface model for fins and flap rudders that combines a vortex-lattice method with a reflection plane, XFOIL section polars at full-scale Reynolds number and a cross-flow non-linearity, (iii) hull up-wash, boundary-layer immersion and fin–rudder vortex interaction, and (iv) a joint optimisation of sail trim, leeway, helm, flap angle, fin incidence and fin deployment. A closed-form result is derived for the minimum side-force cost, together with the yaw-balance capacity and the break-even side force for fin deployment. The theory reproduces the non-linear optimum within 1.7% and predicts the fin break-even side force (1.92 MN) within 2.1%. Route-level evaluation with two real wind datasets (NOAA buoy 46002 and the NREL WIND Toolkit) shows that, at a sail-area ratio of 0.6, 12 kn and a 10° helm limit, all appendage options change annual savings by less than 0.05 percentage points while a flap rudder reduces the time spent above 8° helm from 1.96% to 0.35%. When yaw balance becomes binding (sail-area ratio 1.2, 10 kn, 5° helm limit), the flap rudder adds 4.66 points to a 40.0% baseline saving, a retractable adjustable fin adds 3.52 points and the combination adds 4.77 points with the fin deployed 16% of the time (Monte Carlo: 4.83 ± 0.56 points). Neglecting propeller unloading overstates the baseline saving by 2.0 points, and sail-first trimming loses 0.83 points relative to joint optimisation.