Ship speed optimisation has a number of variants, depending on the objective of the problem under consideration, such as ship scheduling, ship routing, ship fleet sizing, and ship fuel bunkering13,14. All ship speed optimisation problem variants require in their mathematical formulation, in the objective and or in the constraints, a relation expressing the variation of ship fuel consumption rate (per unit time) with ship speed. This relation may be determined employing the Holtrop-Menen procedure15,16(in two steps) to determine the relation between ship fuel consumption rate (per unit time) and ship power propulsion rate (per unit time). From data describing the relation between ship propulsion rate (per unit time) and ship speed, the required variation of ship fuel consumption rate (per unit time) with ship speed is finally obtained. This variation is nonlinear, typically in the form