Towards an optimisation of mooring design for floating offshore wind turbines: Mathematical formalisation of a novel physically-based motion-related constraint

Early-stage mooring design for Floating Offshore Wind Turbines (FOWTs) relies on empirical poorly standardised motion-related constraints that neglect system dynamics. This work proposes a novel performance-driven methodology that dynamically links allowable offsets to the physical response of the system. A validated OpenFAST model of the NREL 5 MW wind turbine on the OC3 Hywind spar-type floating platform, Magnitude-Squared Coherence, and Pearson’s correlation analyses, were used to investigate FOWT dynamics and identify key physical relationships underpinning the proposed motion-related design constraint. Structural offset, redefined as the distance between static and dynamic equilibrium positions, captures the surge-pitch effects, identified as the primary drivers of mooring tension. This offset exhibits a monotonic relationship with tension asymmetry across mooring lines, peaking under rated wind conditions in operation and under extreme wind conditions in parked states. Based on these findings, a motion-related design constraint is formulated through a new metric, the Asymmetry Coefficient. A Proof of Concept demonstrates that the proposed formulation reduces load asymmetry, prevents line slack, and ensures compliance with strength requirements. Overall, the proposed metric reduces conservatism, lowers material usage, and streamlines early-stage design by reducing computational effort and simulation complexity, thereby supporting more efficient engineering workflows and potentially lowering project costs.