<p>Large-scale energy storage is increasingly required to support offshore renewable generation, motivating interest in floating mechanical storage systems. Here we study the large-scale storage of kinetic energy via a floating offshore flywheel. We develop a simple mathematical model for the flywheel dynamics subject to hydrodynamic drag, bounded applied torque, and time-varying electricity prices, with optional wind-driven torque from surface-mounted sails. The operation of the system is formulated as an optimal control problem that maximises net energy revenue over a periodic operating cycle. The resulting optimal control problem is studied using a combination of asymptotic analysis and numerical optimisation. We show that across a wide range of physically relevant parameters, optimal operation reduces to a regime of near-constant angular velocity. In this regime, charging and discharging are governed by a simple switching rule based on a critical electricity price that can be determined directly from price data. Wind-driven torque enhances performance but does not alter the basic switching control structure. Case studies using idealised price profiles and German electricity market data demonstrate how the resulting switching-based control strategy operates under realistic conditions.</p>