Finite Ice Floe Geometry Cases for Modeling Ice Crushing Forces of a Ship-Ice Impact

Abstract The Popov–Daley method calculates the ice crushing force of a ship-ice impact event using energy methods, where the calculated available kinetic energy of the impact is dissipated into ice crushing energy. One important factor of the model is the local geometries of the ship and the ice at the point of impact, as they define the contact area growth over the course of the collision. Several geometry cases exist, though one of the original uses of the Popov–Daley method was as part of the design ice load model of the International Association of Classification Societies (IACS) Unified Requirements for Polar Class Ships (Polar URs), where in one scenario, the bow of the ship impacts with an ice wedge in a glancing blow resulting in an assumed triangular contact geometry. The Polar URs impact scenarios do not directly consider the limited thickness or size of the impacted ice when determining the nominal contact geometry and rely on flexural failure limit models to prevent unrealistic contact patch growth. More recently however, the Popov–Daley ice crushing model has seen use in an expanded range of impact scenarios, and as such, geometry cases considering the limited ice thickness have been developed, including a thickness-limited ice wedge impact case. As a continuation of this work, the present study derives additional collision geometries that consider finite floes for other commonly used ice impact scenarios. Two thickness-limited area-indentation relationships are thus derived for stem impact cases, and one is derived for floes of finite size where the edge impacts are nearly parallel to the ship hull.