An analytically derived solution for the time history of a ship-ice impact

The Popov-Daley method is a closed form analytically derived model used for calculating contact forces of a ship-ice impact. It consists of determining the available kinetic energy of the ship-ice system which is then dissipated into indentation energy. This method has been applied in multiple areas, with the International Association of Classification Societies (IACS) Unified Requirements for Polar Class Ships (Polar URs) using the Popov-Daley method as part of its design ice load model, assuming that all energy is dissipated through ice crushing, whereas other studies involving non-ice strengthened ships allow for structural deformation and thus consider both ice and structural indentation energies. More recently, the Popov-Daley method has seen use in multiple academic studies where its application over a period of time is desired, but a solution for the time – history derived from the underlying energy balance equations does not currently exist. With this in mind, a method for analytically solving the time – history of a Popov-Daley style ship-ice collision model has been developed, with equations derived for the indentation depth – time relationship as well as for the total time of the collision using the same assumptions employed in the Polar URs. The proposed models were found to be in very good agreement with numerical and preliminary experimental results. Applications of the models and further necessary validation work are both discussed.