Considering frictional effects on the ice crushing force of a ship-ice impact

The Popov-Daley method is the current standard for analytically determining ship-ice collision forces and involves converting the available kinetic energy of an impact into ice (or ice + structural) indentation energy. It is part of the current design ice load model in the International Association of Classification Societies (IACS) Unified Requirements for Polar Class Ships (Polar URs) and has seen use in multiple academic studies with ship-ice impact scenarios ranging from thick ice and heavy icebreakers to non-ice strengthened ships (NISS) encountering finite floes. The Popov method reduces a six degree of freedom impact between two bodies into a single degree of freedom collision normal to the contact plane by deriving a reduced mass through which the available kinetic energy of the impact is determined. One assumption associated with this method is that frictional effects do not have a substantial effect on impact loads. The present study tests this assumption with a rederivation of the original method that considers frictional effects. Different impact scenarios relevant to both the Polar URs and to more recent studies involving NISS are reviewed, with impact forces calculated by converting the available kinetic energy into ice crushing energy using a process pressure-area relationship as applied by Daley and in the Polar URs. Minimal percent differences in the force levels were found across all tested scenarios. Lower differences were found with scenarios involving smaller ice floes, and the difference level never exceeded 1.5 % across all scenarios tested. This confirms the suitability of the friction related assumption from the original Popov method. An investigation into friction coefficients required for a significant percent difference in force levels resulted in coefficients of as least 0.34, which may occur in different ship collision scenarios but is not realistic for steel-ice contact.