1 ENERGY BASED ICE COLLISION FORCES Claude Daley 1 1 Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 3X5 ABSTRACT Ice collision forces can be determined by energy considerations. A variety of interaction geometry cases are considered. The indentation energy functions for eight different cases are derived and expressed in a common format. The indentation functions are expressed as functions of the indentation model parameters, assuming a pressure-area representation. Two types of collisions are identified; simple impacts which can be treated as equivalent to one- dimensional collisions, and beaching collisions which involve two-dimensional behaviour (indentation and sliding). Solutions for the impact cases are presented for all geometry cases. A solutions procedure is presented for the beaching collision, with an exact solution for a linear case. Design equation development and future directions are discussed. 1. INTRODUCTION Ice forces on ships and structures are typically the result of collisions. The magnitude of the force is determined by some form of limit (see e.g. Croasdale, 1980, Daley, Tuhkuri and Riska 1998). In some cases the ice strength is the determining factor, while in others the force may be limited by available kinetic energy. In such cases the available kinetic energy is expended in crushing (irrecoverable) and potential (recoverable) energy. Energy methods provide a simple method of determining forces, and have long been used to do so (see Popov et. al. 1967). This paper will summarize the general energy approach, derive some old and new cases and provide examples. 2. GENERAL APPROACH The problem under discussion is one of impact between two objects. It is assumed that one body is initially moving (the impacting body) and the other is at rest (the impacted body). This concept applies to a ship striking an ice edge, or ice striking an offshore structure. The energy approach is based on equating the available kinetic energy with the energy expended in crushing and potential energy: PE IE KE e + = (1) The available kinetic energy is the difference between the initial kinetic energy of the impacting body and the total kinetic energy of both bodies at the point of maximum force. If Expanded version (full derivations) of paper for POAC 99, Proc. of the 15th International Conference on Port and Ocean Engineering under Arctic Conditions, Helsinki University of Technology in Espoo, Finland on August 23-27, 1999.