# Analysis of a Collision-Energy-Based Method for the Prediction of Ice Loading on Ships
## 1 Introduction  
Maritime activity in the Arctic is on the increase, driven by the extraction of Arctic natural resources, trans-Arctic shipping and Arctic tourism. To manage related risks, the maritime industry must ensure that Arctic ships are safe and sustainable. To this end, ships operating in Polar water must be approved under the International Code for Ships Operating in Polar Waters, or the Polar Code [1], enforced by the International Maritime Organization (IMO). The specific objective of the Polar Code is to ensure the same level of safety for ships, persons and the environment in Polar waters, as in other waters [2]. Towards this end, it supplements the International Convention for the Safety of Life at Sea (SOLAS) and the International Convention for the Prevention of Pollution from Ships (MARPOL) to account for Arctic-specific safety hazards, such as sea ice, icing, low temperatures, darkness, high latitude, remoteness, the lack of relevant crew experience and difficult weather conditions. A ship approved in accordance with the Polar Code is issued a Polar Ship Certificate that classifies the ship as one of the following:  
* Category A, for ships allowed to operate in at least medium-thick first-year ice. * Category B, for ships allowed to operate in at least thin first-year ice. * Category C, for ships allowed to operate in ice conditions less severe than those included in Categories A or B. In addition to the ship's category, the ice certificate determines detailed operational limits concerning, for instance, the minimum temperature and the worst ice conditions in which a ship can operate. The Polar Code is fundamentally goal-based, determining mandatory provisions in terms of goals, functional requirements FR(s), and regulations to meet those goals. As a result, a ship can be approved either as a prescriptive design or as an equivalent design. A prescriptive design is a design that meets all of the prescriptive regulations associated with the FR(s), whereas an equivalent design is a design that is approved in accordance with Regulation 4 of SOLAS Chapter XIV. The latter case results in a so-called alternative or equivalent design. Per regulation 4--\"Alternative design and arrangement\" of SOLAS Chapter XIV [3], where alternative or equivalent designs or arrangements are proposed, they are to be justified by the following IMO Guidelines:  
* \"Guidelines for the approval of alternatives and equivalents as provided for in various IMO instruments\", MSC.1/Circ.1455 [4]. * \"Guidelines on alternative design and arrangements for SOLAS chapters II-1 and III, MSC.1/Circ.1212 [5]. * \"Guidelines on alternative design and arrangements for fire safety\", MSC/Circ.1002 [6]. A general principle is that any alternative design should be at least as safe as a design determined by prescriptive rules. Many of the prescriptive regulations of the Polar Code, in particular, those related to a vessel's structural strength, include references to the International Association of Classification Societies' (IACS) Polar Class (PC) ice class standards [7]. These consist of in total seven PC notations, ranging from PC 1 (highest) to PC 7 (lowest), corresponding to various levels of operational capability in ice and hull strength. For instance, as per the Polar Code, for a Category A ship to meet FR(s) regarding structural strength, the ship must be constructed in accordance with PC 1-5, whereas a Category B ship must be constructed in accordance with PC 6-7. Alternatively, the scantlings must be determined in accordance with a standard which offers an equivalent level of safety following the above-described principle of design equivalency. Because the ship-ice interaction process is complex, stochastic and not fully understood, predicting the level of ice loading that a ship will be exposed to is challenging. Multiple different methods to predict ice loading have been proposed, including analytical, numerical and empirical methods [8].