# Analysis of a Collision-Energy-Based Method for the Prediction of Ice Loading on Ships
## 1 Introduction
However, to date, none of the existing methods can be considered complete and sufficiently validated to enable them to support direct goal-based structural design following the Polar Code. Thus, in practice, designers are dependent upon the application of the PC standards to obtain regulatory approval for ships designed for operation in ice-infested waters. For the assessment of design ice loading, the PC standards apply a method based on the principle of the conservation of momentum and energy in collisions, presented by [PERSON], et al. [9]. The method, in the following referred to as the Popov Method, is relevant for the assessment of ice loading on ships interacting with all types of sea ice. Despite the method being fundamentally analytical, its practical applications, including its application in the PC standards, rely on several assumptions. These concern the modelling of the collision scenario (e.g., type of collision, ship-ice contact geometry), as well as the material properties of ice [10; 11]. Because many of the assumptions are empirically determined, the PC standards can be considered semi-empirical, meaning that they might not be efficient when applied on design and operating conditions different from those for which the assumptions were determined [12]. Against this background, this study aims to help designers to make better-informed decisions in the design of Arctic ships by analysing the role and effects of the collision scenario assumptions behind the application of the Popov Method [9]. Specifically, the study addresses the following research questions:How do assumptions behind the modelling of the collision scenario and the description of the operating conditions affect the ice load estimate? What collision scenario assumptions should be applied to obtain reliable ice load estimates for typical operation in level and broken ice? Because the Popov Method in principle makes it possible to assess ice loading for a wide range of ship designs and operating scenarios, the method is highly relevant in the context of goal-based design. Thus, by addressing the above research questions, we also aim to support progress towards the goal-based design of Arctic ships, as per the above-described principle of equivalent design. The study is limited to issues concerning ice material properties and non-accidental ship-ice interactions resulting in no or minor structural deformation with relatively thick ice, where the dominant failure mode is crushing. We do not consider the following:  
* Issues concerning hydrodynamic effects. These are assumed to have a limited effect on the types of collision scenarios considered [13]. * Issues concerning structural resistance. * Local plastic deformations. Thus, although the method can do so, we do not consider local plastic deformations, which could affect the obtained load estimate [14; 15]. It can be mentioned that allowable plastic deformations are not clearly defined in the PC rules [16]. * Interactions with thin ice, which in addition to crushing would require the consideration of flexural failure and dynamic effects [17]. [PERSON] & [PERSON] [18] indicate that when dynamic effects are considered, the design normal force is increasing with increasing impact velocity [6]. * Secondary impacts (i.e., reflected collisions). [PERSON] & [PERSON] [19], among others, demonstrate that when operating in thick ice, reflected collisions may result in critical loads, in particular on the mid-ship area. * Moving loads along the hull that may result from a collision with pack ice, glacial ice, or ice channel edges are not considered. [PERSON] et al. [20] and [PERSON] & [PERSON] [21] indicate that moving ice loads may cause more damage than stationary loads of similar magnitude. Consideration of moving loads would require the consideration of additional factors such as sliding contact, nonlinear geometric and material behaviours in structural components, requiring the application of the finite element analysis [22].