# Analysis of a Collision-Energy-Based Method for the Prediction of Ice Loading on Ships
## 5 Discussion and Conclusions  
This study analyses a collision-energy-based method for the prediction of ice loading on ships known as the Popov Method. Even though the method is fundamentally analytical, due to unknowns related to the ship-ice interaction process and the material properties of sea ice, its practical application relies on numerous assumptions, some of which are empirically determined. To analyse the role of the assumptions, we compare ice load calculated for various assumptions with two different series of full-scale ice load measurements, referred to as data set A-B. Both of the data series originate from the same voyage, but differ in terms of operating conditions and modes. Data set A includes measurement data from operation in level and broken ice, including specific manoeuvres such as repeated ice ramming and reversing in ice. Data set B, on the other hand, mainly consists of measurement data from operation in broken and level ice without stops. Towards addressing the research questions of Ch. 1, we calculate ice loads for two different types of collisions, namely the ship-ice floe and ship-ice field collisions. For each assumed collision type, we calculate loads for two different load length assumptions, namely 0.4 m and 0.8 m, and for four types of contact geometries, namely angular, right-apex oblique, round and symmetric \(\
u\) wedge. In response to RQ1, we find that the obtained ice load prediction is very sensitive to assumptions concerning the modelling of the collision scenario and the operating conditions. For instance, depending on the assumed type of contact geometry, the obtained maximum load estimate might vary between 4%-122% of the corresponding full-scale measurement. This finding indicates that to get a reliable load estimate, the applied assumptions concerning the collision scenario and operating conditions (e.g., type of ice, floe size and ice thickness) must closely correspond to the actual condition. Figure 11: Comparison of line loads from the Popov Method for different ice edge opening angles of angular contact geometry. In practice, this means that when applying the Popov Method, for instance in the context of goal-based design, multiple different ship-ice interaction scenarios must be considered to account for the often complex operating conditions of an Arctic ship. In response to RQ2, we find that the best agreement with the full-scale measurements is obtained by applying the following combination of the assumptions: (a) Ship-ice floe collision, (b) angular contact geometry, and (c) load length of 0.4 m. Application of these assumptions overestimated the 10-min mean and extreme values of data set A by 33% and 32%, respectively. For data set B, on the other hand, the same assumptions underestimated the 10-min mean and extreme values by 1% and 36%, respectively. All other combinations of assumptions resulted in load estimates where either the mean or the extreme value deviated from either or both of the data series by more than 40%. When applying an angular contact geometry, it is necessary to assume the value of the ice edge opening angle (\(\phi\)). To investigate the role of this value, we calculated ice load estimates for \(\phi\)-values between 90\({}^{\circ}\)-150\({}^{\circ}\). We find that the calculated mean and extreme loads are negatively dependent on the ice edge opening angle. We conclude that the resulting underestimation of loads of data set B using the above defined preferred combination of assumptions could have been avoided by assuming an ice edge opening angle of around 110\({}^{\circ}\) instead of the applied value of 145\({}^{\circ}\). Assumptions behind the Popov Method and the related PC rules do not only concern the ship-ice interaction scenario, but also the material properties of ice, specifically the ice crushing strength.