A simplified method to predict full-scale ship performance in pack ice fields

2.1 Prediction of Open Water Resistance Component

Resistance, propulsion, and propeller open water tests are typically used to evaluate full-scale performance. These tests are the most appropriate method for assessing full-scale ship resistance and propulsion performance in open water and, therefore, are essential for predicting full-scale performance. Specifically, model tests conducted in calm waters can identify the open water resistance component. These tests are generally performed in open water, but can sometimes be carried out after the ice tests when broken ice pieces have been removed from the ship's track. In such cases, it is referred to as resistance in ice-free water and differs from open-water resistance, but the difference is negligible (ITTC [10]). Moreover, the thrust deduction factor can be obtained from the resistance and propulsion test results. The open water resistance component is essential for predicting full-scale ship performance. Since ice resistance plays a more dominant role in ice conditions, with open-water resistance accounting for only about 5–10% of the total, a simplified open-water resistance equation that depends on the ship's speed is employed to estimate the ship's performance in real-world, full-scale scenarios. In this study, open-water resistance performance at full scale was established through model testing in a KRISO towing tank (MOERI [11]). Based on the experimental results, the full-scale open water resistance can be determined as follows:

In Equation (1), the quantity R_ow is expressed in newton, and v is knots.

2.2 Formulation of the Pack Ice Resistance Component

When a ship moves through ice, if ice resistance exceeds net thrust, the ship becomes stuck. Therefore, ensuring sufficient thrust to overcome ice resistance is vital for icebreaking vessels. Full-scale ice trials generally help predict a vessel's performance in ice conditions. Although the data from these trials can be helpful, accurately forecasting ice resistance remains challenging. This study proposes a straightforward approach to estimate a ship's ice performance using the direct power method (ITTC [12]; Jeong et al.[13]).

First, the power delivered to the propeller, P_Dms, is calculated from the measured shaft power, P_Sms, using the following formula:

where η_S represents the shaft efficiency, which is assumed to be 0.97 in this study.

Then, the torque coefficient under ice trial conditions, K_Qms, is calculated with the following formula:

where ρ_s represents the seawater density, n_ms, and D denotes the measured propeller revolution rate and diameter, respectively, and η_Rms indicates the design propeller's efficiency during ice trials. The value of η_Rms is assumed to be 1.04 based on resistance and propulsion tests.

Additionally, the curves of the thrust coefficient, K_Tms, and torque coefficient, K_Qms, derived from open water characteristic data for the design propeller, obtained through model testing in a towing tank, is suggested by the following formulas.:

where J_ms represents the advance coefficient for the design propeller, while a_T, b_T, and c_T are the characteristics of the thrust coefficient curve, similarly, a_Q, b_Q, and c_Q are the characteristics of the torque coefficient curve.

Hence, the advance coefficient for the design propeller under ice-trial conditions, J_ms, is calculated using the subsequent formula.

If there is no dedicated sensor to measure thrust in the POD propulsion system, the thrust data will not be obtained directly. As a result, the thrust coefficient of the design propeller under trial conditions, K_Tms, is calculated using Equation (4) along with the thrust coefficient. This allows for determining the load factor of the design propeller under ice trial conditions, τ_Pms, as well as the thrust of each propeller, T_S, as follows :

where J_TS is based on the full-scale features of the design propeller.

The ice-propeller interaction in pack ice was not regarded as significant compared to level ice. Thus, this study did not consider the increase in torque excitation by ice floes and the resulting increase in delivered power. In addition, the wave effect was negligible due to the high ice-floe concentrations during the ship trials; therefore, the wave-induced added resistance component was not considered, and the ship's wind resistance was also ignored. Based on the above assumption, the effective thrust, T_eff, needed to overcome pack ice resistance, R_pack, can be expressed based on the thrust generated by the design propeller and the thrust deduction factor t.

where t is the thrust deduction factor of 0.14, derived from the resistance and propulsion test results. R_ow represents the open water resistance component.

3.1 Overview of the ice trials

Between November and December 2019, comprehensive ice trials were carried out in the Ross Sea region of Antarctica under various conditions (see Figure 1). The research employed pack ice data to evaluate the ship's performance in ice interaction, with particular emphasis on the relationships between speed and resistance, as well as speed and power.

Figure 1:

Bridge view image during the ice trials

A vessel onboard monitoring system is a valuable tool that is key to evaluating the ship's ice performance. The system can provide real-time information, including the ship's position, engine output, propeller revolution, speed, heading angle, etc. The Korea Research Institute of Ships and Ocean Engineering (KRISO) has embarked on the project to develop an integrated onboard monitoring system and has completed it. During the ice trials, the prototype was installed on the IBRV Araon as a performance evaluation tool. Therefore, the system can help evaluate a ship's performance in ice. It can collect data on hull strains, ship motions, voyage data recorders (VDR), alarm monitoring systems (AMS), and ice conditions.

In particular, the hull strain data can be used to determine the local ice pressures using the inverse method for the influence coefficient matrix, and the global ice load can also be determined by solving the equations of motion during the icebreaking process. However, this study is focused on ship performance prediction, such as speed-resistance and speed-power characteristics. Therefore, this study does not include the hull strain and ship motion data.

During these trials, network cameras installed on the bridge, bow, stern, and parallel areas recorded ice thickness and concentration measurements. The ship's operational data—such as heading angle, speeds, draft, power output, propeller revolutions, and propulsor unit angles—were recorded via the VDR and AMS systems (see Figures 2 and 3).

Figure 2:

Configuration of the developed onboard monitoring system

Figure 3:

Monitored ship performance data during ice trial

The strength characteristics may depend on several parameters, such as salinity, temperature, and density. Therefore, field measurements were conducted to determine the ice's strength properties. Based on these data, the flexural and compressive strength of the ice was calculated using empirical formulas (Timco and Frederking [14]; Timco and O'Brien [15]). The average flexural and compressive ice strengths were 257 kPa and 3.88 MPa, respectively (see Table 1).

Table 1:

Calculated compressive and flexural strengths of the ice (Jeong et al.[13]).

3.2 Data Processing for Analysis of the Ship's Ice Performance

This study defined criteria for data selection and analysis to identify stable conditions during the ice trials. Additionally, since the time interval significantly affects accuracy, it was set to three times the ship's length to achieve reliable results in a steady state. A correlation analysis was conducted on the heading and propulsion unit angles to determine whether direction changes were intentional. If the correlation coefficient was relatively high (i.e., greater than 0.4), the vessel's heading angle changes were considered intentional actions to avoid heavy ice conditions during navigation through the pack ice fields. In that case, the data were excluded from the analysis process to eliminate intentional steering operations. Finally, the coefficient of variation (CV) was determined. Usually, the CV is a statistical metric that shows how data points are dispersed around the mean. It reflects the extent of data variation within a sample relative to the population mean and provides a standardized method for comparing various data series. The CV is computed as:

where σ and μ denote the standard deviation and the mean of the data set, respectively.

This study outlines criteria for datasets used to assess ship performance under steady conditions.

• 1) The correlation coefficient between the propulsion system and the ship's heading must be less than 0.4. A value greater than this indicates a deliberate measure to avoid severe icing conditions.
• 2) The power output should exceed 30% of the maximum continuous rating (MCR) to avoid getting stuck in ice and to maintain continuous icebreaking. Additionally, the coefficient of variation (CV) for engine output must stay below 0.1.
• 3) When the main engine can continuously break ice, the CV for propeller speed should be less than 0.1.
• 4) The CV for the ship's speed through water (STW) must be kept under 0.2.
• 5) The ship's heading CV must remain below 0.2 during the specified period.

Figure 4 shows the CV values and correlation coefficients for the collected dataset. Five datasets were used in the data processing procedure. According to the proposed thresholds, the selected variables were tightly clustered and maintained reasonable levels during data extraction.

Figure 4:

Distribution of CV values and correlation coefficients for the comprehensive dataset (Jeong et al., 2025).

As mentioned above, ice thickness was extracted using a digital image-processing method. Figure 5 shows histograms of ice thickness measured across the five ice trial runs. Here, the frequency distribution represents the number of thickness profile images captured within each ice thickness interval.

Figure 5:

Thickness histogram of ice across five test events. The bin width for thickness was 0.2

3.3 Comparison of the Predictions Obtained from Ice Trial Data and the Calculations based on the Empirical Formula

An empirical formula for calculating pack ice resistance was proposed in a previous study, which also confirmed its accuracy (Jeong et al. [16]). In that study, the main parameters were ice floe size, ice concentration, and channel width. The developed prediction formula is defined by

where F_h denotes the Froude number for pack ice conditions, and $$ \frac{d_{floe}}{B}$$ represents the ratio of ice floe size to ship width. In addition, C_conc denotes the pack ice concentration, and W_ch and h represent the channel width and ice thickness, respectively.

Based on earlier research, the resistance of pack ice diminishes as the channel widens. Nonetheless, the findings are consistent when the channel width is eight times the ship's beam; hence, W_ch/B was designated as 8. Furthermore, the formula was optimised for vessels with dimensions similar to those of the IBRV Araon; this limitation should therefore be considered when using it.

The ice performance evaluation aims to determine an attainable ship speed and predict full-scale ship resistance. Thus, the attainable ship speed is estimated using the method proposed in this study and the empirical formula from previous research. The ice information was used in the calculation process, as summarized in Table 2. Here, the trial groups were divided into five groups based on ice conditions.

Table 2:

Information on ice conditions derived from bridge and side-view images.

Figure 6 shows the predicted and calculated results obtained using two approaches. The predictions are slightly higher than the calculations, except for speed sections below 11.7 knots. The main reason for these underestimates and overestimates is believed to be the variability of the ice environment during ice trials. To compensate for this, if data are collected under conditions with minimal changes in ice conditions, more accurate performance estimates are expected.

Figure 6:

Comparison of ship attainable speeds based on results calculated through empirical formulas and results predicted through the method proposed in this study

According to the two approaches, the attainable ship speed is 13.7 and 14.2 knots, respectively. The attainable ship speed derived from the prediction method proposed in this study is slightly lower than that derived from the empirical formula. However, the results show that the proposed method can reasonably estimate ships' operational performance in ice.

A key factor for ice-going ships is the speed–power relationship, which indicates how ice resistance affects performance. When a ship moves through an ice field, its speed decreases while power output increases rapidly, entirely due to ship–ice interaction. During the ice trials, power output was plotted against the corresponding speed to produce a speed-power curve, and the delivered power ranged from 4938.4 kW to 7963.1 kW (see Figure 7). In addition, the propulsion power required to overcome ice resistance was higher than in open water. The average power needed in pack ice was roughly 5.7 times greater at a ship speed of 10 knots. This significant difference offers essential insights into power demands during overload operations and can help assess the required propulsion power capacity. In addition, the delivered power characteristics in ice-covered waters can be used to determine minimum propulsion power requirements, thereby optimizing engine performance.

Figure 7:

Comparison of delivered power in ice and open water conditions

Author Contributions

Conceptualization, Methodology, and Writing-Original Draft Preparation & Editing, S. Y. Jeong; Data Curation & Visualization, E. J. Oh.