Friction Correction for Model Ship Resistance and Propulsion Tests in Ice at NRC's OCRE-RC

International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420

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International Journal of Naval Architecture and Ocean Engineering

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Friction correction for model ship resistance and propulsion tests in ice at NRC's OCRE-RC

Michael Lau

National Research Council, Kerwin Pl., P.O. Box 12093, Station A, St.John's, Newfoundland, A1B 3T5, Canada article info abstract

Article history: This paper documents the result of a preliminary analysis on the influence of hull-ice friction coefficient Available online 20 March 2018 on model resistance and power predictions and their correlation to full-scale measurements. The study is based on previous model-scale/full-scale correlations performed on the National Research Council - Keywords: Ocean, Coastal, and River Engineering Research Center's (NRC/OCRE-RC) model test data. There are two Model test objectives for the current study: (1) to validate NRC/OCRE-RC's modeling standards in regarding to its Ice resistance practice of specifying a CFC (Correlation Friction Coefficient) of 0.05 for all its ship models; and (2) to Power develop a correction methodology for its resistance and propulsion predictions when the model is Friction correction fi Correlation friction coefficient prepared with an ice friction coef cient slightly deviated from the CFC of 0.05. The mean CFC of 0.056 and 0.050 for perfect correlation as computed from the resistance and power analysis, respectively, have justified NRC/OCRE-RC's selection of 0.05 for the CFC of all its models. Furthermore, a procedure for minor friction corrections is developed. Crown Copyright © 2018 Production and hosting by Elsevier B.V. on behalf of Society of Naval Architects of Korea. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

1. Introduction Moores, 2002; Jones and Lau, 2006). The CFC obtained from each of these correlation studies (Spencer, 1992; Spencer and Jones, Measurements of ice-hull friction coefficient at full-scale 2001; Jones and Lau, 2006; Wang and Jones, 2008) suggest a (Makinen€ et al., 1994; Schwarz, 1986) result in a very wide range good correlation between model test data and full-scale measure- of values from 0.01 to 0.6; therefore, at early days most ice tanks ments by painting the models with a hull-ice friction coefficient of tested a model at two or more hull-ice friction coefficients, and the 0.05e0.07. Lau (2015) performed additional assessment by cor- friction coefficient that gives the best correlation with full-scale recting model ice resistance to a hull ice friction to 0.05 prior to data was found. This is called the “Correlation Friction Coeffi- comparison with full-scale measurements. From these studies, cient” (CFC). This standard friction is then used for other models. good correlation is evident for a smooth-hulled ship breaking This concept is analogous to the correlation allowance used in snow-free ice in most cases with a coefficient of 0.05 (Lau, 2015). clear-water testing. If the CFC falls in a narrow band of values for all Credit is due to Spencer and Jones for their pioneer works on ships of similar hull surface condition, it is assumed that full-scale developing ice model testing standards and procedures as well as performance for another similar hull can be predicted from model the model-scale/full-scale correlation methodology and procedure tests based on the same CFC. (Lau, 2015). adopted in OCRE-RC. For details of the NRC/OCRE-RC's standard The validity of CFC concept has been studied using good-quality method for analyzing resistance and propulsion tests in ice, and its full-scale information (Edwards et al., 1979; Williams et al., 1991, model-scale/full-scale correlation methodology and procedure us- 1992; Noble and Comfort, 1979; Cowper, 1991; Sodhi et al., 2001) ing the concept of CFC, the reader is referred to Jones and Moores and model test data for five icebreaker models in the NRC/OCRE- (2002), Jones and Lau (2006), and Spencer and Jones (2001), RC's model test database (Newbury and Williams, 1986; Spencer, respectively. 1987; Spencer et al., 1988, 1992; NORDCO Ltd, 1989; Jones and NRC has adopted a CFC of 0.05 as the standard frictional preparation for their ship model surfaces. Sometimes, a poor control of the frictional preparation may result in a friction coefficient deviating from the target, and hence, affecting the test result. A reliable E-mail address: [email protected]. correction methodology is needed for correcting resistance and Peer review under responsibility of Society of Naval Architects of Korea. https://doi.org/10.1016/j.ijnaoe.2018.02.008 2092-6782/Crown Copyright © 2018 Production and hosting by Elsevier B.V. on behalf of Society of Naval Architects of Korea. This is an open access article under the CC BY- NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 414 M. Lau / International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420 propulsion predictions when the model is prepared with an ice friction coefficient slightly deviated from the expected friction target. This paper documents the result of a preliminary analysis on the influence of model hull-ice friction coefficient on model resistance and power predictions and their correlation to full-scale measurements with the objective of developing such correction methodology. Due to the preliminary nature of this investigation, only selected works from NRC/OCRE-RC's publications were reviewed. The study is based on 5 sets of full scale trials and their respective model tests conducted at the National Research Council. The full-scale trial and model test data are summarized, and the analysis procedure presented. The mean CFC of 0.056 and 0.050 for correlation as computed from the resistance and power analysis, respectively, are found to fit the dataset, and a correction procedure is established for minor friction correction.

1.1. Current friction correction procedure

NRC/OCRE-RC has been painting its model ships with its old paint formula to 0.05 CFC with a close tolerance and there was no Fig. 1. The ratio between extrapolated model scale ice resistance and measured full scale ice resistance plotted versus the coefficient of friction in model scale to justify need for friction correction for its full-scale prediction. When the correction of minor friction derivation (taken from ITTC, 2002). vender replaced the old paint with a new formula, the repeatability and control of the frictional preparation were lost, resulting in a friction coefficient deviating from the target as much as 0.02. These required a friction correction procedure to be developed at NRC/ for the CFC. A friction correction equation is used to correct the ship OCRE-RC, while it explores and develops a new surface treatment resistance to that of 0.05. technique. In this study, we adopted ITTC friction correction method as given in the ITTC recommended procedures and 2. Full-scale trial and model test data guideline for the testing and extrapolation methods for resistance test in level ice 7.5-02-04-02.1 (ITTC, 2002). The relevant para- The model tests and associated sea trials used in this study are graphs are excerpted as follow for quick reference: summarized in Table 1 and they are briefly described as follows. For “If the surface treatment of the model does not result in a details, please refer to the cited publications. desired friction between the model and the ice, some further corrections are needed. The best correction is to repaint the 2.1. CCGS R-Class icebreakers model to the desired surface roughness. However, if the difference between the measured friction coefficient and the target Several full-scale speed-power icebreaking trials have been value is small, instead of a new surface treatment, a friction conducted with the R-class icebreakers CCGS Pierre Radisson and correction coefficient may be applied. The friction coefficient CCGS Sir John Franklin. may be taken into account by the following equation: The CCGS icebreaker Pierre Radisson was tested soon after de- livery in 1978 during transit in the Central Arctic with ice thickness ¼ Ri;corr CmRi;p (1) in the range of 0.8e1.3 m and ice flexural strength estimated at 200 kPa. In February 1979, further tests were conducted in thinner but stronger ice in the St. Lawrence River where ice thickness fl The friction correction coefficient can be based on the coefficient ranged from 0.2 to 0.7 m and ice exural strength varied from 400 of the measured model ice friction and a comparison between to 500 kPa (Edwards et al., 1979). The ice-hull friction was not full-scale tests results and model tests with different model/ice- measured, but the ship was new and there was little snow cover friction coefficients. Actual test results (Fig. 1) can be used to during trials. derive the friction correction coefficient. If the correction is Tests were conducted on the CCGS icebreaker Sir John Franklin assumed to be linearly proportional to the coefficient of friction, in Notre Dame Bay, Newfoundland in February 1991, where ice fl then from Fig. 1 the following formula is obtained: thickness was between 0.5 and 0.6 m, and exural strength ranged between 200 and 300 kPa (Williams et al., 1991, 1992). A hull roughness survey was conducted on the Sir John Franklin in l3 Ri:m 1 December 1989 used a BSRA hull roughness analyzer Mk IIa. The ¼ ¼ a þ fIDb (2) Ri;p Cm overall mean hull peak-valley roughness from 90 locations was 316 mm. It varied from a mean of 364 mm over the starboard bottom to 277 mm on the port side. In general, the hull was rough by modern standards. Spencer et al. (1990) gave further details. where f is the dynamic model ice friction coefficient and a and ID Model level ice resistance tests were conducted at NRC/OCRE-RC b are empirical coefficients (From Fig. 1, a ¼ 0.8 and b ¼ 5.8). This on a 1:20 scale model covering a wide range of speed, ice formula is valid for a new ship with a hull surface in good thickness and strength with three hull-ice friction coefficients of condition.” 0.03 & 0.09 (Spencer et al., 1992) and 0.071 (Newbury, 1988). Newbury and Williams (1986) summarized R-Class icebreaker NRC/OCRE-RC's testing standard require a nominal value of 0.05 model test results. M. Lau / International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420 415

2.2. CCGS icebreaker Terry-Fox

The full-scale trial for the CCGS icebreaker Terry-Fox used in this study was conducted in 1990 by Fleet Technology Limited (Cowper, 1991). The ice thickness was 1.55 m and the flexural strength was 150 kPa. The ice-hull friction was measured using a rotating arm tribometer. The ice samples were mount at the end of the arm with Wang and Jones, 2008 Spencer, 1992 their upper surface slid along the hull surface. The average friction coefficient of the “INERTA”-coated surface was 0.07. In this trial, the Terry-Fox was towed by the MV Ikaluk to measure resistance directly. Self-propulsion tests were also conducted to measure power and thrust. A 1:21.8 scale model has been tested with three different hull- ice friction coefficients (0.11, 0.045 and 0.005) and several ice conditions over a period of more than 20 years. The datasets used in this review were from Spencer et al. (1988) with a hull-ice friction coefficient of 0.11, NORDCO Ltd (1989) with a hull-ice friction coefficient of 0.045 and Spencer (1990) with a hull-ice friction coefficient of 0.005. Spencer 1992 Ltd., 1992 2.3. CCGS icebreaker Louis S. St. Laurent 0.11 Spencer et al., 1988; Nordco Ltd, 1989; cient Reference Reference 0.09 Newburg and Williams, 1986 Spencer and Jones, 2001 0.09 Newburg and Williams, 1986 Spencer and Jones, 2001 0.09 Newburg and Williams, 1986 Spencer and Jones, 2001 & fi Full-scale data was obtained from ARCTEC Canada (Noble and & & & Comfort, 1979) in its July 1979 Strathcona Sound trials. Immedi- 0.13 Spencer, 1987; Fleet Technology

& ately prior to these trials, a new INERTA 160 coating was applied over the ship's bow and waterline regions; thus the hull condition

Model Test Correlation during these trials may be similar to a new ship on its maiden voyage. Ice thickness varied from 0.76 to 1.36 m, and mean flexural strength was only 150 kPa averaged over five cantilever beam tests. Snow cover was very light and was not a factor in these trials. Shipboard measurements were shaft speed (RPM) and ship speed. Ship resistance was estimated from RPM only in model overload tests. Resistance of the 1:15 scale model of Louis S. St. Laurent was extensively measured at NRC/OCRE-RC (Spencer, 1987) with a hull- Reference Friction Coef ice friction coefficient of 0.13 and ice thicknesses of 47, 67 and 100 mm corresponding to 0.7, 1.0 and 1.5 m full-scale for the ship. The target ice strength was 30 kPa corresponding to 450 kPa full- 500 Edwards et al., 1979 0.03, 0.071 300 Williams et al., 1991, 1992 0.03, 0.071 scale. It was subsequently refinished and tested with a 0.075 e e hull-ice friction coefficient (Fleet Technology Ltd., 1992) and the Strength (kPa) same target ice thickness and ice strength.

3. Results 1.3 200 Edwards et al., 1979 0.03, 0.071 0.7 400 0.6 200 1.4 150 Noble and Comfort, 1979 0.075 e e e e Preliminary analysis on 5 sets of full scale trials and their 0.5 respective model tests is given in this paper. More detailed analysis on the inﬂuence of hull ice friction on ice resistance and power as a function of relevant parameters, e.g., ice thickness and ice strength, will be explored in next phase of the study. The conﬁdence level of the correction procedure as proposed in this report will also be assessed and further datasets may be added to the analysis. Central Arctic 0.8 Bay, NL Since the model test set-up uses a towed resistance and propulsion arrangement, and full-scale trial was conducted in free propulsion, a brief procedure to compute resistance from full-scale August

& measurement, and the power estimated from the model towed propulsion tests were described before presenting the comparison. Date Location Thickness (m) Flexural July 1978 Feb. 1991 Notre Dame Feb. 1979 St. Lawrence River 0.2

3.1. Resistance

NRC/OCRE-RC standard method for analyzing resistance tests in ice (Jones and Moores, 2002) was followed to compute model resistance in ice and then it was scaled to full-scale according to Froude's law prior to comparison. The resistance correlation was performed for 5 sets of full-scale Ship Sea Trial CCGS Pierre Radisson (R-Class) CCGS Sir John Franklin (R-Class) CCGS Pierre Radisson (R-Class) CCGS Louis S. St. Laurent 1979 Strathcona Sound 0.8 CCGS Terry-Fox 1990 Central Arctic 1.55 150 Cowper, 1991 0.005, 0.045

Table 1 Summary of model-scale/full-scale studies. data, including the trials for the CCGS icebreaker Louis S. St. 416 M. Lau / International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420

Laurent, CCGS icebreaker Terry-Fox, CCGS icebreaker Pierre Radi- of ship operational speeds. At each speed, propeller revolutions sson and CCGS icebreaker Sir John Franklin (See Table 1). were varied to cover a range of power, from the ship self-propulsion The correlation between full-scale and model scale tests in ice is point to full power. shown in the following manner. First, full-scale open water bollard The full-scale resistance in ice for the ship is then determined by and speed-power trials are compared with corresponding model subtracting the open water thrust from total ship thrust measured tests to confirm that the model tests accurately predict the ship in ice and the thrust deduction factor mentioned above. This was performance in open water. In general, a ship moving through an then compared with the ice resistance from the model tests. ice sheet is in an overload condition. Thus, a thrust deduction factor Detailed procedure is given in Spencer and Jones (2001). is determined from open water and overload model tests. While it The result of the ship resistance correlation is given in Figs. 2e4. would be preferable to measure the thrust deduction factor at full- In these figures, the Ratio of Model to Full Scale Resistances scale, these tests are expensive. An alternative is to use thrust (RMFSR) was plotted against the model's friction coefficient. In deduction factors derived from model overload tests at a full range Fig. 2 data from individual dataset were fitted with a linear

Fig. 2. The ratio between full-scale predicted and measured ice resistance versus the model's coefficient of friction: Linear fittofive individual datasets. M. Lau / International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420 417

Fig. 3. The ratio between full-scale predicted and measured ice resistance versus the model's coefﬁcient of friction: Linear ﬁt to all datasets.

Fig. 4. The ratio between full-scale predicted and measured ice resistance versus the model's coefficient of friction: Second order polynomial fit to all datasets. relationship to examine the trend exhibited from individual data- Table 2 set. In Figs. 3 and 4, all data were fitted with a linear relationship Result of resistance analysis: Summary of the equation for the individual dataset. ¼ and a second degree polynomial, respectively, to give overall Dataset m b CFC Ri:mp/Ri;f @fID 0.05 trends. The level line at RMFSR equal to1 indicates perfect CCGS Louis S. St. Laurent 13.78 0.3062 0.050 0.995 correlation. CCGS Pierre Radisson, 1978 13.85 0.3621 0.046 1.055 From Fig. 2, assuming a linear relationship between the RMFSR CCGS Pierre Radisson, 1979 11.22 0.3325 0.059 0.894 ratio and ice friction, the following formula is obtained: CCGS Sir John Franklin 10.68 0.3092 0.065 0.843 CCGS Terry-Fox 2.79 0.8389 0.058 0.978

Ri:mp ¼ b þ fIDm (3) Ri;f where R : and R ; are the model prediction and full-scale mea- i mp i f 1 b surement for ice resistance, fID is the ice-hull friction of the model, CFC ¼ (4) m is the slope and b is the y-intercept for the linear ﬁt. The equation m for the individual dataset is summarized in Table 2. If the CFC is known, the model prediction at CFC can be corrected The targeted ice friction, i.e., CFC for perfect correlation, for the from model prediction with the same model of any arbitrary fric- individual dataset can be computed as follow: tion preparation, i.e., 418 M. Lau / International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420

present time, the power correlation was performed on 3 sets of full- R ¼ i;mp scale measurements including two trials for the CCGS icebreaker Ri;f (5) ðfID CFCÞm þ 1 Pierre Radisson and one for the CCGS icebreaker Sir John Franklin (see Table 1). Fig. 2 shows a good correlation between the full-scale prediction NRC/OCRE-RC's standard method for analyzing propulsion tests and the sea trial measurement for a CFC within a narrow range of in ice includes propulsion overload tests in open water combined 0.046e0.065. On average, the CFC is at 0.056 with a standard with limited ice tests. The principle of the method is that overload derivation of 0.074. experiments in open water are used to predict the hydrodynamic If we assume the CFC equals to 0.05, the corresponding R : /R ; i mp i f torque required to develop a thrust sufficient to move the hull ranges from 0.84 to 1.06 for individual dataset with an average of against a force equal to the hull resistance in ice. Because such open 0.953. Hence, there were a maximum of 6% over-prediction and 16% water tests cannot take account of any iceepropeller interaction, it under-prediction among the datasets at the adopted CFC of 0.05, is necessary to conduct a corresponding experiment in ice to which is acceptable within modeling uncertainty. The result is determine the increase in torque due to propellereice interaction. summarized in Table 2. It is assumed that propellereice interaction has a negligible effect As shown in Figs. 3 and 4, linear and second order polynomial on the thrust developed by the propulsion system. This has been fits give the following equations, respectively: shown to be true for small values of h/D where h is the ice thickness R and D is the diameter of the propeller (Molyneux, 1989). The i:mp ¼ : þ : 0 3382 12 329fID (6) background and theory of the method is given in Jones and Lau Ri;f (2006). The result of the ship power correlation is given in Figs. 5 and 6. R i:mp ¼ : þ : þ : 2 In these figures, the ratio of Model to Full Scale Power (RMFSP), 0 5022 6 3466fID 44 623fID (7) R ; fi i f Pi:mp/Pi;f , was plotted against the model's friction coef cient. Again, data from individual dataset were fitted with a linear relationship The CFCs at perfect correlation are 0.054 and 0.056 for the linear in Fig. 5 to examine the trend exhibited from individual dataset. In and second order polynomial fits, respectively. Since the second Fig. 6, all data were fitted with a linear relationship to give overall order polynomial fits better the data, we recommend adopting Eq. trends. (7) for the friction correction to the CFC of 0.056. Assuming all ships Fig. 5 shows a good correlation between the full scale model following the same trend, the ratio R : /R ; corresponding to a i mp i f prediction and the sea trial measurement for a CFC within a narrow particular model friction can be obtained directly from the equa- range of 0.045e0.062. On average, the CFC is at 0.056 with a stan- tion, with which the model prediction R : obtained from a i mp dard derivation (STDEV) of 0.0098. The result is summarized in particular model friction finish f can be corrected to the expected ID Table 4. full-scale measurement R ; . For convenience, the ratio R : /R ; for i f i mp i f As shown in Fig. 6, linear fit for all data give the following a range of f is tabulated in Table 3. ID equation with the CFC equal to 0.050496: The mean of 0.054 or 0.056 for perfect correlation has justified NRC/OCRE's current practice in regarding to its adoption of a value Pi:mp of 0.05 for its CFC. It should be noted that all datasets used in this ¼ 0:1186 þ 17:455fID (8) P ; preliminary analysis are from mid-to-large size icebreakers, and in i f the absence of full-scale trial data, vessels from other classes and Again, the mean of 0.050496 for perfect correlation has justified sizes are assumed to follow similar trend. Possible inclusion of NRC/OCRE's practice in regarding to specifying a standard value of vessels from other classes would further refine the proposed 0.05 for the CFC. correction procedure, including the selection of the CFC and the Assuming all ships following the same trend, the power ratio associated correction method. Pi:mp/Pi;f corresponding to a particular model friction can be ob- In a previous analysis of the same datasets, Lau (2015) pointed tained directly from Eq. (8), with which the model prediction Pi:mp out that the correlation was better with thicker ice, i.e., the range of obtained from a particular model friction finish fID can be corrected interest, which corresponds to higher resistance. There was sub- to the expected full-scale measurement Pi;f . For convenience, the stantial uncertainty on ice thickness and ice strength within the full ratio Pi:mp/Pi;f is tabulated in Table 5. scale data sets that contributes to data scattering as shown in e Figs. 2 4. 3.3. Summary of friction correction procedure

3.2. Ship power 3.3.1. Friction correction to full-scale ice resistance prediction at CFC, i.e., 0.056, from any arbitrary model friction fID Similar analysis was performed with the power data. At the The full-scale ice resistance predicted from a model test measurement Ri:mp with a particular model friction fID can be corrected to that corresponding to the CFC, i.e., 0.056, by dividing the full- Table 3 scale ice resistance prediction with the ratio R : /R ; @ f as ﬁ i mp i f ID The ratio Ri,mp/Ri,f for a particular model's friction coef cient. given in Table 3. For example, the ice resistance at CFC is 1/0.827 or

fID Ri:mp/Ri;f @fID fID Ri:mp/Ri;f @fID fID Ri:mp/Ri;f @fID 20.9% higher that obtained from a model with a model ice friction 0.000 0.502 0.045 0.878 0.090 1.435 of 0.04. 0.005 0.535 0.050 0.931 0.095 1.508 0.010 0.570 0.055 0.986 0.100 1.583 3.3.2. Friction correction to full-scale ice resistance prediction for 0.015 0.607 0.060 1.044 0.105 1.661 ﬁ 0.020 0.647 0.065 1.103 0.110 1.740 ships with any friction coef cient from CFC, i.e., 0.056 0.025 0.689 0.070 1.165 0.115 1.822 There are limited data in full-scale to extract the dependency of 0.030 0.733 0.075 1.229 0.120 1.906 ice resistance on the hull-ice friction. Until further full-scale data 0.035 0.779 0.080 1.296 0.125 1.993 are available with ships tested in difference friction, we assume the 0.040 0.827 0.085 1.364 0.130 2.081 trends as observed in model tests, i.e., the regression equation given M. Lau / International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420 419

/ ﬁ ﬁ Fig. 5. The ratio between model prediction and measured full-scale ice power Pi:mp Pi;f versus the model's coef cient of friction: linear t to three individual datasets.

/ fi fi Fig. 6. The ratio between model prediction and measured full-scale ice power Pi:mp Pi;f versus the model's coef cient of friction: linear t to all datasets. in Fig. 4, is representative of that at full-scale; hence, the full-scale friction of 0.1 is 58.3% higher than the hull with the CFC. ice resistance corrected from CFC can be corrected to ice resistance corresponding to any arbitrary hull-ice friction by multiplying the 3.3.3. Friction correction of towed propulsion data full-scale ice resistance prediction @ CFC with the ratio Ri:mp/Ri;f @ Based on the limited data used, the ice power correction is of fID as given in Table 3. For example, the ice resistance for an ice hull lesser confidence although the data show similar trend observed 420 M. Lau / International Journal of Naval Architecture and Ocean Engineering 10 (2018) 413e420

Table 4 and Labrador. Result of power analysis: Summary of the equation for the individual dataset. ITTC, 2002. ITTC e Recommended Procedures and Guidelines 7.5-02-04-02.1, Testing and Extrapolation Methods - Ice Testing - Resistance Test in Level Ice. ¼ Dataset m b CFC Pi:mp/Pi;f @fID 0.05 ITTC, 2002, Rev 01. Jones, S.J., Lau, M., 2006. Propulsion and maneuvering model tests of the USCGC CCGS Pierre Radisson, 1978 20.70 0.0750 0.045 1.110 Healy in ice and correlation with full-scale. In: Proceedings of the 7th Inter- CCGS Pierre Radisson, 1979 14.58 0.1081 0.061 0.837 national Conference and Exhibition on Performance of Ships and Structures in CCGS Sir John Franklin 11.52 0.2841 0.062 0.860 Ice, 16e19 July 2006. Banff, Alberta. Paper 104. Jones, S.J., Moores, C., 2002. Resistance tests in ice with the USCGC Healy. In: Pro- ceedings of the IAHR 16th International Symposium on Ice, Dunedin, New Zealand, vol. 1, pp. 410e415. Table 5 Lau, M., 2015. Model-scale/full-scale correlation of NRC/OCRE's model resistance, / fi The ratio Pi:mp Pi;f for a particular model's friction coef cient. propulsion and maneuvering test results. In: Proceedings of the 34th Interna- tional Conference on Ocean, Offshore and Arctic Engineering, Volume 8: Ian fID Pi:mp/Pi;f @fID fID Pi:mp/Pi;f @fID fID Pi:mp/Pi;f @fID Jordaan Honoring Symposium on Ice Engineering. St. John’s, Newfoundland, Canada. 0.000 0.119 0.045 0.904 0.090 1.690 Makinen,€ E., Liukkonen, S., Nortala-Hoikkanen, A., Harjula, A., 1994. Friction and 0.005 0.206 0.050 0.991 0.095 1.777 hull coatings in ice operations. In: Proceedings of the IceTech ’94, SNAME 0.010 0.293 0.055 1.079 0.100 1.864 E1eE22. 0.015 0.380 0.060 1.166 0.105 1.951 Molyneux, W.D., 1989. Self-propulsion experiments for icebreakers in ice and open 0.020 0.468 0.065 1.253 0.110 2.039 water. In: Proceedings of the 22nd American Towing Tank Conference. ATTC, 0.025 0.555 0.070 1.340 0.115 2.126 National Research Council, Ottawa, pp. 326e331. 0.030 0.642 0.075 1.428 0.120 2.213 Newbury, S., 1988. Icebreaking Experiments with 1:20 and 1:40 Scale Models of the 0.035 0.730 0.080 1.515 0.125 2.300 CCG R-class Vessels. NRC/OCRE-RC report TR-AVR-10. Ocean, Coastal and River 0.040 0.817 0.085 1.602 0.130 2.388 Engineering Research Center, National Research Council Canada, St. John’s, Newfoundland and Labrador. Newbury, G.S., Williams, F.M., 1986. “R-class” Icebreaker Model Experiment Results. Ice Technology, Computational Mechanics. Springer-Verlag, Berlin, for the resistance data. Assuming all ships following the same pp. 333e348. Noble, P., Comfort, G., 1979. Ice Trials to Evaluate Low Friction Coating on C.C.G.S. trend, the ratio Pi:mp/Pi;f corresponding to a particular model fric- Louis S. St. Laurent. ARCTEC Canada report FR357C-4. tion, i.e., CFC or an arbitrary ship hull friction can be obtained NORDCO Ltd, 1989. Report on Resistance Tests of Model 417 (Terry-Fox/Kalvik) in directly from Eq. (8). Please note the CFC from the power correlation the Ice Tank. NRC/OCRE-RC report CR-1989-25. Ocean, Coastal and River Engi- ’ was 0.05. For convenience, the ratio P /P is tabulated in Table 5. neering Research Center, National Research Council Canada, St. John s, i:mp i;f Newfoundland and Labrador. For example, the delivered power measured at CFC is expected to be Schwarz, J., 1986. Advances in icebreaker technology in West Germany. In: Pro- 1/0.817 or 22.4% higher than that from a model with an ice friction ceedings of the International Polar Transportation Conference, vol. 1. D.F. e of 0.04, and on the other hand the delivered power is 86.4% higher Dickins Assoc., Vancouver, pp. 201 219. Sodhi, D.S., Griggs, D.B., Tucker, W.B., 2001. Healy ice trials: performance tests in ice. for a hull furnished with a friction of 0.1 rather than the CFC. In: Proceedings of the 16th International Conference on Port and Ocean Engi- neering under Arctic Conditions, vol. 2, pp. 893e907. 4. Conclusions Spencer, D., 1992. Model-scale/Full-scale Ice Resistance Correlation for the CCGS Louis St. Laurent - Part II. NRC/OCRE-RC report LM-1992-05. Ocean, Coastal and River Engineering Research Center, National Research Council Canada, St. A re-analysis of NRC/OCRE-RC's model-scale/full-scale correla- John’s, Newfoundland and Labrador. tion studies on the CCGS icebreaker Terry-Fox, CCGS R-Class ice- Spencer, D., 1990. Ice Resistance Tests of Model 417 M.V.’s Terry Fox/Kalvik Hull-ice Friction ¼ 0.005. NRC/OCRE-RC report TR-1990-09. Ocean, Coastal and River breakers Pierre Radisson and Sir John Franklin and CCGS icebreaker Engineering, National Research Council Canada, St. John’s, Newfoundland and Louis S. St. Laurent has confirmed a good agreement between NRC/ Labrador. OCRE-RC model test predictions and full-scale measurements in Spencer, D.S., 1987. Ice Model Tests on CCG Louis St. Laurent e Phase I: Models M395A, M395B, and M395C. NRC/OCRE-RC report TR-AVR-01. Ocean, Coastal resistance and power using its standard CFC friction coating of 0.05. and River Engineering Research Center, National Research Council Canada, St. Eqs. (7) and (8) for resistance and power adjustment, respec- John’s, Newfoundland and Labrador. tively, are recommended for minor friction corrections, i.e., f Spencer, D., Jones, S.J., 2001. Model-scale/Full-scale correlation in open water and ID ‘ ’ e within the range of 0.04e0.06. ice for Canadian Coast Guard R-class icebreakers. J. Ship Res. 45 (4), 249 261. Spencer, D., Molyneux, D., Keinonen, A., 1988. Model Tests of M.V.’s “Terry-Fox”/ It should be noted that all datasets used in this preliminary ”Kalvik“ and their Correlation to Full Scale. NRC/OCRE-RC report TR-AVR-12. analysis are from mid-to-large size icebreakers. In the absence of Ocean, Coastal and River Engineering Research Center, National Research ’ full-scale trial data, vessels from other classes and sizes are Council Canada, St. John s, Newfoundland and Labrador. Spencer, D.S., Williams, F.M., Hackett, P.J., 1990. Full-scale Speed/power Trials with assumed to follow similar trend. Possible inclusion of vessels in CCGS Sir John Franklin. NRC/OCRE-RC report TR-1990-10. Ocean, Coastal and next phase of analysis from other classes would further refine the River Engineering Research Center, National Research Council Canada, St. ’ proposed correction procedure, including the selection of the CFC John s, Newfoundland and Labrador. Spencer, D., Williams, F.M., Newbury, S., 1992. Model-scale/full-scale Ice Resistance and the associated correction method. Correlation for the CCG R-class Icebreakers. NRC/OCRE-RC report LM-1992-20. Validation of results should be accepted with caution due to the Ocean, Coastal and River Engineering Research Center, National Research limited datasets. We plan to continue the validation with additional Council Canada, St. John’s, Newfoundland and Labrador. Wang, J., Jones, S.J., 2008. Resistance and propulsion of CCGS Terry Fox in ice from model/full scales data in the future. model tests to full scale correlation. In: Proceedings of the 8th International Conference and Exhibition on Performance of Ships and Structures in Ice, References 20e23, Banff, AB. Williams, F.M., Spencer, D., Mathews, S.T., Bayly, I., 1992. Full-scale trials in level ice with Canadian R-class icebreaker. Trans. SNAME 100, 293e313. Cowper, B., 1991. Resistance and Propulsive Performance Trials of the MV Terry-Fox Williams, F.M., Spencer, D., Parsons, B.L., Hackett, P.J., Gagnon, R.E., Everard, J., and MV Ikaluk in Level Ice. Transport Canada. Report Number TP10845E. Butt, S., 1991. Full-scale Icebreaker Trials CCGS Sir John Franklin Indian Arm/ Edwards Jr., R.Y., et al., 1979. Result of Trials in Ice and Open Water of CCGS Pierre Little Burnt Bay 1991. NRC/OCRE-RC report TR-1991-03. Ocean, Coastal and Radisson. Report 245C-8, 2 vols. ARCTEC Canada Ltd. River Engineering Research Center, National Research Council Canada, St. Fleet Technology Ltd, 1992. Low Friction Coefficient CCG Louis St. Laurent e Test John’s, Newfoundland and Labrador. Report. NRC/OCRE-RC report CR-1992-01. Ocean, Coastal and River Engineering Research Center, National Research Council Canada, St. John’s, Newfoundland