• Trim

Trim tended to increase in volume as the speed increased at *FN* of 0.247 or below and decreased at *FN* above 0.247. Trim was significant with superstructures when *FN* was 0.2 or below and without superstructures when *FN* was 0.2 or above.

• Sinkage

Sinkage tended to increase as the speed increased. In the absence of superstructures, sinkage was significant with a difference of approximately 3% to 9% in the cases with superstructures. However, even as the speed increased, the quantitative difference remained consistent at approximately 0.0004.

• Total resistance coefficient

Under the five speed conditions, *CTM* differed by a maximum of approximately 2% between ships, with and without superstructures. Here, when *FN* was 0.2 or less, the resistance was higher in the case without superstructure and when *FN* was 0.2 or above it showed the opposite results.

*CTS* differed by approximately 1% to 5%, under the six speed conditions. The difference increased to approximately 5%, when *FN* was at a relatively low speed of 0.192 or below. Overall, using an empirical formula overestimated the resistance performance of a full-scale ship in comparison to direct numerical analysis, when considering superstructures.

• Air resistance

To identify the effects of *CDA*, *CAA* was calculated using the method proposed by Kristensen and Lützen [17] and the Fujiwara formula [18]. The total resistance of the full-scale ship was estimated by incorporating the above result.

Both methods showed similar results as those of the numerical simulations that considered superstructures, when compared with the results obtained with *CDA* of 0.8, which was the ITTC-proposed default value. However, a difference of approximately 4% was observed at the low speed of *FN* = 0.192 or below. It is believed that the resistance performance of a full-scale ship could be more accurately estimated by calculating and using the *CDA* obtained through wind tunnel testing, empirical formulas, and numerical analysis, rather than using the default value suggested by ITTC.

In addition, significant differences observed at low speeds were considered to be caused by the use of identical *CAA* at all speeds. This is because *CDA* was calculated in the high-speed range where the effects of the Reynolds number was absent through the Reynolds effect test, in the wind tunnel test or numerical simulation. Therefore, it might have led to errors in estimating the resistance performance of the ship at low speeds.

As mentioned above, it showed the difference in resistance performance between empirical methods and CFD with superstructure. This is because it was calculated only for the wind resistance, using the area of the superstructure and the wind load coefficient in the empirical methods. Thus, it did not consider the increase in resistance due to a change in the attitude of the ship in the empirical methods. Therefore, it was thought that a numerical simulation including superstructure for increasing accuracy about estimation of resistance performance should be performed. Especially, it was expected to be more useful for ships such as automobile ferries and LNG carriers, with a constant superstructure under ballast conditions. However, it was deemed necessary to conduct further studies on the methods of calculating air resistance, in relation to the presence or absence of superstructures and on various types of ships with large superstructures, in order to accurately estimate the resistance performance of a full-scale ship.

**Author Contributions:** J.S.; writing—original draft preparation; J.-C.P.; writing—review and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Technology Innovation Program (20000721, Development of Autopilot applicated collision avoidance technology for medium and large vessel) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).

**Conflicts of Interest:** The authors declare no conflict of interest
