*4.3. Prediction of Maneuverability in Shallow Water*

## 4.3.1. Derivation of Maneuvering Hydrodynamic Coefficients

As a result of verification of the validation of the corrected empirical formula performed in deep water for the target fishing vessel, it was not possible to accurately predict the unique characteristics (interaction force-related) of the target fishing vessel. However, it was confirmed that improved results could be derived compared to using the Kijima et al. empirical formula developed for the merchant ship type. Therefore, in this section, the hydrodynamic coefficients in shallow water were derived by applying the correcting factor proposed by Kijima et al. to the target fishing vessel derived from the corrected empirical formula. Table 8 and Figure 9 show the change in the typical linear coefficient values based on the ship-draft to water-depth ratio among the hydrodynamic forces affecting the hull. As the ship-draft to water-depth ratio decreases, that is, as the water depth decreases, the Y 0 <sup>β</sup>(h) and N<sup>0</sup> <sup>β</sup>(h) values tend to increase, and the N<sup>0</sup> r (h)value tends to decrease. In addition, the Y 0 <sup>r</sup> − (m<sup>0</sup> + m<sup>0</sup> x )(h) value shows the tendency to decrease until a ship-draft to water-depth ratio of H/d 1.5, and shows the tendency to rapidly increase thereafter. And it can be confirmed that all linear coefficient values have significant changes in the H/d 1.5 zone in common.


**Table 8.** Linear hydrodynamic coefficients by ship-draft to water-depth ratio.

**Figure 9.** Change of linear hydrodynamic coefficients by ship-draft to water-depth ratio.

#### 4.3.2. Discriminant of Course Stability by Ship-Draft to Water-Depth Ratio

The values of linear hydrodynamic coefficients of the target fishing vessel changed depending on the ship-draft to water-depth ratio. It was confirmed that a large change occurred in the zone of around H/d 1.5. As a result of judging the course stability by the ship-draft to water-depth ratio, from H/d 6.0 to 1.5, the course stability showed the tendency to become unstable at minute intervals, and then stabilized steeply immediately after H/d 1.5, and the value of 'C' was positive (+) at 1.2 (Figure 10). It can be concluded that when H/d becomes less than 1.5, the effect of external forces on maneuvering performance increases rapidly, such as frictional resistance affecting the hull increases and rudder effect decreases.

**Figure 10.** Course stability index by ship-draft to water-depth ratio.

#### 4.3.3. Conditions for Maneuverability Evaluation

The conditions for maneuverability in shallow water were set identically with the conditions for evaluating IMO maneuverability in deep water suggested in Section 4.2.2, except for item 1 (deep, unrestricted water). Table 9 below shows the simulated conditions for predicting target fishing vessel maneuverability in shallow water.


Water depth H/d : 6.0, 1.5, 1.2

**Table 9.** Conditions for evaluating maneuverability in shallow water.

Ship draft (m) fwd: 5.3

Test speed (kts) port: 14.04

4.3.4. Simulation for Turning Motion

Table 10 and Figure 11 indicate the simulation results of the turning motion in shallow water ±40 ◦ of the target fishing vessel. According to the ship-draft to water-depth ratio, the Advance was increased by an average of 60 m (0.7 L, 26%), and the Tactical Diameter was increased by an average of 203 m (2.4 L, 80%). This means that when entering shallow water, the turning radius does not increase identically overall, but increases more laterally. The reason for this is that as the ship starts to turn resistance rapidly increases and speed decreases, while the turning resistance moment increases rapidly as the angular velocity decreases [38].

aft: 5.3

st'bd: 14.04

fwd: 5.3 aft: 5.3

port: 14.04 st'bd: 14.04


**Table 10.** Conditions for evaluating maneuverability in shallow water.

**Figure 11.** Comparison of turning motion simulation results by ship-draft to water-depth ratio.

#### 4.3.5. Simulation for 10/10 zig-zag

As a result of the 10/10 zig-zag simulation based on the ship-draft to water-depth ratio for the target fishing vessel, the overshoot angle of H/d 1.5 was larger than that of 6.0, but it was confirmed that the overshoot angle was smaller than 6.0 at 1.2 (Table 11, Figure 12). It was confirmed that a large change in the hydrodynamic coefficient values occurs around H/d 1.5, as shown in the course stability discriminant index (Figure 10) in Section 4.3.2. That is to say that, as in the turning motion test, the rudder pressure moment decreased around H/d 1.5, while the angular velocity decreased as the turning resistance moment increased. The turning curve is relatively slight, and the time of occurrence of the overshoot angle appears late.

**Table 11.** Comparison of 10/10 zig-zag simulation results by ship-draft to water-depth ratio.


**Figure 12.** Comparison of 10/10 zig-zag simulation results by ship-draft to water-depth ratio.

#### **5. Conclusions**

Although fishing vessels generally meet the IMO maneuverability standard, according to statistics gathered over the last 5 years, it has been confirmed that marine accidents related to maneuverability, such as collision and grounding, occur 3 to 5 times more often to fishing vessels than to merchant ships. The human factor is the main cause of these accidents, but the problem of the maneuverability of the vessel cannot be overlooked. In particular, fishing vessels are often navigated at high speed in shallow water ports because they frequently enter and depart familiar ports, which causes accidents related to maneuvering.

Based on these accident statistics, the authors derived a corrected empirical formula assumed to be more accurate in predicting the maneuverability of a fishing vessel. A study has been conducted to predict the maneuverability in shallow water for the target fishing vessel. As a result, we found that the target fishing vessel shows a significant change in maneuverability near H/d 1.5, and it has been determined that this is mainly due to the decrease in the rudder pressure moment and the increase in the turning resistance moment, among various reasons.

Since this study is about a single newly built trawler, there may be limitations in applying these results to all types of fishing vessels, and reliability issues may be raised.

However, during the research process, the validity of the corrected empirical formula was confirmed once again, and it showed great significance in estimating maneuverability in shallow water using the hydrodynamic force coefficients derived from the corrected empirical formula. It was also able to determine possible improvements in predicting the maneuverability of fishing vessel types.

It is expected that the accumulation of the ship shape-related data of the fishing vessel types obtained from this study will be of great help in performing simulations for the analysis of fishing vessel marine accidents, as well as providing the unique parameters of the type of fishing vessels in the development of autonomous vessels.

**Author Contributions:** Conceptualization, S.-H.K.; methodology, S.-H.K.; software, C.-K.L.; analysis, S.-H.K.; writing—original draft preparation, Y.-B.C.; writing—reviewing and editing, C.-K.L.; supervision, S.-H.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

**Acknowledgments:** This research was supported by the 'Development of Autonomous Ship Technology (20200615)' funded by the Ministry of Oceans and Fisheries (MOF, Korea).

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

#### **Nomenclature**


## **References**

