Design Analysis Using Evaluation of Surf-Riding and Broaching by the IMO Second Generation Intact Stability Criteria for a Small Fishing Boat

Abstract

An evaluation was conducted to assess the surf-riding/broaching vulnerability of a 9.77-ton fishing boat by applying the regulations for stability assessment proposed by IMO (International Maritime Organization). Both Level 1 and 2 assessments were conducted and included a range of parameters along with the IMO second-generation intact stability criteria. In particular, it is considered three cases of wave forces acting on the hull for the surf-riding/broaching vulnerability Level 2 assessment calculations: (a) Froude-Krylov force (f_FK) + 0.1M, (b) Froude-Krylov force (f_FK) + added mass of the ship (M_a), and (c) Froude-Krylov force (f_FK) + diffraction force (f_D) + added mass of the ship (M_a). Previous results provided by IMO correspond to (b), and accurate calculation of wave forces helps to obtain more design margins. The design margins are high in the order (a) < (b) < (c), as described in the classification criteria. However, in certain cases, the assessment results may not differ significantly, so the hydrodynamic approximation assumption may be useful.

1. Introduction

The behavior of ships in waves is a crucial issue related to maritime safety, and the International Maritime Organization (IMO) has been working to establish stability criteria for safe ship operations and apply these criteria to all ships to ensure safer navigation at sea. As part of these efforts, the IMO has been preparing the Second Generation Intact Stability Criteria (SGISC) for all ships over the past decade, with the goal of implementing these new criteria after 2020. The final development work for these new stability criteria is currently underway [1,2,3]. In fact, thousands of fishing boat accidents occur every year, causing casualties equivalent to dozens of deaths and disappearances and hundreds of injuries every year, according to maritime accident statistics provided by the Ministry of Oceans and Fisheries of the Republic of Korea [4]. Most casualties from maritime accidents occur on small vessels, including fishing boats. This is because maritime accidents involving small vessels often result in capsizing, flooding, or sinking immediately after they occur, making rapid response and evacuation difficult. Marine accidents most commonly involve engine damage and engulfment of floating objects, but these accidents rarely result in loss of life. However, capsizing, collisions, sinking, and flooding in Figure 1 have a relatively low frequency of accidents, but when they occur, the probability of causing casualties is very high. Capsizing accidents of small fishing boats occur for various reasons, including bad weather, breakdowns in old vessels, overloading and unbalanced loading, and errors in judgment during operation. Therefore, if the capsizing of a vessel can be predicted and avoided, the number of casualties due to accidents can be significantly reduced. Recent studies have revealed that the main reason for capsizing small fishing vessels is loss of stability due to surf-riding/broaching [5,6,7,8,9,10].

The International Marine Organization (IMO) discovered that ships that met static stability standards did not reflect the loss of stability caused by waves during navigation, and developed second-generation intact stability standards to supplement this. The second-generation intact stability criteria, unlike the first-generation ones, take into account the effects of waves and are classified into a total of five causes of loss of stability (Pure loss of stability, Parametric roll, Surf-riding/Broaching, Dead ship condition, Excessive acceleration). The current second-generation intact stability criteria consist of a three-step verification method and another operation guide [11,12,13,14]. Of the five modes, the mode that has the greatest impact on the loss of stability of small vessels is the surf-riding/broaching mode. At this time, the water trajectory at the wave crest is in the direction of wave progression, and the water trajectory at the wave bottom is in the opposite direction. The different water trajectories at the stern and bow generate a yaw moment for the ship, which may cause the ship to deviate from its course and capsize due to loss of controllability and reduced restoring force. Broaching, which occurs after surf-riding, refers to a condition in which the hull loses controllability and stability when it encounters a following sea or a stern-quartering sea during sailing. Although the IMO has established second-generation intact stability criteria to prevent loss of stability in waves, it is unclear whether the standards will be applied to domestic small fishing boats as they are not subject to IMO regulations. In addition, since domestic small fishing boats are mainly manufactured by small- and medium-sized shipbuilders with weak research and development support, second-generation intact stability criteria are often not taken into consideration in the ship design. If we can check the changes in the stability of fishing vessels in operation and prepare for loss of stability, it will help reduce the number of capsizing accidents of fishing vessels, thereby reducing damage to fishermen’s lives and property, and creating a stable fishing environment. Therefore, in this paper, the second-generation intact stability calculations of surf riding/broaching mode were performed by applying the design data of a 9.77-ton small fishing boat manufactured in a domestic shipyard based on the latest update draft defined by the IMO SDC subcommittee [15,16,17]. In addition, calculations for various cases were performed and the design margin was presented through hydrodynamic analysis. The analysis was conducted by adding hydrodynamic assumptions to the Level 2 assessment calculation process suggested by IMO. Level 2 evaluation calculations were performed by dividing the case into three cases to approximate the added mass (M_a) of 10% of the ship mass described above and to consider the diffraction effect in the excitation force due to incident waves.

2. Assessment Process of Surf-Riding/Broaching for the Level 1

This study presents a hydrodynamic modeling and calculation procedure for detailed Level 1 and Level 2 assessments based on the latest draft defined by IMO SDC. If the Level 1 criterion is not satisfied, the assessment proceeds to the Level 2 criterion. A schematic diagram of the entire calculation process is shown in Figure 2, and, in particular, the evaluation process at Level 2 is specifically divided into four parts. The Level 1 vulnerability assessment criteria are simply determined by the Froude number (Fn) based on the ship’s length and speed [15]. If the conditions presented in Equation (1) are met, the ship is considered not vulnerable to surf-riding/broaching. However, if the evaluation criteria of Level 1 are not satisfied, Level 2 evaluation is required, which involves a complex calculation process. Therefore, the calculation process for performing Level 2 evaluation is explained in the next chapter.

$$L>200 \left(\mathrm{m}\right)\mathrm{or} Fn=u/\sqrt{gL}$$

(1)

where u is the ship’s speed (m/s), L is the length of the ship (m), and g is the gravitational acceleration (m/s²).

3. Assessment Process of Surf-Riding/Broaching for Level 2

This chapter describes the calculation process for the Level 2 vulnerability criteria assessment for surf-riding/broaching mode. The overall flow chart is shown in Figure 1, and detailed descriptions of parts 1–4 are provided in the references [18]. In a Level 2 vulnerability assessment, Equation (2) must be satisfied to determine that the vessel is not vulnerable to surf-riding/broaching.

$$C={\displaystyle \sum _{H_s}{\displaystyle \sum _{T_z}\left(W2\left(H_s,T_z\right){\displaystyle \sum _{i=1}^{N_{\lambda }}{\displaystyle \sum _{j=1}^{N_a}{W}_{ij}C{2}_{ij}}}\right)\le R_{SR}(=0.005)}}$$

(2)

where W2 is used to describe values that take into account factors related to short-term sea conditions and is presented in

Table 1. Wave case occurrences. These data are adapted [15] with permission from [IMO SDC 7/WP.6], [2020].

Number of Occurrences: 100,000/Tz (s) = Average Zero Up-Crossing Wave Period/Hs (m) = Significant Wave Height
Tz →	3.5	4.5	5.5	6.5	7.5	8.5	9.5	10.5	11.5	12.5	13.5	14.5	15.5	16.5	17.5	18.5
Hs ↓
0.5	1.3	133.7	865.6	1186	634.2	186.3	36.9	5.6	0.7	0.1	0	0	0	0	0	0
1.5	0	29.3	986	4976	7738	5569.7	2375.7	703.5	160.7	30.5	5.1	0.8	0.1	0	0	0
2.5	0	2.2	197.5	2158.8	6230	7449.5	4860.4	2066	644.5	160.2	33.7	6.3	1.1	0.2	0	0
3.5	0	0.2	34.9	695.5	3226.5	5675	5099.1	2838	1114.1	337.7	84.3	18.2	3.5	0.6	0.1	0
4.5	0	0	6	196.1	1354.3	3288.5	3857.5	2685.5	1275.2	455.1	130.9	31.9	6.9	1.3	0.2	0
5.5	0	0	1	51	498.4	1602.9	2372.7	2008.3	1126	463.6	150.9	41	9.7	2.1	0.4	0.1
6.5	0	0	0.2	12.6	167	690.3	1257.9	1268.6	825.9	386.8	140.8	42.2	10.9	2.5	0.5	0.1
7.5	0	0	0	3	52.1	270.1	594.4	703.2	524.9	276.7	111.7	36.7	10.2	2.5	0.6	0.1
8.5	0	0	0	0.7	15.4	97.9	255.9	350.6	296.9	174.6	77.6	27.7	8.4	2.2	0.5	0.1
9.5	0	0	0	0.2	4.3	33.2	101.9	159.9	152.2	99.2	48.3	18.7	6.1	1.7	0.4	0.1
10.5	0	0	0	0	1.2	10.7	37.9	67.5	71.7	51.5	27.3	11.4	4	1.2	0.3	0.1
11.5	0	0	0	0	0.3	3.3	13.3	26.6	31.4	24.7	14.2	6.4	2.4	0.7	0.2	0.1
12.5	0	0	0	0	0.1	1	4.4	9.9	12.8	11	6.8	3.3	1.3	0.4	0.1	0
13.5	0	0	0	0	0	0.3	1.4	3.5	5	4.6	3.1	1.6	0.7	0.2	0.1	0
14.5	0	0	0	0	0	0.1	0.4	1.2	1.8	1.8	1.3	0.7	0.3	0.1	0	0
15.5	0	0	0	0	0	0	0.1	0.4	0.6	0.7	0.5	0.3	0.1	0.1	0	0
16.5	0	0	0	0	0	0	0	0.1	0.2	0.2	0.2	0.1	0.1	0	0	0

as data consisting of functions of significant wave height (H_s) and period (T_z).

In addition, W_ij in Equation (3) is a probability density function based on the Pierson-Moskowitz (PM) type wave spectrum, which is a spectrum mainly used in fully developed wave data observed in the North Atlantic.

$$W_{ij}={\displaystyle \frac{4\sqrt{g}}{\pi \nu }}{\displaystyle \frac{L^{5/2}{T}_{01}}{{H_s}^3}}{s_j}^2{r_i}^{3/2}\left({\displaystyle \frac{\sqrt{1+{\nu }^2}}{1+\sqrt{1+{\nu }^2}}}\right)\Delta r\Delta s\exp \left(-2{\left({\displaystyle \frac{L{r}_i{s}_j}{H_s}}\right)}^2\left\{1+{\displaystyle \frac{1}{{\nu }^2}}{\left(1-\sqrt{{\displaystyle \frac{g{T_{01}}^2}{2\pi r_{i}L}}}\right)}^2\right\}\right)$$

(3)

where s_j is the wave steepness, r_i is the wavelength-to-ship length ratio, T₀₁ (=1.086T_z), and υ (=0.425) are constants defined in the latest draft IMO [15]. C2_ij in Equation (2) is given by Equation (4), which is set to 0 or 1 by comparison with the critical Froude number Fn_cr.

$$C{2}_{ij}=\left\{\begin{array}{c}1 \mathrm{if} Fn>F{n}_{cr}\\ 0 \mathrm{if} Fn\le F{n}_{cr}\end{array}\right.$$

(4)

4. Surf-Riding/Broaching Assessment Based on Level 1 Vulnerability Criteria for Target Ship Models

In this paper, the design data of the domestic fishing boat in

Table 2. Design data specifications for small vessels.

Parameter ↓/Ship →	9.77-ton Fishing Boat	Fishing Boat (IMO SDC7/INF.2 [11])
Length L (m)	18.59	34.5
Midship location (m)	0.0	0.0
Displacement (ton)	66.0	425.184
Dp (m)	1.24	2.6
Wp	0.15	0.156
tp	0.1	0.142
Number of propellers	1 (single)	3 (else)

and the small ship provided by IMO SCD7/INF.2 [16] for verification were secured to evaluate the stability of the surf riding/broaching mode.

In

Table 3. Parameters according to the cross-sectional area of the 9.77-ton fishing boat.

x (m)	Area (m2)	dx (m)	x (m)	Area (m2)	dx (m)
−8.665	0.568	0.630	0.000	4.781	1.319
−8.232	0.640	0.640	0.866	4.638	1.259
−7.799	2.961	0.653	1.733	4.496	1.198
−7.365	3.141	1.834	2.600	4.350	1.137
−6.932	3.324	1.804	3.466	4.200	1.076
−6.066	3.592	1.743	4.333	4.052	1.016
−5.199	3.764	1.683	5.199	3.627	0.955
−4.332	3.790	1.622	6.066	2.887	0.892
−3.466	3.775	1.561	6.932	2.064	0.832
−2.600	3.728	1.501	7.365	1.540	0.741
−1.733	3.677	1.440	7.799	1.208	0.734
−0.866	3.627	1.379	8.232	0.903	0.724

, x (m) is the cross-sectional location of the vertical axis based on the center of the hull, Area (m²) is the cross-sectional area of the submerged part at each x position, and d_x (m) is the local draft at each x position of the 9.77-ton fishing boat.

The cross-sectional area according to the longitudinal section location of a 9.77-ton fishing boat is shown in Figure 3. It can be seen that the hull of the fishing boat is relatively small and thin. The length of the ship is L = 18.59 m, and the evaluation performed for the surf-riding/broaching vulnerability criterion Level 1 depending on the given operating speed is shown in Figure 4. When the Froude number is Fn = 0.3 or less, the section that can maintain the stability of the ship by passing the Level 1 criterion (○, Satisfied), and the section that exceeds the Froude number 0.3 (×, Unsatisfied) is the section that does not pass the Level 1 criterion and needs to carry out calculations for the Level 2 criterion. Referring to the results, when the Froude number is 0.3, the ship’s speed is 8 knots, and considering that the ship’s operating speed is 14 knots, Fn = 0.533, which exceeds 0.3, the Level 2 criterion evaluation should be performed. Therefore, the C value was calculated according to the Level 2 vulnerability criteria evaluation procedure in Section 3 of this paper.

5. Surf-Riding/Broaching Assessment Based on Level 2 Vulnerability Criteria for Target Ship Models

Level 2 vulnerability assessment is consistent with IMO regulations and addresses potential failure modes of surf-riding/broaching. For the calculation of part 1 of Figure 1, the values included in the total resistance and propeller thrust-related parameters are important factors in understanding the response of the vessel to hydrodynamic forces and environmental conditions. The experimental data of the resistance and propulsion curves for the vessel were approximated by high-order polynomial functions according to Equations (5) and (6). The approximated coefficients are expressed in

Table 4. Resistance curve coefficients in Equation (5).

r1	r2	r3	r4	r5
−44,601.028	22,900.249	−3996.917	311.880	−9.081

and

Table 5. Resistance curve coefficients in Equation (6).

k0	k1	k2
0.374	−0.410	0.058

, and the fitting was verified in Figure 5 and Figure 6.

$$R(c_i)=r_1{c}_i+{r_2{c}_i}^2+{r_3{c}_i}^3+{r_4{c}_i}^4+{r_5{c}_i}^5$$

(5)

where $c_i=\sqrt{{\displaystyle \frac{g}{k_i}}}$, $k_i={\displaystyle \frac{2\pi }{{\lambda }_i}}$ and λ is the wavelength.

$$K_T(J)\approx k_0+k_{1}J+k_2{J}^2$$

(6)

where $J={\displaystyle \frac{u(1-w_p)}{n{D}_p}}$ is the advanced ratio (w_p: wake fraction).

It can be seen that the fitting curve calculated using the coefficients in Table 4 and Table 5 matches the experimental data very well, ensuring reliability in the calculation. The equation for the critical rotational speed (n_cr) of the propeller in part 1 is solved by the coefficients obtained above. Using the obtained value of n_cr, the solution of the fifth-order equation with the critical speed (u_cr) of part 2 as an unknown is found, and the critical Froude number (Fn_cr) is calculated. When solving the equations for the unknown n_cr, the term for the added mass coefficient of the ship in the surge direction and the term for the hydrodynamic force acting on the hull are included. The added mass coefficient in the surge direction is calculated by an in-house code with reference to the potential theory [19] and is shown in Figure 7. The added mass coefficient according to the wave steepness and the ratio of the wavelength to the ship length varies very little, ranging from 0.1 to 0.12. In fact, there is a phrase in the IMO draft [16] that states that if there is no specific data, the added mass coefficient is assumed to be 0.1. In the experiment conducted by Motora [20], the added mass coefficient was similar to that of 0.1. This affects the evaluation of the Level 2 vulnerability criteria compared to the calculation results.

The amplitude of the hydrodynamic force due to waves acting on the hull in the surge direction is as shown in Equation (7), and this force is called the Froude–Krylov force. The components of the force are expressed by Equations (8) and (9).

$$f_{ij}=\rho g{k}_i{\displaystyle \frac{H_i}{2}}\sqrt{{F_{C_i}}^2+{F_{S_i}}^2}$$

(7)

$$F{c}_i={\displaystyle \sum _{m=1}^N\Delta x_{m}S\left(x_m\right)\sin \left(k{x}_m\right)\exp \left(-0.5k_{i}d\left(x_m\right)\right)}$$

(8)

$$F{s}_i={\displaystyle \sum _{m=1}^N\Delta x_{m}S\left(x_m\right)\cos \left(k{x}_m\right)\exp \left(-0.5k_{i}d\left(x_m\right)\right)}$$

(9)

where x_m is the longitudinal distance from the center of mass of the ship to the m-th station [m], d(x_m) is the draft at the m-th section in the calm water [m], S(x_m) is the submerged area at the m-th station in calm water [m²], and N is the number of stations.

In this IMO regulation, when calculating the excitation force (f_wave) due to waves, only the Froude–Krylov force (f_FK) due to the incident wave is considered [19], but it is generally more accurate to calculate by considering the force due to diffraction (f_D) in Equation (10).

$$f_{wave}=f_{FK}+f_D$$

(10)

Therefore, based on the evaluation procedure of Figure 1, the values obtained from the equation of motion of parts 1 and 2 are applied to the probability distribution values of waves in parts 3 and 4 to analyze the results for the vulnerability criterion value of Level 2. First, to verify the in-house code developed in this study, the calculation results for the C value of Equation (2), which is the criterion for evaluating the Level 2 step obtained by applying the fishing vessel data provided in the IMO regulations [16] in Table 2, are shown in Figure 8. With reference to Figure 8, we can confirm that the results are almost identical to those provided by IMO SDC7/INF.2 [16], thus completing the verification of the developed code. Level 2 criteria assessment satisfies the vulnerability assessment if the C value is less than the R_SR(=0.005) value in Equation (2), but concludes that it is vulnerable to surf-riding/broaching if it is greater than 0.005. Therefore, it can be seen that in order to evaluate the vulnerability modes of the ship around the R_SR values in detail, it is necessary to perform calculations at fine intervals over the interval of Froude number between 0.3 and 0.35. Figure 8 shows the results of an in-depth evaluation of the Level 2 surf-riding/broaching vulnerability mode judgment criteria between Froude numbers 0.3 and 0.35. Level 2 evaluation calculations were performed by dividing the case into three cases to approximate the added mass (M_a) of 10% of the ship mass described above and to consider the diffraction effect in the excitation force due to incident waves.

(a)

Only Froude–Krylov force (f_FK) + 0.1M;

(b)

Only Froude–Krylov force (f_FK) + Added mass of the ship (M_a);

(c)

Only Froude–Krylov force (f_FK) + Diffraction force (f_D) + Added mass of the ship (M_a).

Basically, the draft IMO regulations give preference to the use of Froude–Krylov force and calculated added mass of the ship, and recommend an added mass of 10% of the mass when specific ship data are not available. By dividing the calculation into three cases, it is possible to intuitively analyze the ship’s design margin for surf riding/broaching. In terms of added mass, we can see that the cases of approximating 0.1M and calculating the exact added mass are almost the same. However, when considering the force due to the diffraction effect, we can see that the C value is slightly lower than the given Froude number. This gives the advantage of a greater design margin, as the ship’s operating speed can be increased, i.e., the Froude number that can pass the Level 2 vulnerability criteria. Regarding the difference in results, Ito et al. [21] mentioned that the accuracy of the calculation may vary depending on how accurately the wave-induced excitation force is calculated, since the external force acting on the hull is calculated by considering only the Froude–Krylove force larger than the external force measured in the actual experiment. Therefore, this study showed that the design margin for surf-riding/broaching was secured by presenting an increased Froude number that satisfies the Level 2 criterion through a more accurate calculation by considering diffraction.

Unlike Figure 9, which shows the results of applying the previous ship design data provided by the IMO draft, Figure 10 shows the results of the Level 2 vulnerability assessment using the data of a 9.77-ton fishing vessel in Table 2. The overall trend is shown in Figure 9. The design margin allowance is high in the order of the division criteria described above (a) < (b) < (c). However, what is different from Figure 9 is that the accurate calculation of the added mass has a greater effect on the C value than the diffraction effect. This is because the size of the target vessel, i.e., the length of the vessel is 18.59 m, which is nearly twice smaller than the size of the vessel considered in Figure 9 (34.5 m), so the effect of diffraction is relatively reduced. From the results in Figure 9 and Figure 10, it can be seen that the more accurate the calculation is by considering all the influences of external forces acting on the ship, the greater the allowable range of design margin that can pass the vulnerability criteria evaluation. Of course, the amount of data required and the cost and time required for calculations increase.

6. Summary and Discussions

An evaluation was conducted to assess the surf-riding/broaching vulnerability of a 9.77-ton fishing vessel by applying the regulations for stability assessment proposed by the IMO. Both Level 1 and 2 assessments were conducted and included a range of parameters aligned with the IMO second-generation intact stability criteria. The purpose of this paper is to quantify the ship’s stability and evaluate the surf-riding/broaching failure modes. The IMO surf-riding/broaching Level 1 vulnerability assessment was performed using the ship’s length and Froude number. The Level 1 assessment results indicated that the vessel was vulnerable to surf-riding/broaching mode under both vessel length and Froude number conditions. Key parameters were analyzed and cross-validated as they were considered fundamental factors in assessing the vulnerability of ships to surf-riding/broaching phenomena. The presented results clearly demonstrate the vulnerability of the vessel to this failure mode under a variety of operating conditions. This analysis emphasizes the importance of considering the hydrodynamic response to a variety of environmental conditions. Following the Level 1 criteria assessment, the Level 2 surf-riding/broaching vulnerability assessment of the vessel was conducted. The analysis was conducted by adding hydrodynamic assumptions to the Level 2 assessment calculation process suggested by IMO. Level 2 evaluation calculations were performed by dividing the case into three cases to approximate the added mass (M_a) of 10% of the ship mass described above and to consider the diffraction effect in the excitation force due to incident waves. The analysis results show that the only way to allow a design margin that can reduce surf-riding/broaching vulnerability is to accurately calculate wave excitation forces including added mass, Froude–Krylov forces, and diffraction effects. Including all cases increases the amount of data required for calculations, as well as the cost and time. In some cases, the evaluation results may not differ significantly, so the hydrodynamic approximation assumption may be useful. The in-house Matlab code developed in this study was verified by comparing it with the results of previous ships. As a result, the 9.77-ton fishing boat has a sailing speed of 14 knots, so it satisfies the IMO surf-riding/broaching Level 2 assessment. Therefore, the vessel is considered safe from surf-riding/broaching phenomena.