# Standard Wave Scatter Table Limitation for Evaluating SGISC Based on Hindcast Data Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Developing Hindcast WST

_{z}is the zero-crossing period, T

_{1}is the mean period, T

_{p}is the peak period and γ is the peak shape parameter (γ = 3.3).

#### 2.2. WST Comparison

#### 2.3. Excessive Acceleration Vulnerability Assessment and Operational Limitation

- a.
- Define the respective WST.
- b.
- Estimate the mean wind speed for the WST at the probability of exceedance = 1.2%. For IMO’s recommended standard WST, the wave height and mean wind speed (${V}_{w}$) at 1.2% probability of exceedance are 8.9 m and 26 m/s, respectively.
- c.
- d.
- Apply excessive acceleration vulnerability criteria one with the modified wave steepness table.

_{w}is mean wind speed and T

_{r}is natural roll period.

## 3. Sample Ship

## 4. Results and Discussion

#### 4.1. WST Comparison

#### 4.2. Excessive Acceleration Level One Operational Limitation

^{2}. Let us assume that 8.1 m/s

^{2}is the cut-off for excessive acceleration for the following discussion. The ship assessed using the standard WST will successfully pass the level one assessment and be allowed to operate unrestricted. However, the same ship which is allowed to operate in all sea areas and seasons failed the season 4 for sea area 9 assessment, which contradicts the stability results estimated with the standard WST. This demonstrates the necessity of using local and regional WSTs rather than a universal WST for the SGISC stability assessment to avoid misinterpretation of stability estimations while improving safety.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- IMO. Interim Guidelines on the Second Generation Intact Stability Criteria. (MSC.1-Circ.1627); IMO: London, UK, 2020. [Google Scholar]
- IMO. Draft Explanatory Notes to the Interim Guidlines on the Second Generation Intact Stability Criteria; IMO: London, UK, 2021. [Google Scholar]
- Petacco, N.; Gualeni, P. IMO second generation intact stability criteria: General overview and focus on operational measures. J. Mar. Sci. Eng.
**2020**, 8, 494. [Google Scholar] [CrossRef] - Marlantes, K.E.; Kim, S.P.; Hurt, L.A. Implementation of the IMO Second Generation Intact Stability Guidelines. J. Mar. Sci. Eng.
**2022**, 10, 41. [Google Scholar] [CrossRef] - Hogben, N. Global Wave Statistics; British Maritime Technology: Feltham, UK, 1986. [Google Scholar]
- IACS. Recommendation No.34 Standard Wave Data-(Corr. Nov.2001); IACS: London, UK, 2001. [Google Scholar]
- Smith, G.A.; Hemer, M.; Greenslade, D.; Trenham, C.; Zieger, S.; Durrant, T. Global wave hindcast with Australian and Pacific Island Focus: From past to present [Data Paper]. Geosci. Data J.
**2021**, 8, 24–33. [Google Scholar] [CrossRef] - BMT. Global Wave Statistics. BMT UK. 2011. Available online: https://www.globalwavestatisticsonline.com/Help/index.htm (accessed on 19 August 2022).
- González, M.M.; Casás, V.D.; Rojas, L.P.; Agras, D.P.; Ocampo, F.J. Investigation of the applicability of the IMO second generation intact stability criteria to fishing vessels. In Proceedings of the STAB2015, Glasgow, UK, 14–19 June 2015; p. 349. [Google Scholar]
- IMO. International Code on Intact Stability; IMO: London, UK, 2008. [Google Scholar]
- Bačkalov, I.; Bulian, G.; Rosén, A.; Shigunov, V.; Themelis, N. Improvement of ship stability and safety in intact condition through operational measures: Challenges and opportunities. Ocean. Eng.
**2016**, 120, 353–361. [Google Scholar] [CrossRef] - Shigunov, V.; Themelis, N.; Bačkalov, I.; Begovic, E.; Eliopoulou, E.; Hashimoto, H.; Hinz, T.; McCue, L.; González, M.M.; Rodríguez, C.A. Operational measures for intact ship stability. In Proceedings of the First International Conference on the Stability and Safety of Ships and Ocean Vehicles (STAB&S 2021), Glasgow, UK, 7–11 June 2011. [Google Scholar]
- Liwång, H.; Rosén, A. A framework for investigating the potential for operational measures in relation to intact stability. In Proceedings of the 13th International Conference on Stability of Ships and Ocean Vehicles, Kobe, Japan, 16–21 September 2018; pp. 488–499. [Google Scholar]
- Petacco, N.; Gualeni, P. An overview about operational measures in the framework of Second Generation Intact Stability criteria. In Proceedings of the 1st International Conference on the Stability and Safety of Ships and Ocean Vehicles, Virtual, 7–11 June 2021. [Google Scholar]
- Paroka, D.; Muhammad, A.H.; Rahman, S. Excessive acceleration criterion applied to an Indonesia Ro-Ro ferry. In Proceedings of the 1st International Conference on the Stability and Safety of Ships and Ocean Vehicles (STAB&S2021), Virtual, 7–11 June 2021; Online Conference Organised by University of Strathclyde: Glasgow, UK. [Google Scholar]
- Rinauro, B.; Begovic, E.; Gatin, I.; Jasak, H. Surf-Riding Operational Measures for Fast Semidisplacement Naval Hull Form. In Proceedings of the 12th Symposium on High Speed Marine Vehicles (HSMV 2020), Napoli, Italy, 15–16 October 2020. [Google Scholar]
- Tompuri, M.; Ruponen, P.; Lindroth, D. Second generation intact stability criteria and operational limitations in initial ship design. In Proceedings of the PRADS, Copenhagen, Denmark, 4–8 September 2016. [Google Scholar]
- Fujii, M.; Hashimoto, H.; Taniguchi, Y.; Kobayashi, E. Statistical validation of a voyage simulation model for ocean-going ships using satellite AIS data. J. Mar. Sci. Technol. (Jpn.)
**2019**, 24, 1297–1307. [Google Scholar] [CrossRef] - Petacco, N.; Gualeni, P.; Stio, G. Second Generation Intact Stability criteria: Application of operational limitations & guidance to a megayacht unit. In Proceedings of the 5th International Conference on Maritime Technology and Engineering, Lisbon, Portugal, 16–19 November 2020. [Google Scholar]
- Bulian, G.; Orlandi, A. Operational measures in second generation intact stability criteria: Effect of source of environmental data. In Proceedings of the International Conference on the Stability and Safety of Ships and Ocean Vehicles, Virtual, 7–11 June; University of Strathclyde: Glasgow, UK, 2021. [Google Scholar]
- Bulian, G.; Orlandi, A. Effect of environmental data uncertainty in the framework of second generation intact stability criteria. Ocean. Eng.
**2022**, 253, 111253. [Google Scholar] [CrossRef] - Hashimoto, H.; Taniguchi, Y.; Fujii, M. A case study on operational limitations by means of navigation simulation. In Proceedings of the 16th International Ship Stability Workshop, Belgrade, Serbia, 5–7 June 2017. [Google Scholar]
- Hashimoto, H.; Furusho, K. Influence of sea areas and season in navigation on the ship vulnerability to the parametric rolling failure mode. Ocean. Eng.
**2022**, 266, 112714. [Google Scholar] [CrossRef] - Durrant, T.; Greenslade, D.; Hemer, M.; Trenham, C. A Global Wave Hindcast Focussed on the Central and South Pacific; CAWCR: Melbourne, Australia, 2014; p. 40. [Google Scholar]
- Shin, D.-M.; Moon, B.-Y. Assessment of Excessive Acceleration of the IMO Second Generation Intact Stability Criteria for the Tanker. J. Mar. Sci. Eng.
**2022**, 10, 229. [Google Scholar] [CrossRef] - Bulian, G.; Francescutto, A. An Approach for the Implementation of Operational Limitations in the Level 1 Vulnerability Criterion for the Dead Ship Condition. In Proceedings of the International Conference on the Stability and Safety of Ships and Ocean Vehicles, Virtual, 7–11 June 2021; University of Strathclyde: Glasgow, UK, 2021. [Google Scholar]

Wave Parameter | netCDF Variable Name | Reference Table Name |
---|---|---|

Significant wave height | hs | Mean sea WST (WSTM) |

Mean period of first frequency moment | t01 | |

Significant wave height of wind sea | phs0 | Wind sea WST (WSTW) |

Peak period wind sea | ptp0 | |

Significant wave height of primary swell | phs1 | Swell sea WST (WSTS) |

Peak period of primary swell | ptp1 |

Filename | Seasons/Period |
---|---|

Annual | Whole year (12 months) |

Season 1 | Mar to May (3 months) |

Season 2 | Jun to Aug (3 months) |

Season 3 | Sep to Nov (3 months) |

Season 4 | Dec to Feb (3 months) |

Height of the navigation deck above the keel, h_{k}, m | 48.72 |

Longitudinal distance of the location where passenger or crew may be present from the aft perpendicular, x, m | 177.41 |

Length, bp, m | 262 |

Beam, m | 40 |

Draft amidships, m | 11.5 |

GM, m | 1.4 |

KG, m | 12.75 |

Block coefficient | 0.56 |

Midship section coefficient | 0.959 |

Bilge keel length ratio (l_{BK}/Lbp) | 0.2921 |

Bilge keel height ratio (h_{BK}/B) | 0.010 |

LES | LAE | LSEP | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Data | BGW | AHD Mean | AHD Wind | AHD Swell | BGW | AHD Mean | AHD Wind | AHD Swell | BGW | AHD Mean | AHD Wind | AHD SWELL |

Sea Area | ||||||||||||

Sea area S | 2.9 | 2.7 | 2.5 | 1.6 | 2.8 | 2.6 | 2.5 | 1.6 | 2.8 | 2.7 | 2.5 | 1.6 |

Sea area 8 | 3 | 2.8 | 2.6 | 1.5 | 2.9 | 2.7 | 2.6 | 1.6 | 2.9 | 2.7 | 2.6 | 1.5 |

Sea area 9 | 2.9 | 3 | 2.8 | 1.6 | 2.8 | 2.9 | 2.8 | 1.7 | 2.8 | 2.9 | 2.8 | 1.6 |

Sea area 15 | 2.6 | 2.4 | 2.1 | 1.3 | 2.5 | 2.3 | 2.1 | 1.3 | 2.5 | 2.3 | 2.1 | 1.3 |

Sea area 16 | 2.8 | 2.8 | 2.6 | 1.7 | 2.7 | 2.7 | 2.5 | 1.7 | 2.7 | 2.7 | 2.5 | 1.7 |

**Table 5.**Statistical comparison of Rayleigh shape parameter for mean, wind and swell sea pdf (sea area S—full year).

IMO Recommended Standard WST | BGW | AHD Mean Sea | AHD Wind Sea | AHD Swell Sea | |
---|---|---|---|---|---|

Mean | 2.833 | 2.773 | 2.68 | 2.50667 | 1.553 |

Standard deviation | 0.148645 | 0.2077 | 0.237447 | 0.1457 |

LES | LAE | LSEP | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Data | Season 1 | Season 2 | Season 3 | Season 4 | Season 1 | Season 2 | Season 3 | Season 4 | Season 1 | Season 2 | Season 3 | Season 4 |

Sea Area | ||||||||||||

Sea area S | 2.8 | 1.9 | 2.8 | 3.8 | 2.7 | 1.9 | 2.7 | 3.7 | 2.7 | 1.9 | 2.7 | 3.7 |

Sea area 8 | 2.9 | 2 | 3 | 3.8 | 2.8 | 2 | 2.9 | 3.7 | 2.9 | 1.9 | 2.8 | 3.8 |

Sea area 9 | 3 | 2.1 | 3.1 | 4.3 | 2.9 | 2.1 | 3 | 4.2 | 2.9 | 2 | 3 | 4.2 |

Sea area 15 | 2.5 | 1.8 | 2.4 | 3.1 | 2.4 | 1.8 | 2.3 | 3.1 | 2.5 | 1.8 | 2.4 | 3.1 |

Sea area 16 | 2.9 | 2 | 2.8 | 3.9 | 2.8 | 2 | 2.7 | 3.8 | 2.7 | 1.8 | 2.6 | 3.7 |

Season 1 | Season 2 | Season 3 | Season 4 | |
---|---|---|---|---|

Mean | 2.76 | 1.9133 | 2.746 | 3.7267 |

Standard deviation | 0.1764 | 0.091548 | 0.2416 | 0.3788 |

S% | 2.6% | 32.46% | 3% | 31.55% |

Data | BGW | AHD | ||||
---|---|---|---|---|---|---|

WST | Annual | Annual | Season 1 | Season 2 | Season 3 | Season 4 |

Sea area S | 8.9 | 8.7 | 8 | 4.8 | 8 | 10.3 |

Sea area 8 | 8.8 | 8.7 | 8.1 | 4.9 | 8.3 | 11.8 |

Sea area 9 | 8.9 | 9.8 | 8.5 | 5.3 | 8.6 | 11.8 |

Sea area 15 | 8.2 | 7.3 | 7.3 | 4.1 | 6.7 | 8.4 |

Sea area 16 | 8.7 | 8.5 | 7.7 | 4.7 | 7.7 | 9.9 |

**Table 9.**Mean wind speed (m/s) corresponding to significant wave height estimated in Table 8.

Data | BGW | AHD | ||||
---|---|---|---|---|---|---|

WST | Annual | Annual | Season 1 | Season 2 | Season 3 | Season 4 |

Sea area S | 25.9902 | 25.5994 | 24.2071 | 17.2204 | 24.2071 | 28.6489 |

Sea area 8 | 25.795 | 25.5994 | 24.4084 | 17.4588 | 24.8086 | 28.0899 |

Sea area 9 | 25.9902 | 27.7141 | 25.2055 | 18.3964 | 25.4028 | 31.3669 |

Sea area 15 | 24.6089 | 22.7736 | 22.7736 | 15.5026 | 21.508 | 25.0074 |

Sea area 16 | 25.5994 | 25.2055 | 23.5981 | 16.9804 | 23.5981 | 27.9023 |

Natural Roll Period, T_{r}, (s) | Wave Steepness Factor, s |
---|---|

$\le $5.9 | 0.100 |

6.9 | 0.098 |

7.9 | 0.093 |

11.8 | 0.065 |

13.8 | 0.053 |

15.7 | 0.044 |

17.7 | 0.038 |

19.7 | 0.032 |

21.7 | 0.028 |

23.6 | 0.025 |

25.6 | 0.023 |

27.6 | 0.021 |

$\ge $29.5 | 0.020 |

Natural Roll Period, T_{r}, (s) | Wave Steepness Factor, s |
---|---|

$\le $6.6 | 0.100 |

7.7 | 0.098 |

8.8 | 0.093 |

13.2 | 0.065 |

15.4 | 0.053 |

17.6 | 0.044 |

19.8 | 0.038 |

22.0 | 0.032 |

24.2 | 0.028 |

26.4 | 0.025 |

28.6 | 0.023 |

30.8 | 0.021 |

$\ge $33.0 | 0.020 |

Data | BGW | AHD | ||||
---|---|---|---|---|---|---|

WST | Annual | Annual | Season 1 | Season 2 | Season 3 | Season 4 |

Sea area S | 8.0099 | 7.9109 | 7.5485 | 4.9814 | 7.5485 | 8.6104 |

Sea area 8 | 7.9412 | 7.9109 | 7.59 | 5.0493 | 7.6997 | 9.1549 |

Sea area 9 | 8.0099 | 8.4068 | 7.8068 | 5.4341 | 7.8405 | 9.1549 |

Sea area 15 | 7.6622 | 7.0663 | 7.0663 | 4.257 | 6.6088 | 7.7345 |

Sea area 16 | 7.9109 | 7.8068 | 7.3522 | 4.8456 | 7.3522 | 8.4707 |

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**MDPI and ACS Style**

Mangalathu Raj, S.; Enshaei, H.; Abdussamie, N.
Standard Wave Scatter Table Limitation for Evaluating SGISC Based on Hindcast Data Analysis. *Appl. Sci.* **2023**, *13*, 1181.
https://doi.org/10.3390/app13021181

**AMA Style**

Mangalathu Raj S, Enshaei H, Abdussamie N.
Standard Wave Scatter Table Limitation for Evaluating SGISC Based on Hindcast Data Analysis. *Applied Sciences*. 2023; 13(2):1181.
https://doi.org/10.3390/app13021181

**Chicago/Turabian Style**

Mangalathu Raj, Samuel, Hossein Enshaei, and Nagi Abdussamie.
2023. "Standard Wave Scatter Table Limitation for Evaluating SGISC Based on Hindcast Data Analysis" *Applied Sciences* 13, no. 2: 1181.
https://doi.org/10.3390/app13021181