Sustainable Marine Structures

A Non-Dimensional Approach Safety Index for Jetty Berthing under Wind, Current, and Tug Assistance

Nik Muhamad Afiz Harom Junoh

Faculty of Maritime Studies, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia

Amir Syawal Kamis

Faculty of Maritime Studies, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia

Ahmad Faizal Ahmad Fuad

Faculty of Maritime Studies, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia

Muhamad Nasir Rahmatdin

Faculty of Maritime Studies, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia

Norhaslinda Yunus

Faculty of Maritime Studies, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia

Azmirul Ashaari

Faculty of Management, Universiti Teknologi Malaysia, Johor Bahru 81300, Johor, Malaysia

Jaffar Lamri

Training Department, Centre of Maritime Excellence Sendirian Berhad, Klang 41200, Selangor, Malaysia

DOI: https://doi.org/10.36956/sms.v8i2.3216

Received: 25 March 2026 | Revised: 20 April 2026 | Accepted: 6 May 2026 | Published Online: 27 May 2026

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Abstract

This paper develops and validates a simple, nondimensional decision metric for jetty berthing that compares the combined environmental disturbance loads from wind and current against the effective corrective capability provided by assisting tugs. The approach formulates wind-induced lateral force using a drag-based expression on the vessel’s exposed lateral area and current-induced force using a hydrodynamic drag formulation on the projected underwater area, while tug control is represented through the sum of available bollard pull adjusted by an efficiency factor. These components are combined into the Approach Safety Index (ASI), defined as the ratio of total environmental forcing to effective tug-assisted control, where lower values indicate greater controllability and values approaching unity indicate insufficient control margin. Model performance is evaluated through a full mission Wärtsilä simulator exercise using a Handysize bulk carrier in ballast, supported by two ASD tugs rated at 36 t bollard pull each, with wind and current progressively increased across scenarios. The computed ASI values align closely with the harbour pilot’s qualitative controllability assessments, distinguishing clearly between manageable, marginal, and unsafe operating states. Based on the simulation outcomes, provisional empirical screening bands were identified to support first-pass pilotage judgement under simplified live berthing conditions. The findings suggest that ASI can serve as a practical decision support and screening tool for pilots and port operators using limited readily available inputs.

Keywords: Jetty Approach Safety; Mathematical Model; Approach Safety Index (ASI); Meteorology-Based Pilotage Decision; Maritime Risk Assessment

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References

[1] Kamis, A.S., Ahmad Fuad, A.F., Ashaari, A., et al., 2021. Wheel over point mathematical model. Ocean Systems Engineering. 11(3), 203–16. DOI: https://doi.org/10.12989/ose.2021.11.3.203

[2] Tetreault, B., Johnson, G.W., 2020. Sharing ships’ weather data via AIS. TransNav: International Journal on Marine Navigation and Safety of Sea Transportation. 14(1), 143–150.

[3] van Hilten, M.J., Wolkenfelt, P.H.M., 2000. The rate of turn required for geographically fixed turns: A formula and fast-time simulations. Journal of Navigation. 53(1), 146–55. DOI: https://doi.org/10.1017/S0373463399008590

[4] Swift, A.J., 2018. Bridge Team Management: A Practical Guide, 2nd ed. Nautical Institute: London, UK.

[5] Fontijn, H., 1983. Ship Berthing to a Vertical Quay-Wall: Fender Forces and Ship Motion. Available from: https://consensus.app/papers/ship-berthing-to-a-vertical-quaywall-fender-forces-and-ship-fontijn/8ce9403017375b64854ecf1ef7761d8f/ (cited 15 February 2026).

[6] Neşer, G., Ünsalan, D., 2006. Dynamics of ships and fenders during berthing in a time domain. Ocean Engineering. 33(14–15), 1919–1934.

[7] Takashina, J., 1986. Ship maneuvering motion due to tugboats and its mathematical model. Journal of the Society of Naval Architects of Japan. 1986(160), 93–102. DOI: https://doi.org/10.2534/jjasnaoe1968.1986.160_93

[8] Honda, K., 1989. A required ZP-tug power in berth manoeuvres of VLCC at half loaded and ballasted conditions. Journal of Japan Institute of Navigation. 80, 17–24. DOI: https://doi.org/10.9749/jin.80.17 (in Japanese)

[9] Zhang, S., Wu, Q., Liu, J., et al., 2023. State-of-the-art review and future perspectives on maneuvering modeling for automatic ship berthing. Journal of Marine Science and Engineering. 11(9), 1824.

[10] Cai, J., Chen, G., Yin, J., et al., 2024. A review of autonomous berthing technology for ships. Journal of Marine Science and Engineering. 12(7), 1137. DOI: https://doi.org/10.3390/jmse12071137

[11] Chen, C., Li, Y., Wang, T., 2023. Real-time tracking and berthing aid system with occlusion handling based on LiDAR. Ocean Engineering. 288, 115929. DOI: https://doi.org/10.1016/j.oceaneng.2023.115929

[12] Lu, H., Zhang, Y., Zhang, C., et al., 2025. A multi-sensor fusion approach for maritime autonomous surface ships berthing navigation perception. Ocean Engineering. 316, 119965. DOI: https://doi.org/10.1016/j.oceaneng.2024.119965

[13] Wang, T.-Q., Li, Y., 2025. Spatial state analysis of ship during berthing and unberthing process based on multi-ship data from 3D LiDAR. Measurement. 244, 116497. DOI: https://doi.org/10.1016/j.measurement.2024.116497

[14] Liu, J., Xu, C., Li, S., et al., 2025. Towards future autonomous tugs: Design and implementation of an intelligent escort control system validated by sea trials. Advanced Engineering Informatics. 65, 103116. DOI: https://doi.org/10.1016/j.aei.2025.103116

[15] Wu, G., Zhao, X., Sun, Y.-S., et al., 2021. Cooperative maneuvering mathematical modeling for multi-tugs towing a ship in the port environment. Journal of Marine Science and Engineering. 9(4), 384. DOI: https://doi.org/10.3390/jmse9040384

[16] Asmara, I.P.S., Kristianto, D., Mustaghfirin, M.A., et al., 2022. Development of the elements of tugboat handling for berthing and unberthing of container ships. IOP Conference Series: Earth and Environmental Science. 1081(1), 12015.

[17] Lee, S.-M., Lee, J.H., Roh, M., et al., 2021. An optimization model of tugboat operation for conveying a large surface vessel. Journal of Computational Design and Engineering. 8(2), 654–675. DOI: https://doi.org/10.1093/jcde/qwab006

[18] Xiao, G., Tong, C., Wang, Y., et al., 2021. CFD simulation of the safety of unmanned ship berthing under the influence of various factors. Applied Sciences. 11(21), 7102.

[19] Choi, J.-H., Jang, J-Y., Woo, J., 2023. A review of autonomous tugboat operations for efficient and safe ship berthing. Journal of Marine Science and Engineering. 11(6), 1155.

[20] Karaçay, Ö.E., Karatuğ, Ç., Uyanık, T., et al., 2024. Prediction of ship main particulars for harbor tugboats using a Bayesian network model and non-linear regression. Applied Sciences. 14(7), 2891. DOI: https://doi.org/10.3390/app14072891

[21] Asmara, I., Kharis, A., Mustaghfirin, M., et al., 2024. Simulation study on the influence of tugboats capacity on the safety of simultaneous emergency un-berthing. TransNav: International Journal on Marine Navigation and Safety of Sea Transportation. 18(3), 547–553. DOI: https://doi.org/10.12716/1001.18.03.08

[22] Tannuri, E., Câmara, J., Silva, D., et al., 2016. Assessment of New Port Operations Using Integrated Analysis: A Case Study in Port of Mucuripe (CE, Brazil). Social Science Research Network. Available from: https://consensus.app/papers/assessment-of-new-port-operations-using-integrated-tannuri-c%C3%A2mara/44ee5c2eede857b4b39ca576d3cbf6f0/

[23] Nguyen, V.S., 2019. Investigation on a novel support system for automatic ship berthing in marine practice. Journal of Marine Science and Engineering. 7(4), 114. DOI: https://doi.org/10.3390/jmse7040114

[24] Perkovič, M., Gucma, L., Bilewski, M., et al., 2020. Laser-based aid systems for berthing and docking. Journal of Marine Science and Engineering. 8(5), 346. DOI: https://doi.org/10.3390/jmse8050346

[25] Shi, H., Wang, X., Zhu, S., et al., 2021. Research on the control strategy and control method of ship’s automatic berthing. Journal of Physics: Conference Series. 2005(1), 12204.

[26] Abdelghany, A., El-Refaae, M., Samy, A., 2024. Evaluation of mooring forces on berths bollards. Engineering Research Journal. 53(1), 150–157.

[27] Paulauskas, V., Simutis, M., Plačienė, B., et al., 2021. The influence of port tugs on improving the navigational safety of the port. Journal of Marine Science and Engineering. 9(3), 342.

[28] Bondarenko, O., Nekrasov, V., Yastreba, O., 2017. Harbour Tug Fleet. Available from: https://consensus.app/papers/harbour-tug-fleet-bondarenko-nekrasov/b9cc18e5f248535aaf3947f9c7410fc4/ (cited 7 January 2026).

[29] Arican, O.H., 2025. Optimal tugboat placement in narrow straits for ship safety: A Fuzzy Delphi and P-Median approach, as exemplified by the Dardanelles Strait. Ships and Offshore Structures. 1–13. DOI: https://doi.org/10.1080/17445302.2025.2502862

[30] Hikmet Arican, O., 2025. Optimizing tugboat assignments for risk management in strategic waterways: A case study of the Istanbul strait. Ships and Offshore Structures. 1–19. DOI: https://doi.org/10.1080/17445302.2025.2588143

[31] Ariana, I.M., Prastyasari, F.I., Putera, R.R., 2021. Technical review of bollard pull calculation to support shuttle tanker from spread mooring system FSO. IOP Conference Series: Materials Science and Engineering. 1052(1), 12027.

[32] Wang, Y., Zou, T., 2024. Optimization of berth-tug co-scheduling in container terminals under dual-carbon contexts. Journal of Marine Science and Engineering. 12(4), 684.

[33] Sano, M., 2023. Mathematical model and simulation of cooperative manoeuvres among a ship and tugboats. Brodogradnja. 74(2), 127–148.

[34] Fuss, F.K., 2023. The dynamics of a turning ship: Mathematical analysis and simulation based on free body diagrams and the proposal of a pleometric index. Dynamics. 3(3), 379–404.

[35] Kamis, A.S., Ahmad Fuad, A.F., Anwar, A.Q., et al., 2022. Assessing the efficacy of the advance transfer technique in calculating the wheel over point through simulation studies. In: Ismail, A., Dahalan, W.M., Öchsner, A. (Eds.). Design in Maritime Engineering. Springer: Cham, Switzerland. pp. 129–144. DOI: https://doi.org/10.1007/978-3-030-89988-2_9