Skip to main content
SpringerLink
Log in

Analysis of ship trajectory during periodically steady turning in waves

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

In this study, ship turning in regular waves is investigated after sufficient time has passed after steering. At that time, the ship reaches the so-called periodic steady turning condition, under which the ship turns periodically with a constant drift in waves. The analytical formulas for the turning trajectory in waves are derived using the Fourier series expansion of the surge velocity, lateral velocity, and yaw rate under periodic steady turning conditions. From the obtained formulas, it is found that the ship turning in waves has the following characteristics. The turning trajectory in waves is deformed by ship drift in proportion to time. The drift velocity and the drift direction during turning are then determined by a combination of the average velocity components and first-order velocity components with the turning frequency. Furthermore, the turning trajectory in waves is composed of periodic circular motions with various frequencies in addition to the drift motion, and it is generally not a perfect circle. As a concrete example, using the derived analytical formulas, the turning trajectory for the KCS model in regular waves is analyzed. For the analysis, two turning trajectories obtained using a simulation method based on a two-time scale concept and a free-running model test are used under the same wave conditions. The reasons for the difference between the two are then clarified analytically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Hasnan MAA, Yasukawa H, Hirata N, Terada D, Matsuda A (2020) Study of ship turning in irregular waves. J Mar Sci Technol 25(3):1–20

    Google Scholar 

  2. Stern F, Sanada Y, Park S, Wang Z, Yasukawa H, Diez M, Quadvlieg F, Bedos A (2022) Experimental and CFD study of KCS turning circles in waves, 34th Symposium on Naval Hydrodynamics, Washington, DC, USA, 26 June - 1 July

  3. Yasukawa H, Hasnan MAA, Matsuda A (2021) Validation of 6-DOF motion simulations for ship turning in regular waves. J Mar Sci Technol 26:1096–1111

    Article  Google Scholar 

  4. Yasukawa H, Hirata N (2023) Effects of wave direction on the ship turning in regular waves. Ocean Eng (under review)

  5. Yasukawa H (2006) Simulation of wave-induced motions of a turning ship. J Japan Soc Naval Arch Ocean Eng 4:117–126 ((in Japanese))

    Google Scholar 

  6. Yasukawa H, Yoshimura Y (2015) Introduction of MMG standard method for ship maneuvering predictions. J Marine Sci Technol 20:37–52

    Article  Google Scholar 

  7. Skejic R, Faltinsen OM (2008) A unified seakeeping and maneuvering analysis of ships in regular waves. J Marine Sci Technol 13:371–394

    Article  Google Scholar 

  8. SIMMAN 2008: Workshop on Verification and Validation of Ship Maneuvering Simulation Methods, Copenhagen, http://www.simman2008.dk

  9. Ueno M, Nimura T, Miyazaki H (2003) Experimental study on manoeuvring motion of a ship in waves. Proc. International Conference on Marine Simulation and Ship Maneuverability (MARSIM’03), Kanazawa, Japan

  10. Kim DJ, Yun K, Park JY, Yeo DJ, Kim YG (2019) Experimental investigation on turning characteristics of KVLCC2 tanker in regular waves. Ocean Eng 175:197–206

    Article  Google Scholar 

Download references

Acknowledgements

The author expresses his sincere gratitude to Prof. F. Stern (IIHR, University of Iowa) and Dr. F. Quadvlieg (MARIN) for their helpful discussions.

Author information

Authors and Affiliations

  1. Graduate School of Advanced Science and Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, Hiroshima, 739-8527, Japan

    Hironori Yasukawa

Authors
  1. Hironori Yasukawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hironori Yasukawa.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

A FSE analysis results data

A FSE analysis results data

In this appendix, the FSE analysis results (amplitude and phase) for u, v, and r, FSE analysis results for x/L and y/L, and results of the amplitude and phase of x/L and y/L obtained using the present theory are shown together (Tables 3, 4, 5).

Table 3 FSE analysis results of u, v, and r
Full size table
Table 4 FSE analysis results of x/L and y/L
Full size table
Table 5 Theoretical calculation results of the amplitudes and phases of x/L and y/L
Full size table

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yasukawa, H. Analysis of ship trajectory during periodically steady turning in waves. J Mar Sci Technol 28, 758–769 (2023). https://doi.org/10.1007/s00773-023-00955-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-023-00955-4

Keywords

Search

Navigation