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Linear and nonlinear analyses of the porpoising dynamics of high-speed planing craft using full-scale trial data

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Abstract

Although it is known from previous studies that porpoising in high-speed planing craft is a Hopf bifurcation, this study examined its occurrence and disappearance using the motion model identified from full-scale test data. Herein, we first analyzed the stability of the system linearized near the equilibrium point. From its results, we reconfirmed the knowledge that porpoising occurs when the system becomes unstable in the vicinity of the equilibrium point. We also found that the system became unstable as the thrust or trim angle of the outboard motor decreased. This finding was consistent with the results of a full-scale craft test performed in a previous study. Second, we confirmed that the limit cycle which is a result of the nonlinearity of the system was stable. The two analyses indicate that porpoising corresponds to the supercritical Hopf bifurcation. Furthermore, in the vicinity of the bifurcation point, it was found that stable equilibrium points and stable limit cycles can coexist. Finally, we confirmed this phenomenon in the full-scale test.

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Acknowledgements

The authors would like to thank the referees for their detailed comments, helpful advice, and suggestions. Experiments for this study were conducted by Mr. Yasushi Iriono of Yamaha Motor Co., LTD. We would like to express our gratitude to Professor Naoya Umeda of Osaka University, Professor Toru Katayama of Osaka Metropolitan University and Professor Hiroyuki Kajiwara of Nagasaki Institute of Applied Science for their helpful discussions. We also thank Mr. Akihiro Onoue, Mr. Toshio Suzuki, Mr. Masaru Suemori, Mr. Yoshiyuki Kadobayashi, Mr. Shintarou Futagwa of Yamaha Motor Co., LTD., and Ms. Manami Oyama of YAMAHA MOTOR ENGINEERING CO., LTD. for continuous discussions. We are grateful to Enago (http://www.enago.jp) for reviewing the English language.

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  1. Osaka University, 2-1 Yamadaoka, Suita, Osaka, Japan

    Satoru Hamada & Atsuo Maki

  2. Yamaha Motor Co., LTD., 2500 Shingai, Iwata, Shizuoka, Japan

    Satoru Hamada

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  1. Satoru Hamada
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  2. Atsuo Maki
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Correspondence to Satoru Hamada.

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Hamada, S., Maki, A. Linear and nonlinear analyses of the porpoising dynamics of high-speed planing craft using full-scale trial data. J Mar Sci Technol 29, 93–104 (2024). https://doi.org/10.1007/s00773-023-00972-3

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