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Contemporary Ideas on Ship Stability pp 275–290Cite as

Prediction of Parametric Rolling in Irregular Head Waves

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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 119))

Abstract

For providing a benchmark data for numerical codes for parametric roll prediction, a model experiment of a post-Panamax C11 class containership whose hull form is slightly modified from its original but opened for public was conducted and significant parametric rolling in irregular head waves was recorded. A 3DOF (degrees of freedom) numerical model based on the nonlinear strip theory is developed. The numerical code for time domain simulations is developed for the prediction of large amplitude of parametric roll both in regular and irregular head waves. Comparisons between the model experiment and the numerical simulations show good agreement under the consideration of dispersion due to practical non-ergodicity . By utilizing the developed numerical model, it was demonstrated that small height of the bilge keels is a major reason why significant parametric roll could happen for a C11 class post-Panamax containership in 1998.

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Abbreviations

\(a_{ij}\) :

Added mass/added moment of inertia

\(b_{1} , b_{2}\) :

Linear and quadratic coefficients of roll damping

\(b_{ij}\) :

Wave-making damping coefficient

\(F_{i}^{DF}\) :

Diffraction force

\(F_{i}^{FK + B}\) :

Froude-Krylov force and buoyancy

\(F_{n}\) :

Froude number

g :

Gravity

H :

Wave height

I xx :

Roll moment of inertia

I yy :

Pitch moment of inertia

m :

Ship mass

t :

Time

\(\xi_{G}\) :

Longitudinal position of centre of gravity

\(\phi\) :

Roll angle

\(\lambda\) :

Wave length

\(\theta\) :

Pitch angle

\(\omega\) :

Angular frequency

\(\zeta\) :

Heave displacement

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Acknowledgements

This work was supported by a Grant-in Aid for Scientific Research of the Japan Society for Promotion of Science (No. 20760558 & 21360427). The authors express their sincere gratitude to the ITTC (International Towing Tank), as well as MARIN, for providing geometric data of the modified C11 class containership for works on the development of the second generation intact stability criteria. The authors thank also Messrs. Yu Sanya and Yasuhiro Sogawa for their great contribution to this work.

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Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, 2-1, Yamadaoka, Suita, Osaka, 565-0871, Japan

    Hirotada Hashimoto & Naoya Umeda

Authors
  1. Hirotada Hashimoto
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  2. Naoya Umeda
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Correspondence to Hirotada Hashimoto .

Editor information

Editors and Affiliations

  1. David Taylor Model Basin/Naval Surface Warfare Center Carderock Division, West Bethesda, MD, USA

    Vadim L. Belenky

  2. School of Naval Architecture and Marine Engineering, National Technical University of Athens, Athens, Greece

    Kostas J. Spyrou

  3. MARIN-Maritime Research Institute Netherlands, Wageningen, The Netherlands

    Frans van Walree

  4. Department of Naval Architecture and Ocean Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Marcelo Almeida Santos Neves

  5. Department of Naval Architecture and Ocean Engineering, Osaka University, Suita, Osaka, Japan

    Naoya Umeda

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Hashimoto, H., Umeda, N. (2019). Prediction of Parametric Rolling in Irregular Head Waves. In: Belenky, V., Spyrou, K., van Walree, F., Almeida Santos Neves, M., Umeda, N. (eds) Contemporary Ideas on Ship Stability. Fluid Mechanics and Its Applications, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-030-00516-0_16

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  • DOI: https://doi.org/10.1007/978-3-030-00516-0_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00514-6

  • Online ISBN: 978-3-030-00516-0

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