Journal of Marine Science and Technology

, Volume 15, Issue 3, pp 218–229 | Cite as

Analytical formulae for predicting the surf-riding threshold for a ship in following seas

  • Atsuo Maki
  • Naoya UmedaEmail author
  • Martin Renilson
  • Tetsushi Ueta
Original Article


Making use of Melnikov’s method, a generalized formula for predicting the surf-riding threshold is developed as an extension to the applications of Kan and Spyrou. A new analytical formula for calculating the surf-riding threshold of a ship in following seas is also proposed in light of nonlinear dynamical system theory. By applying a continuous piecewise linear approximation to the wave-induced surge force, a heteroclinic bifurcation point is obtained analytically with an uncoupled surge equation. Results calculated using these formulae are presented, and they show good agreement with those obtained utilizing numerical bifurcation analysis. Further, it was confirmed that the surf-riding threshold obtained using the proposed formulae agrees reasonably well with that obtained experimentally for an unconventional vessel.


Analytical formulae Surf-riding threshold Heteroclinic bifurcation IMO vulnerability criteria Following seas 



The work was supported by a Grant-in Aid for Scientific Research from the Japan Society for Promotion of Science (No. 21360427) and the US Office of Naval Research contract No. 0014-06-1-0646 under the administration of Dr. Patrick Purtell. The work described here was partly carried out as a research activity for the stability project of the Japan Ship Technology Research Association, funded by the Nippon Foundation.


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Copyright information

© JASNAOE 2010

Authors and Affiliations

  • Atsuo Maki
    • 1
  • Naoya Umeda
    • 2
    Email author
  • Martin Renilson
    • 3
  • Tetsushi Ueta
    • 4
  1. 1.Graduate School of Maritime SciencesKobe UniversityKobeJapan
  2. 2.Department of Naval Architecture and Ocean Engineering, Graduate School of EngineeringOsaka UniversitySuitaJapan
  3. 3.Australian Maritime CollegeNewnhamAustralia
  4. 4.Centre for Advanced Information TechnologyTokushima UniversityTokushimaJapan

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