Effect of above-waterline hull shape on broaching-induced roll in irregular stern-quartering waves

  • Thet Zaw Htet
  • Naoya Umeda
  • Akihiko Matsuda
  • Daisuke Terada
Original article


In this paper, the effect of the above-waterline hull shape on broaching danger in irregular stern-quartering waves was numerically investigated using the US Office of Naval Research (ONR)-tumblehome and ONR-flare hulls. To indicate the danger of broaching, the probability of a broaching-induced large roll angle of the two vessels was examined along with the probability of broaching. The numerically estimated broaching-induced roll angles were compared with the time histories of the free-running model experiments. Then, the effects of above-waterline hull shape on broaching danger in the North Atlantic were simulated for various speeds, autopilot courses and rudder gains.


Effect of above-water hull form ONR-tumblehome ONR-flare Broaching Broaching-induced roll Irregular stern-quartering waves 



Rudder force increase factor


Rudder area


Rudder normal force


Rudder lifting slope coefficient


Advance coefficient of propeller


Correction factor for flow-straightening effect due to yaw rate


Rudder-induced yaw moment


Ship speed


Resultant rudder inflow velocity


Longitudinal inflow velocity component to rudder


Lateral inflow velocity component to rudder


Wake coefficient at propeller position


Wake coefficient at rudder position


Calm-water ship resistance


Longitudinal position of additional lateral force due to rudder


Longitudinal position of rudder


Rudder-induced sway force


Rudder inflow angle


Drift angle


Flow-straightening coefficient for drift angle


Rudder angle


Ratio of wake fraction at propeller and rudder position


Water density


Pitch angle


Propeller inflow speed increase constant


Ratio of propeller diameter to rudder span


Longitudinal position of the centre of the ship’s gravity from a wave trough


Roll angle


Heading angle from wave direction



This work was supported by the US Office of Naval Research Global Grant no. N62909-13-1-N257 under the administration of Dr. Woei-Min Lin and a Grant-in Aid for Scientific Research from the Japan Society for Promotion of Science (JSPS KAKENHI Grant no. 15H02327). The authors would like to thank Enago ( for the English language review.


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Copyright information

© JASNAOE 2018

Authors and Affiliations

  1. 1.Department of Naval Architecture and Ocean EngineeringOsaka UniversitySuitaJapan
  2. 2.National Research Institute of Fisheries EngineeringJapan Fisheries Research and Education AgencyKamisuJapan

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