Mathematical Model of Roll Decay Motion for a Surfaced Submarine

Creative Commons License

Cansız M. Y., Yıldız B.

Gemi ve Deniz Teknolojisi Dergisi, no.219, pp.107-123, 2021 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Journal Name: Gemi ve Deniz Teknolojisi Dergisi
  • Journal Indexes: TR DİZİN (ULAKBİM)
  • Page Numbers: pp.107-123
  • Yıldız Technical University Affiliated: Yes


Among all ship motions, the most critical one is the roll motion for a submarine. The excessive roll motion can be harmful to both ship's crew and equipment, especially in surfaced condition. For this reason, it is important to predict the roll motion during the design stage to overcome excessive roll amplitudes. A mathematical model of the roll motion can be used to predict the motion responses of a submarine. Estimation of the roll damping is the most critical part to develop the mathematical model for a better prediction of the roll motion. The roll damping can be obtained experimentally, numerically and empirically. Experimental methods are expensive and time-consuming and empirical methods cannot be applied for all ship types. For this reason, numerical methods are frequently used due to the development of computer technologies in recent years, being economical and fast. In this study, the mathematical model of roll decay motion for a submarine at surfaced condition was obtained. The roll damping term was obtained numerically by carrying out roll decay simulations using a commercial Computational Fluid Dynamic (CFD) code. The inertia and restoring terms were obtained empirically by using the submarine geometry. The mathematical model was obtained and the roll decay motion of the surfaced submarine was calculated with a 20 degrees initial roll angle at zero speed and 5 kn, 7.5 kn and 10 kn forward speeds. The results were compared with numerical results and a good agreement was observed.