An Experimental Study on Characteristics of Rolling in Head Waves for a Vessel with Nonlinear GZ-curve

Abstract

In this study, the characteristics of rolling in head waves for a vessel with strong nonlinear GZ-curve, which includes parametric rolling , are investigated. Rolling is measured for systematically changed wave length and height under the same forward speed, which is service speed in heavy weather. As a result, the range of T_e/T_ϕ (T_e and T_ϕ are encounter wave period and the roll natural period of the model) when oscillatory rolling occurs is wider than that of previous results by Taguchi et al. (Model Experiment on Parametric Rolling of a Post-Panamax Containership in Head Waves. Proceedings of the Ninth International Conference on Stability of Ships and Ocean Vehicles, 2006), and the range spreads out wide area of T_e/T_ϕ > 0.5. Especially, in the range of T_e/T_ϕ > 0.5, oscillatory rolling is caused by large wave height and roll amplitude becomes larger than that at T_e/T = 0.5. It is supposed that the result is caused by change of roll natural period caused by nonlinear GZ-curve. In order to confirm it, numerical simulations are carried out for several variations of GZ-curve. Additionally, roll measurements in irregular waves with Pierson-Moskowitz spectrum are also carried out.

Appendix

1.1 The Number of Times of Test in Irregular Head Waves

From wave height, pitch motion and roll motion, each variance and ensemble mean by Eqs. (29.3), (29.4). Figure 29.21 shows calculated result. In these figure, a vertical axis is a ratio ensemble mean to standard deviation. Upper and middle figure uses 20 samples and bottom figure uses 30 samples. (1 sample = 40 s) From upper and middle figure, it is found that wave height and pitch motion convergence with 5 samples. On the other hand, roll motion does not converge until 15 samples. So, this study uses 20 samples.

Fig. 29.21

Standard deviation of wave elevation, pitching and rolling. (1/3 significant wave height = 0.04, 0.05, 0.06 m)

$$\sigma^{2} (t) = \sum\limits_{{j=1}}^{{n_{s} }} {\frac{{(X_{j} (t_{j} ) - \bar{X}(t))^{2} }}{n - 1}}$$

(29.3)

$$\sigma_{erg}^{2} = \frac{{\sum\nolimits_{i = 1}^{N} {\sum\nolimits_{j = 1}^{n} {\frac{{(X_{i} (t_{j} ) - \overline{{X_{i} }} )^{2} }}{n - 1}} } }}{N}$$

(29.4)