Comparison of Idealized 1D and Forecast 2D Wave Spectra in Ship Response Predictions

Abstract: Commonly, when calculating ship responses one uses idealized wave spectra to represent the sea. In the idealized model, the sea is frequently assumed to consist of swell and windwaves, which are usually represented by idealized 1D wave spectra, and the directionality of wind-waves is accounted for by multiplication with a standard spreading function. In operational response predictions these idealized spectra are typically generated by extracted parameters from real directional 2D wave spectra obtained from a weather forecast, i.e. spectra that reflects the sea state conditions for the particular place and time. It is generally not known in a statistical sense how large the errors become when idealized wave spectra are used to represent 2D wave spectra, especially not regarding the directionality. The objective with the study is hence to assess the errors that arise when adopting this simplification. The analysis compares three ship types that cover different combinations of hull form, load condition and operational conditions: a 153m RORO ship, a 219 m PCTC and a 240m bulk carrier. Chosen response parameters are roll motion, vertical acceleration and wave added resistance, which were calculated in 12240 sea states, for 10 speeds and 36 courses for each ship. The sea states are forecast 2D spectra from the North Atlantic 25th of September 2012. Transfer functions were generated from the hull geometry and realistic load conditions at speeds 2-20 knots. For each sea state-speed-course combination, responses were calculated for 2D wave spectra and corresponding generalized spectra. The error is taken as the difference in response between results obtained with 2D and idealized spectra, using 2D-results as reference. Several statistical measures were used to represent the errors for one sea state with only one number, and among them the root-mean-square error (RMSE) and the worst possible error (WPE) are regarded most relevant. The results show that the relative error decreases with increasing share of wind waves and decreasing share of swell. Multi-directionality of wind waves causes large errors only for small waves, and it is concluded that for higher sea states (for which the wind waves are predominant) the Bretschneider representation with spreading function leads to small relative errors. Absolute errors are considered the only relevant for investigating the effect of the error on seakeeping calculations. In general, the RMS acceleration levels are in the order of percentages of one g for all ships. For the bulker, WPE and RMSE for wave added resistance was found to be 8.3% and 3.8% of the total calm-water hull resistance in general, and almost 50% in worst case. The roll angle bias could reach up to 15. Also, the effect of ship speed was investigated, and it shows that the error increases in general with higher speed. It is concluded that it is necessary to use 2D spectra in order to avoid large errors, and to keep performance predictions correct on average.