Study on Simplified Formula for Long-term Predictions of Ship Response in Waves for Hull Structural Design

Abstract

In this paper, the authors proposed simplified formulae of the long-term maximum wave-induced vertical motion (surge acceleration, heave acceleration, and pitch angle) of exceedance probability of 10^-8 expressed as the explicit function of dominant hullform parameters. First, the dominant factors of the long-term maximum response were identified in a general discussion that did not depend on the types of response, and the methodology for the development approach of simplified formulae was demonstrated. In the process, the ratio of long-term maximum response and peak value of response amplitude operator (RAO) was defined as “Equivalent Regular Wave height" H_ERW. Then, it was clarified that H_ERW was dominated by the kurtosis of nondimensional RAO and peakwavelength of RAO as scale-dependent parameter. Furthermore, it was confirmed that long-term maximum response can be expressed by only the peak value of RAO when the RAO has certain properties; “kurtosis-invariant" and “peak value and peak-wavelength compatibility". Based on those consideration, as concrete examples, simplified formulae of the long-term maximum response of the vertical motion were derived. The obtained results were verified by comparison with numerical analysis using actual 154 merchant ships. The proposed development approach of simplified formula is effective regardless of the ship type as well as type of response. However, it should be noted that the proposed method is based on linear theory and is verified only for low speeds. Consideration of speed effect in high-Froude number and nonlinearly should be discussed in future work.