We have considered Melnikov's method for assessing ship safety against capsize in beam waves when there is some steady heel due, for example, to beam wind loading. For a generic restoring lever parameterized with respect to the degree of lever asymmetry ("bias") we have derived closed-form relationships characterizing capsizability and linking the critical wave-slope, the amount of bias, and the damping. Qualitative differences in the safe basin characteristics are identified, which depend on whether the bias is small or large. A critical look into the accuracy of the Melnikov formulas is also presented for nearly symmetric and for strongly asymmetric rolling, based on comparisons with numerical predictions.

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