Quantifying channel width thresholds for safe inland navigation under excessive cross-flow conditions

Existing standards rely primarily on cross-flow velocity limits, whereas the cumulative influence of cross-flow length on ship drift and channel safety remains insufficiently quantified. In this study, a flow-field-driven manoeuvring assessment framework that integrates a steady two-dimensional nonuniform flow model with a standard 3-DOF MMG manoeuvring model is developed, and numerical simulations are performed for representative inland cargo ships operating in China's Class I-V waterways under conservative upstream conditions. The key contributions of this study are as follows: (i) Introduction of the acceptable maximum safety cross-flow length (AMSCL), defined as the maximum cross-flow zone length that allows a ship to exit the zone within safety boundaries without requiring channel widening at a given excessive cross-flow velocity. (ii) Across Class I-V waterways, the AMSCL values range from 7.78 to 54.98 m for cross-flow velocities between 0.35 and 0.60 m/s, demonstrating the strong combined effects of cross-flow velocity and length on safety margins. (iii) Based on the AMSCL and simulated trajectories, chart-based criteria are developed to determine the required local channel widening and to quantify its approximately linear relationship with cross-flow velocity and length. (iv) A confluence case study (Guangping River-Pinglu Canal) confirms that the proposed widening scheme improves heading stability and reduces cross-flow-induced navigation risk. This research provides a quantitative framework for enhancing navigation safety and optimizing channel design in inland waterways subject to excessive cross-flow.