A dimensionless criterion for underwater-explosion shock-wave loading of small-scale maritime structures based on diffusion theory and potential-flow assumptions

Small underwater targets may have characteristic dimensions comparable to the spatial width of an underwater-explosion shock pulse, making conventional local-loading assumptions unreliable. This paper develops a physics-based loading selection criterion by combining a diffusion-based shock-wave width model with a linear potential-flow impulse formulation. A dimensionless global-loading dominance number, Λ, is defined to quantify the relative target scale to shock-wave width and to guide the choice between global and local surface loading. The formulation is extended from 1D translation to 2D/3D vector decomposition for oblique incidence. Coupled Eulerian–Lagrangian simulations are performed for six representative unmanned underwater vehicles and compared with analytical solutions. Global loading consistently provides smaller errors and higher agreement; for Hydroid Micro-REMUS, RMSE is reduced by 44% and R² exceeds 0.95. Based on Λ–error phase maps, local loading is recommended for Λ≤0.8 and global loading for Λ≥1.2, with intermediate cases assessed using interaction indicators.