Slender ship theory

Slender-ship theory is an asymptotic potential-flow method that exploits a hull’s small beam-and-draft to length ratio, expanding the flow in that small parameter so each transverse section is solved as a near-two-dimensional inner problem matched to a slowly varying outer field along the length. It linearizes the free-surface condition and yields wave resistance, ship motions, and squat at lower cost than full three-dimensional theory, while retaining longitudinal coupling that strip theory drops. The thin-ship Michell theory is a related limit. Accuracy degrades for beamy, full forms and at low Froude number where the slenderness assumption is weak.