Michell's integral

Michell’s integral is the 1898 thin-ship theory for wave-making resistance, giving R_w as a single integral over a wave-angle parameter of the squared modulus of an amplitude function built from a double integral of the hull slope dy/dx over the centerplane. It linearizes the free-surface and body boundary conditions by assuming small beam relative to length, replacing the hull with a centerplane source distribution proportional to longitudinal slope. It needs no empirical input, captures the oscillatory humps and hollows of resistance versus Froude number, and remains a reference for ship wave resistance, though it overpredicts for full forms where the thin-ship assumption fails.