Wave Loading Calculator

The dispersion relation ω² = g·k·tanh(k·d) can't be solved algebraically for k because it appears both linearly and inside a hyperbolic tangent — the calculator starts from the deep-water approximation k ≈ ω²/g and refines it with up to 50 Newton's-method iterations, converging to within 1e-10 in practically every realistic case. This is the standard numerical approach used in wave mechanics software.

Drag force scales with velocity squared while inertia force scales with acceleration, and under linear wave theory these two peak at different phases of the wave cycle rather than simultaneously — velocity peaks when acceleration is zero, and vice versa. Simply adding the two component peaks would overstate the true maximum, so the calculator reports the SRSS combination as a conservative, non-simultaneous upper bound rather than pretending the two forces occur together.

KC compares how far water particles travel relative to the member diameter during one wave period — below about 2, the flow is inertia-dominated (thin members in relatively long waves), and above about 20 it's drag-dominated (thick members or short, steep waves). It's worth checking after you get your result, because the Cd and Cm coefficients you entered are only strictly valid within the flow regime they were derived for.

Wave particle velocity and acceleration attenuate with depth according to the ratio cosh(k(z+d))/sinh(kd), which decays roughly exponentially in deep water — forces near the seabed can be dramatically smaller than at the surface, especially when the wave motion barely reaches the bottom. In shallow water this attenuation is much gentler, so the same member sees comparatively little force reduction between the surface and the seabed.