Oared Longboat

What is modelled

The crew delivers a fixed power, part of which is lost at the oars. The boat settles at the speed where the power left over equals resistance times speed. Resistance has two parts: skin friction, which grows roughly with the square of speed, and wave drag from the waves the hull makes, which grows far faster as the length of the wave it makes approaches the length of the boat. That happens at the hull speed, where the boat sits in a trough between its own bow and stern waves. In each stroke the oars push for part of the cycle only, so the boat speeds up and slows down around its mean.

Equations

• Hull speed v = √(g L / 2π), from a wave whose length equals L, Froude number Fn = v / √(g L) about 0.40.
• Friction Rf = ½ ρ v2 S (Cf + Ca), Cf = 0.075 / (log10 Re − 2)2, wetted area S = 2.6 √(∇ L).
• Wave drag Rw = ½ ρ v2 S Cw(Fn) with an illustrative fit that rises as Fn4 and levels off.
• Power balance η N P = R(v) v; surge m dv/dt = Foar(t) − R(v) with 10 % added mass.

Checks run in the page

• Hull speed from the water-wave dispersion relation.
• Power balance by bisection against Newton iteration.
• The friction line against the Prandtl-Schlichting law.
• Energy balance and mean speed of the stroke simulation.

Honest simplifications

The wave-making coefficient is a smooth illustrative fit scaled by the fineness you choose, not a measured curve for a particular hull, the wetted area is an approximation, the oar efficiency is fixed at 0.7, the thrust follows a simple half-sine and there is no wind, current or crew fatigue.

• Press Short and full and watch the wave drag eat the crew power.
• Press Long and slim for a higher hull speed.
• Press Tired crew and read the fall in speed.