Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Hull speed — where it appears

The rule-of-thumb speed of a displacement hull, at a Froude number near 0.4, where its transverse wave is as long as the hull. It marks the steepest part of the wave-resistance curve, which peaks nearer a Froude number of 0.5.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The Kelvin wake, and the angle it comes out at. The wake behind something moving over deep water. Each curve joins everything radiated at one moment, wherever it has since travelled to. All of it stays inside a wedge whose half-angle is the inverse sine of one third, about nineteen and a half degrees, and that number does not depend on the speed, on gravity, or on the size of the vessel.

The angle that does not care

Every ship on deep water leaves a wake inside a wedge of the same angle. Not roughly the same — the same, for a rowing boat and a supertanker, at any speed either of them can manage, on any planet with any gravity.

regimes · Froude Hull speed is not the hump. The wave-resistance coefficient of the Wigley hull, R/(½ρU²S) in thousandths, against the Froude number U/√(gL), from Michell's thin-ship integral. The curve rises through a series of humps and hollows and peaks at Fr = 0.499. The hull-speed rule's Froude number, 1/√(2π) = 0.399, where the transverse wave is as long as the hull, is neither: it lies on the steep climb between the last hollow, at 0.346, and the main hump.

Hull speed is not the hump

The hull-speed rule says a displacement vessel meets a wall where its wave is as long as its hull, at a Froude number of 0.4. Michell's thin-ship integral, computed for a standard hull, puts that speed on the steep climb between the last hollow and the main hump, and the hump itself at 0.5. Past the hump the wave resistance grows more slowly than the speed. The hollows sit where the hull's own transverse wave switches off, and a bulb that cancels at one speed multiplies the resistance at another.

regimes · Froude The integral's hull is fine-ended slow and full-ended fast. The waterline half-breadth, bow to the right, of the hull of least wave resistance with the Wigley hull's length, draught, depth profile and displacement, designed for Froude numbers of 0.25, 0.30, 0.40 and 0.50, beside the Wigley hull's parabola. At low speed the optimum pulls volume into its middle and leaves long, fine ends; at high speed it pushes volume out towards the ends. Every one is symmetric fore and aft.

The hull Michell's integral prefers

Michell's integral gives a thin ship's wave resistance as a quadratic in the hull's offsets, so the hull of least resistance at a given speed and displacement is a quadratic minimisation. Allowed only to reshape its waterline, the integral rediscovers the naval architect's oldest rule: fine ends for a slow ship, full ends for a fast one. Allowed to reshape its depth too, it drains the waterline and piles volume at the keel until the hull is not a ship. And it cannot grow a bulb at the bow, because it cannot tell the bow from the stern.

regimes · Froude

Named alongside it

The objects these essays reach for when they reach for this one.

Froude numberDispersionGroup velocityInterferenceKelvin wakeLinearisationModel limitWave resistanceOptimisationRegime

All concepts