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

Displacement hull — where it appears

A ship's hull that is supported by buoyancy at every speed, pushing water aside rather than rising onto it. Its resistance is friction plus the energy carried away by the waves it makes, which depends strongly on the Froude number.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

With a wake, the bulb belongs at the bow. The Wigley hull's wave resistance with a spherical bulb, as a fraction of the bare hull's, against Froude number, with a wake fraction of 0.25: the bulb just ahead of the bow, and the same bulb just behind the stern. Without a wake the two curves are one. With it they separate: the stern's waves are made by slowed water and are weaker, so the bulb's cancelling wave has less to cancel there, and at the design speed of 0.30 the bow bulb leaves 0.443 of the bare resistance and the stern bulb 0.624.

The stern's wake puts the bulb at the bow

Michell's thin-ship integral cannot tell a ship's bow from its stern: reverse any hull and its wave resistance is unchanged, so the least-resistance hull is symmetric and a bulb is worth as much at the stern as at the bow. Real ships are fuller aft and put their bulbs forward. Let the stern's waves be made by water the hull's own boundary layer has slowed, and both follow: the optimum hull leans aft, and a bulb at the bow cuts the waves by far more than the same bulb at the stern.

regimes · Froude A wake held at the stern moves the volume aft a third as far. The least-resistance hull's centre of volume, in per cent of the half-length from midships, negative aft, against the design Froude number, holding the Wigley hull's length, draught, depth profile and displacement. With the linear wake it sits 2.8 per cent aft at Fr 0.30; with the shaped wake of the same propeller-disc fraction, 0.86 if uniform in depth, 1.5 if deepest at the waterline, and 0.11 if deepest at the keel, where the sources make the fewest waves.

A wake held at the stern keeps the bulb and loses the lean

A wake that slows the water steadily from bow to stern makes Michell's least-resistance hull fuller aft and puts its bulb at the bow. A real ship's wake is nearly nothing along most of the hull and strong only in its last few metres, deepest at the keel. Held there, with the same wake at the propeller, it moves the hull's volume aft by a twentieth to a half as much, and it keeps a third to two-thirds of the bulb's preference for the bow. The lean was a property of the water along the run, and the bulb a property of the water at the stern.

regimes · Froude

Named alongside it

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

Boundary layerFroude numberModel limitOptimisationSourceSymmetryWakeWave resistanceSuperposition

All concepts