Concept

Hydrofoil — where it appears

A wing designed to work in water, lifting a hull clear of the surface or turning a flow as a keel or centreboard does. Near the free surface its lift and drag depend on its depth, because the surface behaves as a second, reflected foil.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A hydrofoil loses lift at speed and gains it slowly, with a dip between. The lift of a flat hydrofoil beneath the surface over its value in deep water, against the chord Froude number U/√(gc) on a logarithmic axis, at depths of half a chord, one chord and two. Slow, the surface is a lid and the foil gains lift, as a wing over the ground does. Fast, the surface is a pressure-release boundary and the foil loses it. Between the two it does not simply pass from one to the other: the lift dips well below its fast value where the foil's waves are longest compared with its depth, and then rises through the lid value before settling back on it.

A hydrofoil loses most lift on the way up

A wing near the ground gains lift, and a hydrofoil near the surface is often described as the same thing upside down. At low speed it is: the surface acts as a lid and the foil gains lift. At high speed the surface is a boundary that cannot hold a pressure, and the foil loses lift instead. But the lift does not pass smoothly from one to the other. Between them, where the foil's waves are a few depths long, it falls well below both — to 43 per cent of its deep-water value half a chord down — and a foil boat meets that speed in the middle of its take-off run.

misconceptions · Ground cushion

A phantom biplane partner doubles the induced drag. Induced drag at a given lift, as a multiple of its deep-water value, against the foil's depth in spans. The surface's image of the foil is an identical wing, equally loaded, twice the depth above it, so the real foil pays its own induced drag plus the mutual drag of a biplane with a gap of twice its depth: 1 + σ, with σ Prandtl's biplane factor. The elliptic biplane's 1 + σ and the aspect-ratio-9 foil's lattice both run to two as the depth closes.

A foil under the surface flies with a phantom

At foiling speed the water's surface cannot hold a pressure, and the image that condition requires is not the reversed one a wall makes. For a horizontal foil it is an identical wing, equally loaded, above the surface — a biplane partner that takes lift and gives nothing back, doubling the induced drag as the foil rises. For the board that pierces the surface it is a reversed copy, which makes the board pay two and a half times what a keel under a hull pays. It is the board, not the foil, that decides how deep a foiling boat rides.

applied · Sailing

Fly level through short waves, follow long ones. The mean drag of the two strategies against wavelength, for a wave 0.4 m high at 8 m/s: flying level at the best mean depth for that sea, and following the surface at the calm boat's best depth, with the flat-water drag as the faint line. Level flight costs about the same whatever the wavelength; following costs the square of the heave it demands and falls away as the waves lengthen. Into the waves the two cost the same at 15.6 m; running with them, where the boat meets each wave slowly, at 5.9 m.

A foil flies level through a short sea and follows a long one

A foiling boat in waves has two ways to fly. It can hold its height and let the surface rise and fall over its foil, or it can follow the surface and heave with every wave. Flying level costs a deeper ride and a few per cent of drag whatever the wavelength; following costs the square of the heave, which grows with the frequency the boat meets the waves at. Into a head sea the two cost the same at a wavelength of about sixteen metres, running with the waves at about six, and the wave's height hardly moves either.

applied · Sailing

Heading into the sea, follow the long waves and fly level through the short. The dinghy's mean drag against the crossover encounter frequency below which it follows the surface, in units of the sea's peak frequency, heading into seas of significant height 0.2, 0.4 and 0.6 m. Following everything — the right-hand end — costs the heave's lift, and flying level through everything — the left — costs the foil's swinging depth and, in the roughest sea, breaches. Between them each sea has a best crossover: for 0.4 m at 2.92 times the peak frequency, 67.6 N against 67.9 flying level and 199 following.

A foil in a random sea follows it up to its peak

In a regular wave a foiling boat chooses between holding its height and following the surface. A real sea is a spectrum, and a wand that filters its signal can do both at once: follow the long waves and fly level through the short. The best place to divide them is close to the frequency of the sea's own peak, the divided control beats either pure strategy, and in a rough sea it is the only one of the three that keeps the foil a safe distance under the surface and the drag near its calm-water value.

applied · Sailing

Named alongside it

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

Free surface Model limit Froude number Induced drag Dimensionless Ground effect Image vortex Measurement Optimisation Biplane Circulation Drag polar

All concepts