energy.

(F.4)

There’s only one thing wrong with this answer: it’s too big, because we’ve

neglected a strange property of dispersive waves: the energy in the wave

doesn’t actually travel at the same speed as the crests; it travels at a speed

called the group velocity, which for deep-water waves is *half* of the speed

*v*. You can see that the energy travels slower than the crests by chucking a

pebble in a pond and watching the expanding waves carefully. What this

means is that equation (F.4) is wrong: we need to halve it. The correct

power per unit length of wave-front is

(F.5)

Plugging in *v* = 16 m/s and *h* = 1 m, we find

(F.6)

This rough estimate agrees with real measurements in the Atlantic (Molli-

son, 1986). (See p75.)

The losses from viscosity are minimal: a wave of 9 seconds period

would have to go three times round the world to lose 10% of its amplitude.

## Real wave power systems

### Deep-water devices

How effective are real systems at extracting power from waves? Stephen

Salter’s “duck” has been well characterized: a row of 16-m diameter ducks,

feeding off Atlantic waves with an average power of 45 kW/m, would deliver

19 kW/m, including transmission to central Scotland (Mollison, 1986).

The Pelamis device, created by Ocean Power Delivery, has taken over

the Salter duck’s mantle as the leading floating deep-water wave device.

Each snake-like device is 130 m long and is made of a chain of four segments,

each 3.5 m in diameter. It has a maximum power output of 750 kW.

The Pelamises are designed to be moored in a depth of about 50 m. In a

wavefarm, 39 devices in three rows would face the principal wave direction,

occupying an area of ocean, about 400 m long and 2.5 km wide (an

area of 1 km^{2}). The effective cross-section of a single Pelamis is 7 m (i.e.,

for good waves, it extracts 100% of the energy that would cross 7 m). The

company says that such a wave-farm would deliver about 10 kW/m.