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
Plugging in v = 16 m/s and h = 1 m, we find
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.
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 km2). 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.