Wave Energy is the ultimate resource; the only problem is that not all of it can be harnessed. The size of waves can depend on three different factors:
- Wind Speed: The faster the wind is moving the more energy it will contain thus larger force on the water.
- Duration: The longer the force is in contact with the water, the greater the energy transfer.
- Distance: The greater the distance the greater the energy transfer.
Using these factors ideal sites around Britain is by Ireland or west of Scotland and of the coast of Cornwall. This is shown in figure 2.
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You can see that from the diagram that waves can reach up to 8m high by Ireland and 7m high by Cornwall. He energy contained in waves can be represented by an equation.
()
is the density of water and g is the acceleration due to gravity, T is the time period of the wave and a is the wave amplitude or height(m). For linear wave theory to work you must think of the wave a sinusoidal curve. The period (T) for one wave to pass this point can be expressed by:
Using both these equations we can work out how much energy we can obtain from a wave. Using figure 2 we can see that the height of waves around Ireland is around 7m. However these figures were most likely taken during a storm after looking at the met office website, the MAWS system (Marine Automatic Weather Station) showed that waves were regularly reaching a height of 3m.
(MAWS System)
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Looking at the Moored buoys at K2 and K1 they were giving readings at 3.4m at a high tide and 2.0 at a low tide. Using these figures we can do calculations.
When the wave height is 3.4m:
G=9.8
Therefore T= 1.476
When the height is 2m the wave period is:
Therefore T= 1.132
Using these figures we can put it into the earlier equation
Therefore P= 663015 KW
Using T = 1.132
P= 175955 KW
We must look at when we got high tides and low tides as this way we can accurately work out how much energy can be obtained during the day. Roughly the tides are split evenly so we can assume twelve hours for a high tide and twelve hours for a low tide. So when there is a low tide only 17.3KW is produced roughly per wave and when there is a high tide 65.1KW per wave is generated. I have obtained figures from the met office using the MAWS system indicating the time so how long it takes waves pass the certain point and the average time taken is 7.674419s so there is roughly 8 waves per minute this is equal to 470 waves per hour. Using this we can than work out that in half a day there is 5640 waves. So we can use this to work how much energy can be obtained:
High Tide:
5640*663015 = 3739405433KW
Low Tide:
5640*175955= 992385137KW
So in a day 4.7bn KW is produced this isn’t sufficient enough for Britain as 358bn KW is required. However we can say that the energy in waves is incredibly high. On the other hand the problem is that most devices created for converting wave energy they aren’t hundred percent efficient. For example a wave power converter used is called the Pelamis device. The Pelamis device consists of a series of semi-submerged cylindrical sections linked by hinged joints. The wave induced relative motion of these sections is resisted by hydraulic rams which pump high pressure oil through hydraulic motors via smoothing hydraulic accumulators. The hydraulic motors drive electrical generators to produce electricity. Power from all the joints is fed down a single umbilical cable to a junction on the sea bed. Several devices can be connected together and linked to shore through a single seabed cable. The disadvantage is that this device is only 15 percent efficient so actually you would only get 709768585 KW. This is the equivalent of 17bn kWhr Also each device is only capable of generating 2.25 Megawatts, which means that you would need about 316 Pelamis device which. This is a large amount of Pelamis devices needed. To get the total amount of energy needed you would need a large amount of devices. To get more energy I looked at other forms of wave power, one suggestion was tidal barrages as Britain has a few areas where I possible to do such things. The energy of the water is either in the form of potential energy (reservoirs) or kinetic energy (e.g. rivers). In both cases electricity is generated by passing the water through large water turbines. Tidal power is a special form of hydropower that exploits the bulk motion of the tides. Tidal barrage systems trap sea water in a large basin and the water is drained through low-head water turbines.
After looking at a book “Andrews & Jelley: Energy Science”, I found an equation for tidal barrages;
Pave =ρgAh2
2T
The total mass of water in the tidal basin above the low water level is m = qAh, where h is the tidal range. The height of the centre of gravity is 1/2 h, so the work done in raising the water is:
A is the area of the tidal basin, is the density of water, and “h” is the tidal range and “g” is the gravitational pull.
If we now do a calculation with similar conditions so wave heights of 7m. However we will be using a time period of 12.5 hours (roughly 4.5 x 104s) as this is how long each tide (high and low) is and the area will be roughly 520km2 (the area of the river Severn basin).
However this isn’t enough energy as only 28577 KW of energy is produced. This is the equivalent of685800 KW hr which means that overall more energy is required as we are still some what nearly 328 bn kWhr short. This means that even more methods of wave power must be discovered.
Another method of wave power is through the potential energy in waves, this is know TAPCHAN (TAPered CHANnel) is a Norwegian system in which sea waves are focused in a narrowed channel on the shoreline. Tapering increases the amplitude of the waves as they broaden through the channel. The water is forced to go up a ramp and go over a wall into a reservoir about 3–5 m above sea level. The potential energy of the water trapped in the reservoir is then extracted by draining the water back to the sea through a low-head Kaplan turbine. Besides the turbine, there are no moving parts and there is easy access for repairs and connections to the electricity grid. Unfortunately, shore-based TAPCHAN schemes have a relatively low power output and are only suitable for sites where there is a deep water shoreline and a low tidal range of less than about a metre. To overcome these limitations, a floating offshore version of TAPCHAN called Wave Dragon is under process.
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The potential energy in waves can be found using the formulae P.E=mgh. First we need to work out the mass of the wave. This is done by working out the volume of the wave and then multiplying it by the density of water.
If the height of the wave is 2m and the base of the wave is 2m and the width of the wave is 5 metres then we get a volume of 10m3 this means we have a total mass of 10300kg as it is 1.03 x 103 Kgm-3. Now we can work out the potential energy in the waves. In the TAPCHAN system the waves, the waves go up 5m and the gravitational pull is 9.8 ms-2 so now we can work it out.
P.E= 10300 x 5 x 9.8
P.E= 403760J
Now we have to assume that this all happens in 5 seconds as then we are able to convert the joules into watts and from the conversion we get 80.75 kW. However we get the same problem with that a Kaplan Turbine is not a hundred percent efficient, it is around 80% efficient which means that only 64.6 kW is produced per wave. Which means in a day 558144 kW is produced. Which is converted to 23256 kWhr. This still isn’t sufficient enough energy for Britain which means that another method has to be discovered. Another method of exploiting the potential energy is with Wave Dragon where it is done off shore and does exactly the same thing but the potential is greater as waves further out at sea have a higher amplitude.
