Renewable Energy -Wind

Original picture courtesy of Gaia Energy Centre, Cornwall

Of all the energy sources, wind is the oldest and arguably most natural. The problems are that it is unreliable - too little, too much, none at all and not synchronised with peak demand!

Wind energy is not new to us!

The government's target for renewable energy - 10% by 2010, looking at 20% by 2020 - will be met by a variety of non-fossil methods, of which wind will form its part.

There's a lot more to building a wind-farm than meets the eye  -the wind patterns, surrounding geography, public opinion to name just three. Even if surrounded by flat farmland, a change in the farmer's use of a field can change the effectiveness of a wind farm!

How much energy is in the wind?

What a wind turbine does is convert the KINETIC ENERGY - i.e. the energy due to movement - into electricity. It does this by first converting the wind energy into rotational energy, and then converting the rotational energy, which is now in the turbine blades, generator and mechanisms, into electricity using a GENERATOR

The amount of harvested wind energy is related to the swept area that the rotating blades cover and the speed of the wind. It is also related to design aspects of the wind turbine's design, too.

Kinetic Energy (E) is given by the formula

E = ¹/₂ * mass * velocity * velocity, or mathematically,

E = ¹/₂*m*v^{2        (i)}

The mass is the amount of air, in kilograms, that we are looking at which is travelling at a velocity of v metres per second. Because the velocity is multiplied by itself, if the wind velocity doubles, then the increase in energy rises by a factor of 4!

At this point, let us look at a difference between speed and velocity. Speed is just that, in any direction. A car travelling at a constant 50 Km/hour has a constant speed, no matter what direction it is going in. Suppose the car is travelling from Shrewsbury to Wales. The overall direction of the car will be westerly, but through winding roads. Suppose that the car travels at a constant speed of 60km/hr, and goes to a location exactly 60km west of Shrewsbury. Will it take an hour? No, it will take longer as some of the time it is not travelling directly west. Velocity takes both speed and direction into account and if the car took 11/2 hours to get to the place 60Km west of Shrewsbury then its westward velocity was distance / time = 60 km/11/2 hours which is 40 km/hour. So, the car travelling (mostly) westerly at a constant speed of 60 km/hour only achieved a westward velocity of 40 km/hr. Some of the journey was spent travelling North and South and maybe even Eastwards.

It is air velocity we must consider, not speed, as the direction of the turbine blades into the wind dictates how much energy can be harvested, too. In practice, note, the turbine head, with the blades on, is able to turn into the prevailing wind, but not every gust where direction changes over a short time period.

Mass of air

How do we know what the mass of air is? Well, it's not too difficult really - we consider a cylinder of air that passes through the blade's swept area:

The size of the cylinder is given by:

Volume (V) = Area * Length

The mass (m) of air is given by air density (D) * Volume (V),

So Mass of air = Density of air * Area * Length  (ii)

This is still not useful - how on earth can we calculate "Length"?

Wind Turbines in action

Picture courtesy of Gaia Energy Centre, Cornwall

We are actually interested in the amount of air that passes through the blades in a given time period - the mass flow. Working is S.I. units, the standard units of distance are metres and time is measured in seconds.

(ii) becomes: Mass flow = Density * Area * Length/time (iii)

Length/time is speed! Or more correctly here, velocity

(iii) finally becomes: Mass flow = Density * Area * Velocity

or M = D*A*V (iv)

Remember (i)? You know, E = ¹/₂mv² 

If, instead of the total mass (m) we use the mass flow (M) then this formula changes to

Power = ¹/₂*M*v^{2   (v)     Power is the amount of energy per second, and is measured in watts.}

^{Now, (iv) gives us the value of M so let us plug this into (v):}

Power = ¹/₂*D*A*V³     _(vi)

This is the power in the wind that can be captured by blades with a swept area of A. The density of the air is dependant upon a number of factors like temperature, moisture and air pressure. 

Note that the power is related to the CUBE of the air velocity. If the air velocity doubles, then the power increases by a factor of 8 (2*2*2 = 8). This is a very nice feature of capturing a moving mass like air.

This formula is simplistic as it does not take into account the effects of a number of effects such as  turbulence and differences in wind speeds across the blades, but it is close enough for here.