Ah, but you appear to be dismising the catalyst that multiplies the resultant conversion of energy by a factor known to be in the order of several magnitudes - bullshit.

It is incredibly difficult to come on these things mid-life, as it were, if you haven't had the advantage of an education either based in physics or one that has at least brushed past the subject close enough to have left residue. The Den Brook documentary demonstrated this during the appeal hearing, when it was obvious that the "technical experts" arguing RES's case could hardly restrain themselves from leaping across the room to batter people who actually had the temerity to ask them to explain themselves; was it not obvious ENOUGH? All the data upon which they'd based their assumptions pointed to them being right, so what was the frigging problem! In one appeal I read earlier this week, the "expert" had been described as 'blunt'. I thought of those scenes at the Den Brook hearing.

What always worries me is that "experts" (and we've had the discussion about the definition of that word elsewhere on here) assume that because they've modelled something it actually represents the real world, that assumption prevailing until another equally well-qualified and similarly experienced "expert" comes along to knock holes in either the methodology, data presentation and/or subsequent interpretation.

MacKay is an example. I was prompted by many references to his authority to actually buy the book. I read it and was singularly impressed. I made the mistake of saying as much on here and was immediately pointed in the direction of a thread on another forum that was highly critical of MacKay (and not just because he took the King's shilling by working for DECC) and some of his claims. I still couldn't see a problem with his basic message, illustrated, in fact underlined, that taking everything into consideration it all had to add up to make any sense. I didn't know enough, you see.

I'm still trying to work out what enough actually is. How much of enough do I need to know, given that people who appear to know more than enough are still open to attack?

Now let us look at the energy in the wind, or the primary energy.
The simple formula of 1/2mass times velocity squared (0.5kgv^2) works well here, note velocity not speed, as this can become important later on.
Air has different densities, and therefore mass for a given volume (m^3), depending on air pressure (Pa) and Temperature (K). This can be calculated by the formula PV/T=C, where P=Pressure (Pa), V=Volume and T=Temperature (K). C is a constant and can, in this instance, be considered the Density (kgm^-3). I shall use 1.2 kgm^-3 as a starting point.
The windspeed (really wind Velocity) is measured in metres per second and can never be lower than 0, but can go infinitely high, but usually not more than 55 ms^-1 (120MPH). In the UK this maximum velocity is a lot lower (in the last 7 years I have only experienced one occasion of 100MPH wind).
So to work out the Kinetic Energy in that wind, we just halve the mass (1.2 kg) and multiply it by the velocity squared.
Therefore at 1 ms^-1 it is half the mass or 0.6 J, at 2 ms^-1 it is 2.4 J, 3 ms^-1=5.4 J and so forth.
Now this is important, in the real world, wind velocity is not constant, it rises and falls, changes direction as well as the temperature and pressure changing. So what may well show good figures in a wind tunnel may be better than out in the field, hence my love of measuring things.
Wind velocity in the real world can be models quite accurately (in engineering terms) by using a Weibull function that is based on the mean wind velocity and a correction factor. What this boils down to is a Wind Velocity Distribution (at last, real statistics). If this is plotted (and I may do it later) you get a chart which is skewed towards the lower wind velocities (a non zero positive skew). Lots of slow winds and a few high winds.
By calculating the area under the line you get the cumulative energy (this is often called the Probability Density Function) for that wind velocity regime.
This is the starting point for working out efficiency.

I'd only add that you can simplify quite a lot of this by making some broad assumptions. Air density can be taken as being 1.225kg/m³ for most practical purposes, and to get the power available from the wind for a given turbine you need to add the turbine effective area to the equation. Normally the effective area is the area swept by the blades.

The power available in the wind (in watts, which are just Joules per second) = 0.5 x rho x A x V³
where:
rho = 1.225kg/m³ and is the air density
A = 78.54m² and is the effective area of a 10m blade diameter wind turbine
V = the wind velocity in m/S

Here's a worked example for the wind power available to a 10m diameter axial wind turbine at some different wind velocities:

A 10m diameter axial turbine will have an effective area of (0.5 x 10)² x 3.14159 = 78.54m²

At 2m/S (4.47mph) the power in the wind will be 0.5 x 1.225 x 78.54 x 2³ = 385W

At 5m/S (11.18mph) the power in the wind will be 0.5 x 1.225 x 78.54 x 5³ = 6,013W

At 10m/S (22.37mph) the power in the wind will be 0.5 x 1.225 x 78.54 x 10³ = 48,106W

At 15m/S (33.55mph) the power in the wind will be 0.5 x 1.225 x 78.54 x 15³ = 162,357W

The cube law impact of wind velocity is pretty clear from the above example and illustrates well why wind turbines perform poorly where average wind speeds are low. The best that a practical wind turbine is likely to be able to extract is around 40% of these potential power figures.

JSH
There is more to come that will fill in the gaps.

Joiner
Busy day at work today, when I work best. :)