In many pro-and-anti-wind energy discussions the topic of subsidies to the wind energy industry comes up.  Just for the record, those subsidies are now larger even in absolute terms (not to mention relative terms) than subsidies for the fossil fuel industries.  The usual response is that all new industries need subsidies.  The underlying theme is that wind energy is in its infancy and has lots of room to mature.

This infancy theme was thrown a monkey wrench when DOE secretary Chu mentioned that onshore wind is already mature.  So is wind infantile or mature?  One indication of which it is might be to look at the efficiency of today’s wind turbines at converting the dynamic energy of the wind into electricity.

It is surprisingly easy to calculate the amount of energy available from a given amount of wind moving through the diameter of a turbines blades.  You multiply the density of the air, it’s speed (cubed) and the swept area, divide by two and voila you’ve got the watts available.  One problem is that it is impossible to extract all the energy from the wind – you’d have to stop the wind to do so, but this wouldn’t allow any new wind to pass through the swept area.  A clever man named Betz (among others) figured out the maximum amount you could extract (now known as the Betz limit), which turns out to be about 59%.

So how close do modern turbines get to the Betz limit?  If they are pretty close then I think it is safe to call the industry mature.  The only way to extract more energy is to go higher and larger, and at some point this becomes self-defeating from both economic and engineering perspectives.  I cranked up a spreadsheet where I calculated the potential energy vs. what turbines are rated at and it produced the following chart (which is clickable to enlarge, thank goodness).The turbine I used for this chart is the Vestas low-wind-speed 1.8MW turbine that is proposed for Amherst Island, but the spreadsheet is set up to allow other turbines to be modeled.  The spreadsheet itself (an xls) is available for the asking.  The most important column is labeled “%age of Betz” which shows how close that turbine comes to perfection.  The subsequent column shows more realistic numbers that take into account the necessary generation/rectification/inversion/sychronization that must take place in a real turbine trying to join a real grid – I used a fixed 5% loss, which I think is probably low.  Over a large percentage of the time (as shown by the far right column) the efficiency of the turbine is quite close to the Betz limit.  I’m not sure how much more maturity we can expect out of turbine design.

Over all wind speeds the efficiency of this model is about 50% of the Betz limit, so perhaps there is some potential design that could capture all the energy at all wind speeds.  Such a design would likely require a shape-changing blade, made of materials that do not currently exist and controlled by a means that doesn’t exist either.  If wind turbines, at 50% of their potential efficiency, are not mature then I think it is hard to claim that coal plants, at 45% of their potential efficiency, are.

The influential 20% by 2030 report partly justifies the extraordinary investments in wind energy by estimating that wind turbines over time will increase their capacity factors from a current 30% to an anticipated 45%.  That would correspond to an increase in efficiency from about 75% of what is possible to 112%.  Too bad all those PhD’s at the DOE didn’t have access to my spreadsheet, or to an earlier posting of mine.

Wind energy supporters have every right to be nervous about all the subsidies flowing their way, so they’ll say whatever they can to keep them coming.  But the infancy theme is, like so much of what they say, simply not defensible.

2 thoughts on “Maturity”

  1. Your chart is not correct because the rated capacities for wind turbines would be the maximum that the generator can supply not what the rotors can gather from the wind. Currently the highest percentage of the Betz’s that a wind turbines can deliver to the generator is about 35%, which is very low. Onshore wind energy is among the cheapest forms of energy at about 9 cents per kWh. With an increase in efficiency say 80% of the Betz limit, Which recent studies show is possible, we can reduce the cost by over half making it the cheapest form of energy available by a long shot.

  2. I’m confused by your comment. My chart does not mention rated capacities at all. As for the percentage of Betz that can be gathered, it appears that your 35% is quite a bit different from my 80%. If you could supply your calculations I’d certainly like to look at them.

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