Energy [kWh] = 2.09 • Diameter 2 [m] • Wind 3 [m/s]
The energy it calculates is in kWh per year, the diameter of the wind turbine rotor is in meters, the wind speed is annual average for the turbine hub height in m/s. The equation uses a Weibull wind distribution with a factor of K=2, which is about right for inland sites. An overall efficiency of the turbine, from wind to electrical grid, of 30% is used. That is a reasonable, real-world efficiency number. Here is a table that shows how average annual wind speed, turbine size, and annual energy production relate:
||Annual Energy (kWh)
|Wind Speed (m/s)
For the metrically challenged, here is the same table using imperial numbers:
||Annual Energy (kWh)
|Wind Speed (mph)
How accurate are these numbers? This is the energy production a good horizontal-axis wind turbine can reach, if installed at the perfect site and height. These are the upper limit though, if your turbine produces anywhere near the number predicted by this table you should be doing your happy-dance! Most small wind turbine installations underperform significantly, in fact, the average seems to be about half of the predicted energy production (and many do not even reach that). There can be many reasons for the performance shortfall; poor site selection, with more turbulent air than expected often has much to do with it. The reports in the ‘real world’ section following below illustrate this point. Many small wind turbines do not reach 30% overall efficiency, some are close to 0% (this is no joke!), so these numbers have only one direction to go. For off-grid battery charging wind turbines you should deduct 20 – 30% of the predicted numbers, due to the lower efficiency of a turbine tied to batteries, and the losses involved in charging batteries.
VAWTs (Vertical Axis Wind Turbines)
HAWT vs. VAWT
The tables above are for HAWTs, the regular horizontal “wind mill” type we are all familiar with. For VAWTs the tables can be used as well, but you have to convert their dimensions. Calculate the frontal area (swept area) of the VAWT by multiplying height and width, or for a curved egg-beater approximate the area. Now convert the surface area to a diameter, as if it were a circle: Diameter = √(4 • Area / Pi). That will give you a diameter for the table. Look up the energy production for that diameter and your average annual wind speed and do the following:
- For a Darrieus or giromill type VAWT (the “egg beater” type): Take at least 25% off of the energy production number
- For a Savonius type VAWT (the “two half oil-drums” type): Take at a very minimum 60% off of the energy production number, leaving just 40% at best
The energy number that is left over should be a good approximation of what you can expect from that VAWT. Compare the resulting numbers with those mentioned in just about all sales brochures of VAWT type turbines and it should be immediately clear that their marketing people are smoking The Good Stuff. There is no relation to physical reality in their numbers, they are consistently much too high. Keep in mind that the energy production numbers calculated here are ‘best case’; for a turbine in nice, smooth air. Most VAWTs are placed very close to the ground, or on buildings, where there is little wind and lots of turbulence. Under those conditions they will do much, much worse than predicted.
Small Wind Turbine Real World Performance
You have read this far, and still want to install a wind turbine? Then it is time for a reality check: Most (some would say all) installed small wind turbines do abysmally poor in comparison with their energy production numbers as calculated above. That is the message from a number of studies, usually on behalf of governments that subsidize wind turbines. Do not just take our word for this, read it for yourself:
The Warwick Wind Trials report, in Great Britain: This evaluates 26 building-mounted small wind turbines. For anyone considering putting a turbine on their roof this is an eye opener; the results are piss-poor. Some turbines used more power than they produced!
The CADMUS Group report, in Massachusetts: 21 sites with small wind turbines were evaluated. The best sites produced around 80% of predicted energy yield, most were around 50% – 60% of predicted energy production.
The British Energy Savings Trust report titled “Location, location, location”: This requires some reading-between-the-lines as the Trust is rather closely aligned with the small wind industry. They looked at 57 turbines for a year, a number of them building mounted, others tower mounted, and concluded that building mounted turbines did very poorly.
The Zeeland small wind turbine test, The Netherlands: Test of 11 small wind turbines at the same site, same height. The original test report is in Dutch, in three parts [part 1, part 2, part 3]. Paul Gipe converted the numbers to English. Most produced less than half of their projected energy production, some much less.
Paul Gipe’s Wind Works articles: If you are still not convinced, a little casual browsing through Paul’s articles should do the job. Paul Gipe is a well respected impartial writer of books and articles about wind energy.
There are several common threads that emerge from all the reports: Building-mounted or roof-mounted small wind turbines do not work. Period. There is little wind at the rooftop, and it is very turbulent. This makes for poor ‘fuel’ for a wind turbine.
Most installers overrate the available wind resource. The majority of small wind turbine installations underperforms their predictions, often by a wide margin. Since wind speed is the most important parameter for turbine energy production, getting that wrong has large consequences (the power in the wind goes with the cube of the wind speed, so double the wind speed and the power in it is 2 * 2 * 2 = 8x as much). You have to be realistic about your annual average wind speed.
Most small wind turbines do not perform quite as well as their manufacturers want you to believe. That should come as no surprise at this point. What may be surprising is that even the turbines of the more honourable manufacturers that are honest about performance fall short, more often than not. The likely cause is turbulence and improper site selection.
The Myth of Low “Cut-In” Wind Speed
It is unfortunate to see how well marketing for small wind turbines is working: I often see people post questions on forums, where they are looking for a wind turbine “with a low cut-in wind speed”. Depending on whom you ask, the cut-in wind speed is either the wind speed where the turbine starts turning, or the wind speed where it starts to produce some power. For most wind turbines it is around 2.5 – 3.5 m/s (5.5 – 8 mph), and it is an utterly meaningless parameter.
There is no energy in the wind at those wind speeds, nothing to harvest for the turbine. While it may make you feel good to see your expensive yard toy spin, it is not doing anything meaningful in a breeze like that: To give you some idea, a wind turbine with a diameter of 6 meters (pretty large as small wind turbines go) can realistically produce just 120 Watt at 3.5 m/s wind speed. That same turbine would be rated at 6 kW (or more, see the next section), so energy production at cut-in really is just a drop in the bucket. What is more, due to the way grid-tie inverters work, you are about as likely to be loosing energy around cut-in wind speed to keep the inverter powered, as you are in making any energy, resulting in a net-loss of electricity production.
Forget about cut-in wind speed. It is not important.
Why You Should Ignore “Rated Power”
Is a 10 kW turbine better than a 6 kW windmill? Wrong! Rated power is one of least interesting parameters of any wind turbine, right after cut-in wind speed.
The trouble with rated power is that it does not tell you anything about energy production. Your utility company charges you for the energy you consume, not power. Likewise, for a small wind turbine you should be interested in the energy it will produce, for your particular site, with your particular annual average wind speed. Rated power of the turbine does not do that. To find out about energy production take a look at the tables presented earlier.
There is more trouble with rated power: It only happens at a “rated wind speed”. And the trouble with that is there is no standard for rated wind speed. Since the energy in the wind increases with the cube of the wind speed, it makes a very large difference if rated power is measured at 10 m/s (22 mph), or 12 m/s (27 mph). For example, that 6 meter wind turbine from the previous section could reasonably be expected to produce 5.2 kW at 10 m/s, while it will do 9 kW at 12 m/s!
Most in the industry agree that 11 m/s (24.6 mph) makes for a good rated wind speed. Go above it and very soon the turbine should be hard at work to protect itself from destruction, by furling, governing, or shutting down. Those that do not will likely face a short and tortured life. If we agree on 11 m/s, an equation for a realistic rated power number is as follows:
Power [Watt] = 192 • Diameter 2 [m]
This equation assumes a 30% over-all efficiency grid-tie horizontal axis wind turbine, with decent blades. Wind turbines with a poor blade profile will have a lower rated power, same for those with inefficient alternators. We have put the same information in a table, both for metric and imperial numbers:
at 11 m/s (Watt)
at 25 mph (Watt)
Rated power of a wind turbine may not be quite as meaningless as cut-in wind speed, though its use is limited. It could have some utility to quickly compare, or get a feel for, the size of the wind turbine, but only if those rated power numbers were taken at the same rated wind speed, and if the manufacturer is giving you a realistic number (many inflate rated power). A much better measure of turbine size is, simply, their diameter. As shown above it is by far the best predictor for power output.
A VAWT Does Not Have Any of ‘Those’ Problems, Right?!