Update, May 2005: While it’s true that WindSave appear to have made their device obey the laws of physics (at least according to their published spec), I’m keeping this posting intact.
If the data on their website are to be believed, WindSave cannot generate the figures they claim. There’s much geeky theory involved, but basically, they’re claiming efficiencies that cannot be attained.
In short, they are claiming coefficients of performance of 0.724 and 0.887 for their turbines. Unfortunately, the theoretical maximum efficiency for a wind turbine â€” the Betz limit â€” is 0.593. So something, somewhere, is screwy. I’m pretty sure it’s not my sums, as they’ve been verified by an external source.
I worry that the UK energy minister, Brian Wilson, has been taken in by this. Five minutes with a calculator and a wind energy primer shows that these things are too good to be true.
Wind Turbine Power is given by:
P = Â½ Ï A Cp v3 Ng Nb
Ï air density (~ 1.225 kg/m3 at sea level) A rotor swept area, m2 Cp Coefficient of performance v wind speed, ms-1 Ng generator efficiency Nb gearbox/bearing efficiency
(from the American Wind Energy Association’s wind power FAQ, http://www.awea.org/faq/windpower.html)
Cp = P / ( Â½ Ï A v3 Ng Nb )
If we assume perfect gearbox and generator efficiency (Ng = Nb = 1):
Cp = P / ( Â½ Ï A v3 )
Since A = Ï€ d2/4, where d is the rotor diameter in metres:
Cp = P / ( Â½ Ï Ï€ ( d2/4 ) v3 )
Plugging in the numbers:
Cp = P / ( 0.48106 d2 v3 )
WindSave‘s website gives the following performance figures for its machines, both at 25mph (12.07ms-1):
- 1m diameter, 750W
- 1.4m diameter, 1200W
which gives for the 750W machine:
Cp = 750 / ( 0.48106 Ã— 12 Ã— 12.073 ) = 0.887
and the 1.4m diameter machine:
Cp = 1200 / ( 0.48106 Ã— 1.42 Ã— 12.073 ) = 0.724
Betz’s Law, a proof of which is given on the Danish Wind Energy Association’s site, http://www.windpower.org/en/stat/betzpro.htm, states that the maximum Cp is 16/27, or 0.593
There’s also the small problem of turbulence. No renewable energy practitioner recommends putting a wind turbine on a roof, as the turbulence from structures causes the machine to run rough, increasing wear and noise. Plus you will very seldom, if ever, see the rated wind speed of 12ms-1 on a domestic rooftop.