{"id":31,"date":"2003-12-11T08:05:15","date_gmt":"2003-12-11T12:05:15","guid":{"rendered":"http:\/\/scruss.com\/blog\/?p=31"},"modified":"2025-04-12T14:29:56","modified_gmt":"2025-04-12T18:29:56","slug":"windsave-all-betz-are-off","status":"publish","type":"post","link":"https:\/\/scruss.com\/blog\/2003\/12\/11\/windsave-all-betz-are-off\/","title":{"rendered":"WindSave: All Betz Are Off!"},"content":{"rendered":"\n

Update, May 2005<\/strong>: While it’s true that WindSave appear to have made their device obey the laws of physics<\/a> (at least according to their published spec), I’m keeping this posting intact.<\/em><\/p>\n\n\n\n

If the data on their website are to be believed, WindSave cannot generate the figures they claim<\/a>. There’s much geeky theory involved, but basically, they’re claiming efficiencies that cannot be attained.<\/p>\n\n\n\n

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 \u2014 the Betz limit \u2014 is 0.593. So something, somewhere, is screwy. I\u2019m pretty sure it\u2019s not my sums, as they\u2019ve been verified by an external source.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n\n\n\n\n

Wind Turbine Power is given by:<\/p>\n\n\n\n

\n

P = \u00bd \u03c1 A Cp<\/sub> v3<\/sup> Ng<\/sub> Nb<\/sub><\/p>\n<\/blockquote>\n\n\n\n

where:<\/p>\n\n\n\n

\n
\u03c1<\/td>air density (~ 1.225 kg\/m3<\/sup> at sea level)<\/td><\/tr>
A<\/td>rotor swept area, m2<\/sup><\/td><\/tr>
Cp<\/sub><\/td>Coefficient of performance<\/td><\/tr>
v<\/td>wind speed, ms-1<\/sup><\/td><\/tr>
Ng<\/sub><\/td>generator efficiency<\/td><\/tr>
Nb<\/sub><\/td>gearbox\/bearing efficiency<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/blockquote>\n\n\n\n

(from the American Wind Energy Association’s wind power FAQ, http:\/\/www.awea.org\/faq\/windpower.html<\/a>)<\/p>\n\n\n\n

Rearranging this:<\/p>\n\n\n\n

\n

Cp<\/sub> = P \/ ( \u00bd \u03c1 A v3<\/sup> Ng<\/sub> Nb<\/sub> )<\/p>\n<\/blockquote>\n\n\n\n

If we assume perfect gearbox and generator efficiency (Ng<\/sub> = Nb<\/sub> = 1):<\/p>\n\n\n\n

\n

Cp<\/sub> = P \/ ( \u00bd \u03c1 A v3<\/sup> )<\/p>\n<\/blockquote>\n\n\n\n

Since A = \u03c0 d2<\/sup>\/4, where d is the rotor diameter in metres:<\/p>\n\n\n\n

\n

Cp<\/sub> = P \/ ( \u00bd \u03c1 \u03c0 ( d2<\/sup>\/4 ) v3<\/sup> )<\/p>\n<\/blockquote>\n\n\n\n

Plugging in the numbers:<\/p>\n\n\n\n

\n

Cp<\/sub> = P \/ ( 0.48106 d2<\/sup> v3<\/sup> )<\/p>\n<\/blockquote>\n\n\n\n

WindSave<\/a>‘s website gives the following performance figures for its machines, both at 25mph (12.07ms-1<\/sup>):<\/p>\n\n\n\n