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BETZ CRITERIA

Albert betz, a German physicist published Betz criteria in 1919.Albert Betz was concluded that no wind turbine can convert more than 16/27 (59.3%) of the kinetic energy of the wind into mechanical energy turning a rotor.The factor 16/27 (0.593) is known as Betz's coefficient.The Betz limit is based on an open disk actuatorWind turbines extract energy by slowing down the wind

For a wind turbine to be 100% efficient it would need to stop 100% of the wind - but then the rotor would have to be a solid disk and it would not turn and no kinetic energy would be converted.The theoretical maximum power efficiency of any design of wind turbine is 0.59 (i.e. no more than 59% of the energy carried by the wind can be extracted by a wind turbine).the real world limit is well below the Betz Limit with values of 0.35-0.45 common even in the best designed wind turbines.

Proof of Betz's law Let us make the reasonable assumption that the average wind speed through the rotor area is the average of the undisturbed wind speed before the wind turbine, V1, and the wind speed after the passage through the rotor plane, V2. the average wind speed V through the rotor is given by: V=(V1+V2)/2 The mass of the air streaming through the rotor during one second is: m =d F (V1+V2)/2

wherem:mass per second, d:density of air F:rotor swept area According to Newton's 2ndlaw(F=ma) the power extracted from the wind by the rotor is equal to the mass times the drop in the wind speed squared: P = (1/2) m (V12- V22) Substitutingminto this expression from the first equation: P = (d/4) (V12- v22) (V1+V2) F The total power in the undisturbed wind streaming through exactly the same area with no rotor blocking the wind is: P0= (d/2) V13F

The ratio between the power extracted from the wind and the power in the undisturbed wind is then: P/P0= (1/2) [1 - (V2/ V1)2] [1 + (V2/ V1)] Ploting the ratioP/P0as a function ofV2/V1

It can be seen that the ratioP/P0 reaches its maximum forV2/V1= 1/3 and that the maximum value for the power extracted from the wind is or 16/27=0,59 of the total power in the wind.