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Perfect Turbine Performance!

 

Wind Turbines are limited by what is called the Betz law.  Simply put, if you capture 100% of the energy available in the wind, you stop the wind.  Obviously, the wind will stop flowing through such a turbine.  The opposite of that is that if you don't capture any energy in the wind, you don't need a turbine.  The wind is able to flow around any major obstruction.  The Betz limit says that essentially, if you capture 59.6% of the energy in the wind, that is the best compromise between stopping the air and forcing it to go around your machine.  You need to maintain the flow of air, that's the compromise any wind machine must make whether it is a horizontal axis (traditional style turbine) or vertical axis turbine, with many blades or few, or any such combination.  It's covered by the Betz limit.

 

I've calculated the energy you can capture per square meter and per square foot for given wind speeds.  There's power curve data, and energy production data to make your life as easy as possible.  Find the swept area of your machine, multiply by the appropriate value, and see if it's even possible!  I've compared my GOOD wind turbine columns with production data from 4 reputable manufacturers' turbines, using their data.  NONE of them are as good as my GOOD turbine columns.  Those are based on an average efficiency of 35%.  It is not terribly likely that you'll find a machine that is more efficient than suggested by this column.  If it's too good to be true, it may very well be!  There are too many caveats in acquiring data that can be fudged to make things look better than they are in reality.  If you have questions, ask me!

 

First, here is the Energy Per Month (given in kWh) that a perfect turbine could produce (Betz limit), and what a good real turbine could produce.  This table assumes a Rayleigh distribution about the mean wind speed.  So, if you have a turbine that captures 10 square feet, in a 10 mph wind, look at the 10 mph row, find the "Good Turbine" per ft^2 value of  2.078.  Multiply it by 10 because you have 10 square feet.  If the manufacturer is claiming it can put out more than 20.78 kWh/month, it is probably too good to be true.  Next, find the Betz limit value of 3.502.  Multiply it by 10.  If the manufacturer claims you can generate more than 35 kWh/month, they have just broken the laws of physics.  It is impossible.  There's something wrong with their data.  That's how you can use this information.

 

Energy Per Month (kWh) 

Wind Speed

mph -[m/s] 

Betz Limit

per m^2 

Good Turbine

per m^2 

Betz Limit

per ft^2 

Good Turbine

per ft^2 

5 - [2.24] 

4.47 

2.65 

0.415 

0.246 

6 - [2.68] 

7.99 

4.74 

0.742 

0.440 

7 - [3.13] 

12.98 

7.70 

1.206 

0.715 

8 - [3.58] 

19.66 

11.66 

1.826 

1.083 

9 - [4.02] 

28.02 

16.63 

2.604 

1.545 

10 - [4.47] 

37.70 

22.36 

3.502 

2.078 

11 - [4.92] 

47.95 

28.45 

4.455 

2.643 

12 - [5.36] 

57.96 

34.38 

5.384 

3.194 

13 - [5.81] 

67.01 

39.75 

6.226 

3.693 

14 - [6.26] 

74.68 

44.30 

6.938 

4.116 

 

What follows is a set of power curve calculations using the Betz limit (a perfect turbine), and a good, real turbine.  Just like in the above graph, you can locate the wind speed.  Here, it is possible a manufacturer may beat the "good" turbine data by a small margin.  These turbines can be more efficient than this for a wind speed or two, but over the entire range, they won't reach this kind of performance.  Once again, in a 10 mph wind, a 10 square foot rotor would likely put out 17.5 watts.  A perfect turbine would put out 29.5 watts.  If the turbine you are looking at does better than that, there's something wrong with their data.

 

Power Curve (Watts) 

Wind Speed

mph -[m/s] 

Betz Limit

per m^2 

Good Turbine

per m^2 

Betz Limit

per ft^2 

Good Turbine

per ft^2 

1 - [0.45] 

0.031 

0.019 

0.00295 

0.00175 

2 - [0.89] 

0.254 

0.151 

0.0236 

0.0140 

3 - [1.34] 

0.857 

0.508 

0.0796 

0.0472 

4 - [1.79] 

2.031 

1.205 

0.1887 

0.1119 

5 - [2.24] 

3.966 

2.353 

0.3685 

0.2186 

6 - [2.68] 

6.854 

4.066 

0.6367 

0.3777 

7 - [3.13] 

10.88 

6.457 

1.01 

0.5998 

8 - [3.58] 

16.25 

9.638 

1.51 

0.8954 

9 - [4.02] 

23.13 

13.72 

2.15 

1.28 

10 - [4.47] 

31.73 

18.82 

2.95 

1.75 

11 - [4.92] 

42.23 

25.05 

3.92 

2.33 

12 - [5.36] 

54.83 

32.53 

5.09 

3.02 

13 - [5.81] 

69.71 

41.36 

6.48 

3.84 

14 - [6.26] 

87.07 

51.65 

8.09 

4.80 

15 - [6.71] 

107.1 

63.53 

9.95 

5.90 

16 - [7.15] 

130.0 

77.10 

12.07 

7.16 

17 - [7.60] 

155.9 

92.48 

14.48 

8.59 

18 - [8.05] 

185.1 

109.8 

17.19 

10.2 

19 - [8.49] 

217.6 

129.1 

20.22 

12.0 

20 - [8.94] 

253.9 

150.6 

23.58 

14.0 

21 - [9.39] 

293.9 

174.3 

27.30 

16.2 

22 - [9.83] 

337.9 

200.4 

31.39 

18.6 

23 - [10.28] 

386.1 

229.0 

35.87 

21.3 

24 - [10.73] 

438.7 

260.2 

40.75 

24.2 

25 - [11.18] 

495.8 

294.1 

46.06 

27.3 

26 - [11.62] 

557.7 

3330.8 

51.81 

30.7 

 



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