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BASIC MATH -
TWICE the wind capture area equals FOUR times the energy captured:
5 foot diameter = 1 Unit of energy
so…
10 foot diameter = 4 Units of energy
TWICE the wind speed equals EIGHT times the energy captured:
5 mph wind = 1 Unit of energy
so…
10 mph wind = 8 Units of energy
COMBINING the above math and example means:
5 foot diameter @ 5 mph = 1 Bulk of energy
so…
10 foot diameter @ 10 mph = 32 Bulk of energy
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ADVANTAGES:
No ugly big aircraft style blades.
No Yaw dampening.
No pitch control or control box.
No tip brakes required.
No furling required for excessive or gusty winds.
No weather vane or tail vane required.
No dangerous high RPMs.
More attractive.
Less noticeable.
Less noise.
Less maintenance.
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NEGATIVES -
Efficiency requires expensive airfoil section blades.
The blades yaw once per revolution and this puts incredible stress on them.
Controls are required on a wind turbine if you want it to last.
Expensive and complicated to prevent overspeed.
VAWTs are harder to control than HAWTs
The wind comes at the blades from one side and then the other each revolution, until they break.
Low speed VAWTs of the Savonius type are different but are slow and inefficient.
Betz Law Maximum Turbine Performance!
Betz Law states that wind turbines are limited in their ability to be efficient. To start, if you capture 100% of the wind energy available, the wind will stop. Then, the wind turbine will also stop! The other extreme is that if you don't acquire any energy from the wind, you don't need a turbine. The wind is able to flow around any major obstruction. Betz math says that if you capture 59.6% of the energy in the wind, you get the best compromise between stopping the air and avoiding the wind. You should attempt to maintain the average flow of air at a compromise, regardless of style, with many blades or few, or any design.
The calculated energy below defines the energy you can gain per square measure at various wind speeds. Look at the swept area of your blades, multiply by the appropriate value, and determine potential results. Results are based on an average efficiency of 35%.
The expected Energy Per Month (given in kWh) that a turbine could produce (Betz limit), and what a good turbine could produce. This data assumes Rayleigh distribution regarding mean wind speed. EXAMPLE:
A turbine that has 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. Then find the Betz max value of 3.502. Multiply it by 10.
|
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 |
The following power curve calculations also use Betz math. EXAMPLE: A 10 mph wind, a 10 square foot rotor puts out approximately 17.5 watts, or 29.5 watts at maximum.
|
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 |