Fundamental Form-s

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How Much Power Can We Extract From The Wind?

wind deflection with airfoil rotor

Typical airfoil blade turbine deflects the wind outward downstream, loosing power.

According to mathematical analysis, wind power is proportional to the cube of the wind speed, or doubling the speed of the wind gives 8 times the power. It has also been analysed by Betz (based on a flat disk zone of power extraction ~ not applicable here) that a maximum of 59% of the mass momentum of the wind molecules, or wind power density (WPD), can be harvested from the wind by reducing the velocity of the wind by up to two thirds.  This is theoretical, without any losses from turbulence or bypassed air molecules.  In actual performance, efficiencies of existing wind turbines have been significantly lower, as shown in the chart below. However, these calculations do not take into consideration other mechanisms of power transfer not present in conventional propeller blades.

By these calculations, the wind power density at a velocity of 10 meters/second (22 miles per hour) is around 613 watts/sq.m Therefore, the theoretical maximum energy that can be extracted from this wind at 10m/sec is 613 x .59 = 362 watts/sq.m.  At a tiny 9.5 sq.ft (0.883 sq.m.) wind shadow our first prototype must extract less than 320 watts from the 10m/s wind. According to analysis of real wind turbine performance, the actual power generated may be less than 35% of the power in the wind, or less than 189 Watts.

I postulate that, due to the advantageous wind deflection profile downstream, the involute turbine can be more efficient than the airfoil blade turbine.  The turbulence behind a fast-moving and relatively fat propeller blade not only looses power by flinging the wind outward down- stream, but also from accelerating a fat propeller through the air at several times the wind speed, an increasingly turbulent wake is generated behind the prop, robbing it of power.

In contrast, an involute shaped turbine, with paper-thin vanes smoothly catches the wind and spins it into the center, gaining power, instead of loosing power as when propeller blades throw the wind out.  The involute vanes act like an ideal venturi shroud, diverting the wind mass continually inward to the central hole, then outward into a low pressure leeward zone.  The Enflo Windtec shrouded turbine achieved over twice the power from a 12.5m/sec wind as a comparable unshrouded blade turbine.  This suggests a potential for comparable efficiencies through the involute spiral vanes of this VAWT technology, but with a lighter, simpler design.

The mostly laminar flow throughout should also improve power-transfer efficiencies, especially at higher speeds.  This needs to be tested in a wind tunnel, along with the other variations mentioned.  Some intriguing questions come to mind ~ is a spinning low-pressure vortex created in the center? ~ What would happen if you open up a center hole in the bottom disk - will it suck in?  - will efficiencies improve or drop?  Ribbons placed in the flow path indicate that there is no upward or downward air-flow tendency, only cross-flow.  Certainly, there are optimum configurations (degrees of involute rotation, size of center-hole, number of vanes) for various wind conditions ~ what are these variables?  We need wind tunnel testing to determine.

The potential application of this geometry for quiet, efficient high-pressure fans should be investigated immediately. It could provide the ultimate Tesla Engine design!  and what about water power?

Top View of Involute-vaned
Vertical-axis Wind Turbine cross-section.

wind deflection with involute vanes02

I now have 23 pages of plans, including 20 technical drawings and 21 photographs and 3D rendered illustrations!  Details include a 5-vaned model 8ft in diameter and
a unique power-to-generator coupling system!

Download a set of plans for free HERE

WIND POWER CHART:

I have been doing some research and calculations on the power available from the wind.  Based on the most accurate figures available (I find these same formulas everywhere, and for standard horizontal axis propeller-blade designs they seem reliable), the theoretical maximum power available from the wind is 59% of the kinetic energy of the wind passing through the turbine. Furthermore, the maximum power that any commercially available wind turbine has been able to harvest from the wind is less than 35% of the total kinetic energy of the wind. This means that, unless we have the most efficient wind turbine in the world, we will not get more power from our small prototype than the Wendy column below right.

Wind Turbine Output is often rated at 35mph, which is far more power than available at an average site.  In other words, we may not get enough power below 6 or 8 mph to overcome the 5 inch-pounds of magnetic drag on the large WindBlue alternator. 

Now I know why many small wind turbines don’t advertise their output!

In contrast, if we had a 16ft diameter turbine, we could get at least 16 times the power from the wind“, up to 2Kw from a 20mph wind. Contrast this with higher efficiencies in water 900 times as dense! ~ barnacle cleaning gets more and more appealing!

LAD

 

 

 

 

theoretical maximum power 59%  ~  Betz' law

 

 

 

 

 

SPEED

SPEED

POWER

POWER

***

Wendy

Randy

^^Eagle

^^Eagle

^^Eagle

^^Eagle

Randy

Wendy

m/s

mile/hr

W/m2

W/ft2

W/ft2

9.5ft2

35.2ft2

19ft2

actual

% efficiency

% efficiency

at 35% eff.

at 35% eff.

0

0.0

 -  

 -  

 

Watts

Watts

Watts

Watts

of 59%max

of wind

Watts

Watts

1

2.2

0.6

0.1

0.0

0.3

1.2

0.6

Winds

Typical of

Whidbey

0.7

0.2

2

4.5

4.9

0.5

0.3

2.6

9.5

5.1

 

 

Island

5.6

1.5

3

6.7

16.5

1.5

0.9

8.6

32.0

17.3

 

 

 

18.9

5.1

4

8.9

39.2

3.6

2.2

20.5

76.0

41.0

44

107%

64%

44.9

12.1

5

11.2

76.6

7.1

4.2

40.0

148.4

80.1

57

71%

42%

87.6

23.7

6

13.4

132.3

12.3

7.3

69.2

256.4

138.4

 

 

 

151.4

40.9

7

15.7

210.1

19.5

11.6

109.9

407.1

219.8

125

57%

34%

240.5

64.9

8

17.9

313.6

29.1

17.3

164.0

607.7

328.0

 

 

 

358.9

96.9

9

20.1

446.5

41.5

24.6

233.5

865.3

467.1

225

48%

29%

511.1

137.9

10

22.4

612.5

56.9

33.7

320.3

1187.0

640.7

 

 

 

701.0

189.2

11

24.6

815.2

75.7

44.9

426.4

1579.8

852.8

400

47%

28%

933.1

251.8

12

26.8

1058.4

98.3

58.3

553.6

2051.1

1107.1

 

 

 

1211.4

326.9

13

29.1

1345.7

125.0

74.1

703.8

2607.7

1407.6

535

38%

23%

1540.2

415.7

14

31.3

1680.7

156.1

92.5

879.0

3257.0

1758.0

 

 

 

1923.7

519.2

15

33.6

2067.2

192.0

113.8

1081.2

4006.0

2162.3

810

37%

22%

2366.0

638.6

16

35.8

2508.8

233.1

138.1

1312.1

4861.8

2624.3

 

 

 

2871.5

775.0

17

38.0

3009.2

279.6

165.7

1573.8

5831.5

3147.7

880

28%

17%

3444.2

929.6

18

40.3

3572.1

331.9

196.7

1868.2

6922.3

3736.5

 

 

 

4088.5

1103.4

19

42.5

4201.1

390.3

231.3

2197.2

8141.3

4394.5

900

20%

12%

4808.5

1297.7

20

44.7

4900.0

455.2

269.8

2562.7

9495.7

5125.5

 

 

 

5608.4

1513.6

21

47.0

5672.4

527.0

312.3

2966.7

10992.4

5933.4

 

 

 

6492.4

1752.2

22

49.2

6521.9

605.9

359.1

3411.0

12638.7

6822.0

 

 

 

7464.7

2014.6

23

51.4

7452.3

692.3

410.3

3897.6

14441.7

7795.2

 

 

 

8529.6

2302.0

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