Wind Energy - Physics - Revision history

Ranisha at 09:38, 12 August 2014

2014-08-12T09:38:13Z

Wiki Gardener at 14:17, 12 June 2014

2014-06-12T14:17:01Z

Katharina Wiedemann: moved The physics of wind energy to Wind Energy - Physics

2012-05-16T10:10:53Z

moved The physics of wind energy to Wind Energy - Physics

Katharina Wiedemann: Reverted edits by Katharina Wiedemann (talk) to last revision by AnkeMaria

2012-05-16T10:09:24Z

Reverted edits by Katharina Wiedemann (*****) to last revision by *****

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Katharina Wiedemann at 10:09, 16 May 2012

2012-05-16T10:09:04Z

Katharina Wiedemann at 10:06, 16 May 2012

2012-05-16T10:06:32Z

Katharina Wiedemann at 10:05, 16 May 2012

2012-05-16T10:05:30Z

AnkeMaria at 07:34, 8 August 2011

2011-08-08T07:34:42Z

Nils Marscheider at 13:44, 31 July 2011

2011-07-31T13:44:08Z

Nils Marscheider at 18:06, 17 May 2011

2011-05-17T18:06:21Z

@@ Line 1: / Line 1: @@
 = Overview - Wind Power =
@@ Line 76: / Line 78: @@
 <math>10^{15}</math> = P peta = 1,000,000,000,000,000
+<br/>
 = Further Information =
-*[[Portal:Wind|Wind Portal on energypedia]]
+*[[Wind Energy - Introduction|Wind Energy - Introduction]]
 <br/>

@@ Line 1: / Line 1: @@
-The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by
+= Overview - Wind Power =
-&nbsp;<math>P=\frac{1}{2}\rho A v^3</math><br>
+The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by
-It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''.&nbsp;
+<math>P=\frac{1}{2}\rho A v^3</math><br/>
-The Power ''P ''is the kinetic energy
+It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''.
-<math>E=\frac{1}{2}mv^2</math>
+The Power ''P ''is the kinetic energy
-of the air-mass ''m ''crossing the area ''A&nbsp;''during a time interval <br>
+<math>E=\frac{1}{2}mv^2</math>
-<math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>.
+of the air-mass ''m ''crossing the area ''A ''during a time interval<br/>
-Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
+<math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>.
-<math>P=\dot{E}=\frac{1}{2}\dot{m}v^2=\frac{1}{2}\rho A v^3</math>
+Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
-The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (<math>v_1</math>) and behind the rotor area (<math>v_2</math>) is <math>v_1/v_2=1/3</math>. The maximum power extracted is then given by<br>
+<math>P=\dot{E}=\frac{1}{2}\dot{m}v^2=\frac{1}{2}\rho A v^3</math>
-<math>P_{Betz}=\frac{1}{2} \rho A v^3 c_{P.Betz}</math>
+The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (<math>v_1</math>) and behind the rotor area (<math>v_2</math>) is <math>v_1/v_2=1/3</math>. The maximum power extracted is then given by<br/>
-where <math>c_{p.Betz}=0,59</math> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of&nbsp;<math>c_{p.Betz}=0,5</math>.
+<math>P_{Betz}=\frac{1}{2} \rho A v^3 c_{P.Betz}</math>
-== Unit abbreviations  ==
+where <math>c_{p.Betz}=0,59</math> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of <math>c_{p.Betz}=0,5</math>.
-{| width="399" cellspacing="1" cellpadding="1" border="0" align="left" style=""
+<br/>
 |-
-| m = metre = 3.28 ft.<br>
+| m = metre = 3.28 ft.<br/>
-| HP = horsepower<br>
+| HP = horsepower<br/>
 |-
-| s = second<br>
+| s = second<br/>
-| J = Joule<br>
+| J = Joule<br/>
 |-
-| h = hour<br>
+| h = hour<br/>
-| cal = calorie<br>
+| cal = calorie<br/>
 |-
-| N = Newton<br>
+| N = Newton<br/>
-| toe = tonnes of oil equivalent<br>
+| toe = tonnes of oil equivalent<br/>
 |-
-| W = Watt<br>
+| W = Watt<br/>
-| Hz = Hertz (cycles per second)<br>
+| Hz = Hertz (cycles per second)<br/>
 |}
-<br>
+<br/>
-<br>
+<br/>
-<br>
+<math>10^{-12}</math> = p pico = 1/1000,000,000,000
-<br>
+<math>10^{-9}</math> = n nano = 1/1000,000,000
-<math>10^{-12}</math> = p pico = 1/1000,000,000,000
+<math>10^{-6}</math> = µ micro = 1/1000,000
-<math>10^{-9}</math>&nbsp;= n nano = 1/1000,000,000
+<math>10^{-3}</math> = m milli = 1/1000
-<math>10^{-6}</math> = µ micro = 1/1000,000
+<math>10^{3}</math> = k kilo = 1,000 = thousands
-<math>10^{-3}</math> = m milli = 1/1000
+<math>10^{6}</math> = M mega = 1,000,000 = millions
-<math>10^{3}</math> = k kilo = 1,000 = thousands
+<math>10^{9}</math> = G giga = 1,000,000,000
-<math>10^{6}</math> = M mega = 1,000,000 = millions
+<math>10^{12}</math> = T tera = 1,000,000,000,000
-<math>10^{9}</math> = G giga = 1,000,000,000
+<math>10^{15}</math> = P peta = 1,000,000,000,000,000
-[[Portal:Wind]]
+<br/>
 [[Category:Wind]]

@@ Line 1: / Line 1: @@
-== Wind Power ==
+<h2> Wind Power  </h2>
-The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by
+<tr>
+<td> m = metre = 3.28 ft.<br />
-&nbsp;[[File:]]
+</td>
+<td> HP = horsepower<br />
-It varies proportional to air density <span class="texhtml">ρ</span>, to the crossed area ''A ''and to the cube of wind velocity ''v''.&nbsp;
+</td></tr>
+<tr>
-The Power ''P ''is the kinetic energy
+<td> s = second<br />
+</td>
-[[File:]]
+<td> J = Joule<br />
+</td></tr>
-of the air-mass ''m ''crossing the area ''A&nbsp;''during a time interval
+<tr>
+<td> h = hour<br />
-[[File:]].
+</td>
+<td> cal = calorie<br />
-Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
+</td></tr>
+<tr>
-[[File:]]
+<td> N = Newton<br />
+</td>
-The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (<span class="texhtml">''v''<sub>1</sub></span>) and behind the rotor area (<span class="texhtml">''v''<sub>2</sub></span>) is <span class="texhtml">''v''<sub>1</sub> / ''v''<sub>2</sub> = 1 / 3</span>. The maximum power extracted is then given by
+<td> toe = tonnes of oil equivalent<br />
+</td></tr>
-[[File:]]
+<tr>
+<td> W = Watt<br />
-where <span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,59</span> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of&nbsp;<span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,5</span>.
+</td>
+<td> Hz = Hertz (cycles per second)<br />
-== Unit abbreviations ==
+</td></tr></table>
+<p><br />
-{| style="" align="left" width="399" border="0" cellpadding="1" cellspacing="1"
+</p><p><br />
-|-
+</p><p><br />
-| m = metre = 3.28 ft.<br/>
+</p><p><br />
-| HP = horsepower<br/>
+</p><p><span class="texhtml">10<sup> &#8722; 12</sup></span> = p pico = 1/1000,000,000,000
-|-
+</p><p><span class="texhtml">10<sup> &#8722; 9</sup></span>&#160;= n nano = 1/1000,000,000
-| s = second<br/>
+</p><p><span class="texhtml">10<sup> &#8722; 6</sup></span> = µ micro = 1/1000,000
-| J = Joule<br/>
+</p><p><span class="texhtml">10<sup> &#8722; 3</sup></span> = m milli = 1/1000
-|-
+</p><p><span class="texhtml">10<sup>3</sup></span> = k kilo = 1,000 = thousands
-| h = hour<br/>
+</p><p><span class="texhtml">10<sup>6</sup></span> = M mega = 1,000,000 = millions
-| cal = calorie<br/>
+</p><p><span class="texhtml">10<sup>9</sup></span> = G giga = 1,000,000,000
-|-
+</p><p><span class="texhtml">10<sup>12</sup></span> = T tera = 1,000,000,000,000
-| N = Newton<br/>
+</p><p><span class="texhtml">10<sup>15</sup></span> = P peta = 1,000,000,000,000,000
-| toe = tonnes of oil equivalent<br/>
+</p><p><br />
-|-
+</p><p><a _fcknotitle="true" href="Portal:Wind">Portal:Wind</a>
-| W = Watt<br/>
+</p>
 [[Category:Wind]]

@@ Line 25: / Line 25: @@
 where <span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,59</span> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of&nbsp;<span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,5</span>.
+== Unit abbreviations ==
 {| style="" align="left" width="399" border="0" cellpadding="1" cellspacing="1"

@@ Line 1: / Line 1: @@
-== Wind Power  ==
+== Wind Power ==
 The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by
-&nbsp;<math>P=\frac{1}{2}\rho A v^3</math><br>
+&nbsp;[[File:]]
-It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''.&nbsp;
+It varies proportional to air density <span class="texhtml">ρ</span>, to the crossed area ''A ''and to the cube of wind velocity ''v''.&nbsp;
 The Power ''P ''is the kinetic energy
-<math>E=\frac{1}{2}mv^2</math>
+[[File:]]
-of the air-mass ''m ''crossing the area ''A&nbsp;''during a time interval <br>
+of the air-mass ''m ''crossing the area ''A&nbsp;''during a time interval
-<math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>.
+[[File:]].
 Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
-<math>P=\dot{E}=\frac{1}{2}\dot{m}v^2=\frac{1}{2}\rho A v^3</math>
+[[File:]]
-The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (<math>v_1</math>) and behind the rotor area (<math>v_2</math>) is <math>v_1/v_2=1/3</math>. The maximum power extracted is then given by<br>
+The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (<span class="texhtml">''v''<sub>1</sub></span>) and behind the rotor area (<span class="texhtml">''v''<sub>2</sub></span>) is <span class="texhtml">''v''<sub>1</sub> / ''v''<sub>2</sub> = 1 / 3</span>. The maximum power extracted is then given by
-<math>P_{Betz}=\frac{1}{2} \rho A v^3 c_{P.Betz}</math>
+[[File:]]
-where <math>c_{p.Betz}=0,59</math> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of&nbsp;<math>c_{p.Betz}=0,5</math>.
+where <span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,59</span> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of&nbsp;<span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,5</span>.
-{| width="399" cellspacing="1" cellpadding="1" border="0" align="left" style=""
 |-
-| m = metre = 3.28 ft.<br>
+| m = metre = 3.28 ft.<br/>
-| HP = horsepower<br>
+| HP = horsepower<br/>
 |-
-| s = second<br>
+| s = second<br/>
-| J = Joule<br>
+| J = Joule<br/>
 |-
-| h = hour<br>
+| h = hour<br/>
-| cal = calorie<br>
+| cal = calorie<br/>
 |-
-| N = Newton<br>
+| N = Newton<br/>
-| toe = tonnes of oil equivalent<br>
+| toe = tonnes of oil equivalent<br/>
 |-
-| W = Watt<br>
+| W = Watt<br/>
-| Hz = Hertz (cycles per second)<br>
+| Hz = Hertz (cycles per second)<br/>
 |}
-<math>10^{3}</math> = k kilo = 1,000 = thousands
+<span class="texhtml">10<sup>− 12</sup></span> = p pico = 1/1000,000,000,000
-<math>10^{6}</math> = M mega = 1,000,000 = millions
+<span class="texhtml">10<sup>− 3</sup></span> = m milli = 1/1000
-<math>10^{9}</math> = G giga = 1,000,000,000
+<span class="texhtml">10<sup>3</sup></span> = k kilo = 1,000 = thousands
-<math>10^{12}</math> = T tera = 1,000,000,000,000
+<span class="texhtml">10<sup>6</sup></span> = M mega = 1,000,000 = millions
-<math>10^{15}</math> = P peta = 1,000,000,000,000,000
+<span class="texhtml">10<sup>9</sup></span> = G giga = 1,000,000,000
 [[Category:Wind]]