Difference between revisions of "Wind Energy - Physics"

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== Wind Power ==
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== Wind Power ==
  
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The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by  
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The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by
  
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&nbsp;<math>P=\frac{1}{2}\rho A v^3</math><br>
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&nbsp;[[File:]]
  
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It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''.&nbsp;  
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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;
  
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The Power ''P ''is the kinetic energy  
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The Power ''P ''is the kinetic energy
  
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<math>E=\frac{1}{2}mv^2</math>
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[[File:]]
  
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of the air-mass ''m ''crossing the area ''A&nbsp;''during a time interval <br>
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of the air-mass ''m ''crossing the area ''A&nbsp;''during a time interval
  
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<math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>.  
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[[File:]].
  
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Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation  
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Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
  
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<math>P=\dot{E}=\frac{1}{2}\dot{m}v^2=\frac{1}{2}\rho A v^3</math>
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[[File:]]
  
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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>
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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
  
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<math>P_{Betz}=\frac{1}{2} \rho A v^3 c_{P.Betz}</math>
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[[File:]]
  
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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>.  
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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>.
  
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== Unit abbreviations  ==
 
  
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{| width="399" cellspacing="1" cellpadding="1" border="0" align="left" style=""
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== Unit Abbreviations<br/> ==
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{| style="" align="left" width="399" border="0" cellpadding="1" cellspacing="1"
 
|-
 
|-
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| m = metre = 3.28 ft.<br>  
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| m = metre = 3.28 ft.<br/>
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| HP = horsepower<br>
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| HP = horsepower<br/>
 
|-
 
|-
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| s = second<br>  
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| s = second<br/>
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| J = Joule<br>
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| J = Joule<br/>
 
|-
 
|-
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| h = hour<br>  
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| h = hour<br/>
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| cal = calorie<br>
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| cal = calorie<br/>
 
|-
 
|-
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| N = Newton<br>  
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| N = Newton<br/>
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| toe = tonnes of oil equivalent<br>
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| toe = tonnes of oil equivalent<br/>
 
|-
 
|-
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| W = Watt<br>  
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| W = Watt<br/>
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| Hz = Hertz (cycles per second)<br>
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| Hz = Hertz (cycles per second)<br/>
 
|}
 
|}
  
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<br>
 
  
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<br>
 
  
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<br>
 
  
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<br>
 
  
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<math>10^{-12}</math> = p pico = 1/1000,000,000,000
 
  
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<math>10^{-9}</math>&nbsp;= n nano = 1/1000,000,000
 
  
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<math>10^{-6}</math> = µ micro = 1/1000,000
 
  
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<math>10^{-3}</math> = m milli = 1/1000
 
  
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<math>10^{3}</math> = k kilo = 1,000 = thousands
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<span class="texhtml">10<sup>− 12</sup></span> = p pico = 1/1000,000,000,000
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<span class="texhtml">10<sup>− 9</sup></span>&nbsp;= n nano = 1/1000,000,000
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<span class="texhtml">10<sup>− 6</sup></span> = µ micro = 1/1000,000
  
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<math>10^{6}</math> = M mega = 1,000,000 = millions
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<span class="texhtml">10<sup>− 3</sup></span> = m milli = 1/1000
  
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<math>10^{9}</math> = G giga = 1,000,000,000
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<span class="texhtml">10<sup>3</sup></span> = k kilo = 1,000 = thousands
  
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<math>10^{12}</math> = T tera = 1,000,000,000,000
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<span class="texhtml">10<sup>6</sup></span> = M mega = 1,000,000 = millions
  
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<math>10^{15}</math> = P peta = 1,000,000,000,000,000  
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<span class="texhtml">10<sup>9</sup></span> = G giga = 1,000,000,000
  
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<span class="texhtml">10<sup>12</sup></span> = T tera = 1,000,000,000,000
  
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<span class="texhtml">10<sup>15</sup></span> = P peta = 1,000,000,000,000,000
  
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[[Portal:Wind]]
 
  
  
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[[Portal:Wind]]
  
 
[[Category:Wind]]
 
[[Category:Wind]]

Revision as of 10:05, 16 May 2012

Wind Power

The power P of a wind-stream, crossing an area A with velocity v is given by

 [[File:]]

It varies proportional to air density ρ, to the crossed area A and to the cube of wind velocity v. 

The Power P is the kinetic energy

[[File:]]

of the air-mass m crossing the area A during a time interval

[[File:]].

Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation

[[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 (v1) and behind the rotor area (v2) is v1 / v2 = 1 / 3. The maximum power extracted is then given by

[[File:]]

where cp.B'e't'z = 0,59 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 cp.B'e't'z = 0,5.


Unit Abbreviations

m = metre = 3.28 ft.
 HP = horsepower
s = second
 J = Joule
h = hour
 cal = calorie
N = Newton
 toe = tonnes of oil equivalent
W = Watt
 Hz = Hertz (cycles per second)





10− 12 = p pico = 1/1000,000,000,000

10− 9 = n nano = 1/1000,000,000

10− 6 = µ micro = 1/1000,000

10− 3 = m milli = 1/1000

103 = k kilo = 1,000 = thousands

106 = M mega = 1,000,000 = millions

109 = G giga = 1,000,000,000

1012 = T tera = 1,000,000,000,000

1015 = P peta = 1,000,000,000,000,000


Portal:Wind

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