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playground:playground [2012-03-31 02:36] – shureplayground:playground [2013-06-09 12:58] (current) – chrono
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 +~~NOCACHE~~
  
 +====== PlayGround ======
 +
 +
 +
 +{{:playground:chart.png?nolink|}}
 +
 +<math>F_{pole} = \frac{1}{2} \times \rho \times C_d \times A_{wind} \times v_{wind}^2</math>
 +
 +<x>F_{pole} = \frac{1}{2} \times \rho \times C_d \times A_{wind} \times v_{wind}^2</x>
 +
 +
 +{{:cache_mathplugin:math_937_274670d8b3ee7744a2b058e90bc1988e.png?nolink|}}
 +
 +<x>\rho</x> = Density of air = about 1.2 Kg/m³ <br />
 +<note warning>C_d = Coefficient of drag = 1.0 (cylinder Re > 100) <br /></note>
 +<math2>A_{wind}</math> = Area of turbine = 4 m² <br />
 +<note tip><math2>v_{wind}</math> = Wind speed in m/s</note>
 +
 +h_1=0.32 m
 +d_1=0.32 m
 +A_1=0.1024 m^2
 +h_2=0.48 m
 +d_2=0.32 m
 +A_2=0.1536 m^2
 +|m/s|km/h|P_{wind_0.1024m^2}[W]|P_{wind_0.1536m^2}[W]
 +|1.8|6.5|0.35|0.5|
 +|4.5|16.00|5.5|8.2|
 +|6.25|22.50|15|22.6|
 +|8.0|29|32|48|
 +|m/s|P_{wind_0.1024m^2} [W]|P_{\rho=0.2}|P_{\rho=0.3}
 +|1.8|0.35|0.07|0.1
 +|4.5|5.5|1.1|1.65
 +|6.25|15|3|4.5
 +|8.0|32|6.4|9.6
 +|m/s|P_{wind_0.1536m^2} [W]|P_{\rho=0.2}|P_{\rho=0.3}
 +|1.8|0.5||0.1|0.15
 +|4.5|8.2||1.65|2.5
 +|6.25|22.6||4.5|6.8
 +|8.0|48||9.6|14.4
 +Assuming a bad (20%) or decent (30%) turbine design \rho_{turbine}=0.26
 +A rather bad permanent magnet alternator with \rho_{alternator}=0.75;
 +A normal synchronous rectifier with superb-by-design perfomance of \rho_{rect}=0.98;
 +A buck-boost inverter with a good performance of \rho_{rect}=0.85;
 +=> \rho_{overall}=0.25*0.75*0.98*0.85=0.16
 +
 +
 +<references />
 +
 +<math>
 +\Rho_{simple drag turbine} = 20%
 +\Rho_{decent} = 30%
 +\Rho_{good} = 30%
 +\Rho_{superb vawt} = 40%
 +</math>
Trace:

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