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Optimized Blade Design for Homemade Windmills

1,716 bytes added, 06:34, 16 April 2010
=== <br>'''Angle of blade and the resulting forces to spin the blades versus surface area exposed''' ===
<br> <br> The angle that the windmill blades are tilted compared to the stream of fluid will determine how much energy can be converted into rotational motion and then be captured by the system for meaningful work. The amount of force is calculated by finding the wind pressure.  The wind pressure exerted by the wind is given by:<math> P = 1/2 (1 + c) * \rho * v^2 </math> *where c is a constant and equals 1.0 for long flat plates.   The force of the wind against the windmill blade is based on the wind pressure multiplied by the area of the blade facing the oncoming flow. In the event that the blade is tilted at an angle to the oncoming airstream, then the area of the blade exposed to the fluid is reduce by a factor of <math>sin \theta </math>. As such, the wind pressure calculation is multiplied by <math>A * sin \theta </math> to obtain the force of the wind on the blades  In addition, the force of the wind converted into rotational motion is related to the angle of the blade in relationship to the oncoming fluid flow. This relationship is given by a factor of <math>cos \theta </math>.  Furthermore, the blades will encounter a drag coefficient related to the angle of the blades as they rotate in their own axis perpendicular to the oncoming flow of fluid. This drag coefficient will be represented by <math>D * cos \theta </math>.  Therefore, the combined calculation to determine the force balance on the blades is: <math> F = \rho * v^2 * A * sin \theta * cos \theta * D * cos \theta </math>  An important relationship to note is that between force and <math> \theta </math>. The combined force balance indicates a relationship between force and <math>sin \theta * cos \theta * cos \theta</math>.
= '''-- Regional Considerations --''' =
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