Power Generated from a Wind Turbine
Darrick Lee, Owen Lu
Floor Location : S 182 P
Our project is focused on wind energy, and more specifically about the relationship between the size of the blade of a wind turbine and the amount of energy it produces in reality. Often formulas tend to mislead us because of their over simplification. We wanted to see how power is affected by different blade sizes at given wind speeds. Our hypothesis is that the largest blade will produce the most energy because of the total surface area swept however the power vs wind speed graph will be different from the generally accepted cubic function.rnrnPreceding testing and experimentation we created a model of a wind turbine with blades that could be easily replaced. The size of the blades were our main variable coupled with wind speeds produced by a fan which we assumed to be constant; we made 4 sets of blades (3 in a set) increasing in size but still proportional to one another in ratio and also angle towards the wind. A small generator was used to transform the kinetic energy from the wind into electrical power that can be measured with a voltmeter and ammeter in a closed circuit. We calculated the power produced by the wind turbine and compared it with the wind speed.rnrnAccording to our test results our hypothesis was partially correct because the power vs wind speed graph was not a cubic however, a major shock was the smallest blade generated the most power by far. The smaller blades produced more power with the same generator in comparison to the larger blades in every given speed we tested. When we used the large blades more energy was consumed by just moving the blade itself. However, even with this in mind the results we attained contradict the traditional formula. To get a greater sense of what was going on we compared the largest blade with the smallest blade and collected the angular velocity of each at the same wind speeds to quantify the rotations. As expected when the angular velocity was greater so the question arose "If the key to power generation is angular velocity why is it not directly mentioned in the traditional formula?". Regarding the shape of our blades through integration we created a new formula regarding power produced by a wind turbine that describes power as a product of the angular velocity multiplied by what we call the "blade constant" which is dependent on each individual dimension of a given blade and also the number of blades. We tested this formula because the division of any two theoretical powers should yield a ratio close to the power outputs observed. Using the lower speeds to reduce the effects of turbulence we found that our formula does not produce the same results as the traditional, in fact, it is closer to our observed values because it takes into account more factors that are specific to our blades. Our further studies indicate that our formula seems to be more accurate for this given experiment.