Wind turbines work by having the wind move blades and generate electricity via magnetic induction. This process is relatively simple when considering the complexity and apparent dissolution surrounding the wind energy industry.
With this in mind, there is a rather rigorous set of equations that go into calculating the maximum power output available for a wind turbine. Before we dive into the mathematics, lets break down the science a little bit.
From high school physics you may remember the equation Ke= ½ mv^2. This, in English, says that the kinetic energy of a given object is equal to one half its mass, times its velocity squared. So, for example, if we were to throw a ball that weighed 1 kilogram 10 meters per second (rather quick I do say), then its kinetic energy would be ½*1*10^2 = 50 joules (the unit for energy).
Just like the ball, air has an inherent kinetic energy, AND, when it is blown quickly, it has a higher kinetic energy. Makes sense, right?
So, in order to calculate how much energy a given wind turbine can generate, we must consider how much kinetic energy the air can transfer to the wind turbine, and spin the rotor.
If we step back, we realize that the amount of air that hits the wind turbine is proportional to the velocity as well. This means that the MASS is proportional to the velocity, and thus our energy from the air is proportional to the velocity cubed.
Additionally, because the total amount of power generated is related to the area that the wind turbine is exposed to, we know that the total power generated is proportional to the diameter of the propeller squared.
A fair amount of empirical (laboratory tested) work was done to determine that the maximum amount of energy that could be converted from a turbine is .59 the amount of energy going in. This is known as the Betz limit.
Combining all of these factors, and coupling them with the appropriate conversion ratios, we are able to come up with a formula for the amount of power generated by a given wind turbine.
P= 2.83* 10^-4 * D^2 * v^3 kW
Note that these units are in kW, kilowatts. Most people should be familiar with this unit as it is the standard by which we measure our electricity capacity. If you are more familiar with the term kilowatt hour, than you can think of a kilowatt as simply the total number of kilowatts hours divided by the total number of hours.
Thus, returning to our equation, you can see that by knowing the velocity in the area, we are able to calculate the maximum power output from a wind turbine.
It should be noted that it is very difficult to achieve efficiencies higher that 20%. Considering that the Betz limit for wind propeller efficiency is 59%, 20% is still close to half of the total amount.
For more information about wind potential in the U.S. take a look at:
http://www.wired.com/wiredscience/2010/02/better-wind-resource-maps/
And as always for all your wind, electricity, or energy news in general stay tuned to www.energygridiq.com
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