How do you calculate the amount of energy that a windmill produces?
This is a question that is often the focus of windmill science fair projects. The answer will help the student to determine if their hypothesis was correct or incorrect. In order to determine how much energy a windmill produces several factors have to be measured and evaluated.
The first component that you will need to measure and evaluate is the average wind velocity at the site of the windmill. This can be tricky to determine as wind speed and availability is not a constant. This means that you will need to calculate the average annual wind velocity for your site. This can be accomplished through the use of data supplied by a local, state or national weather service. For the most accurate results you will want to collect wind data for a number of years, at least five, and produce a five year average wind velocity.
The next step is to measure the blade diameter of your windmill. A diameter is the distance across a circle that passes through the midpoint of the circle. In a windmill the diameter can be measured by doubling the distance from the tip of one blade to the center of the turbine nose.
To calculate the amount of energy that a windmill produces in an average year in kilowatts, you will need to use this formula:
KWH/year = .01328(D^2)(V^3)
In this formula D stands for the diameter measurements of the windmill and V stands for the average wind velocity for the windmill’s site.
This formula can be used for a number of purposes. First of all it can be used to determine how much energy is produced by a windmill. This is accomplished by simply plugging in the measurements from your windmill. The second use is to predict how a specific manipulation will impact the energy produced. In this case you can first produce the normal kilowatts per year measurement for your initial windmill design, and then change either the diameter measurement or the velocity measurement to predict the changes in kilowatts per year.
The final use of this formula is to determine what measurements are needed to produce a specific kilowatts per year output. For example, if you need to power one house with your windmill it will need to produce an average of 10,000 kilowatts per year. If the velocity of wind at your house is 15 miles per hour then how long do the blades need to be?
To solve this problem just plug in the numbers that you know:
10,000KWH/year = .01328(D^2)(15^3)
10,000KWH/year = .01328(D^2)(3375)
223.1146809460062 = D^2
14.93702383160736 = D