Swept Area and Rated Power
The power output of a wind turbine is directly related to the area swept by the blades. The larger the diameter of its blades, the more power it is capable of extracting from the wind.
Rotor Diameter – This number is listed on most wind turbine spec sheets. It is simply the diameter the blades cover.
Swept area –This refers to the area in square feet of the rotor. It is also called the ‘capture area’.
pi x Radius² = Area Swept by the Blades.
Now let’s go over the basic relational facts surrounding wind power and what they mean to you. Some of these things have been mentioned before but we will look at them as a package.
Energy in the wind is not linear. Double the wind speed and the energy increases not by double but by a factor of 8. As speed increases the power is increased by a cube factor.Calculate wind energy at 10 mph vs 20 mph
10 x 10 x 10 = 1,000
20 x 20 x 20 = 8,000
Energy captured by the rotor is linear. If you double the swept area, you double the amount of energy it can capture. This means if we want to compare similar turbines, we need to use the formula to get the swept area if the rotor diameter is different. Let’s double the rotor diameter and see what happens to the swept area.
Calculate a 10 foot vs a 20 foot rotor diameter
10 foot diameter = 5 foot radius
20 foot diameter = 10 foot radius
Using the formula
pi x Radius²
3.14 x 25 = 78.5 square feet
3.14 x 100 = 314 square feet
The rotor diameter doubled in size but the swept-area increased by four times.
Let’s look at the difference that just one foot in rotor diameter makes. Calculate the difference in a 9 foot vs 10 foot diameter.pi x Radius² = swept area by the Blades
9 foot Diameter
3.14 x 20.25 = 63.6 Square Feet 10 foot Diameter
3.14 x 25 = 78.5 Square Feet
A one foot increase in diameter yields a 23% increase in swept area. A wind turbine is all about harnessing wind energy and the most common way is to increase the area of collection. Now we have a starting point to view comparable machines.