Analyzing a New Wind Turbine

Here’s what the inventor of a new wind turbine tells us in the video below:

He’s standing in a wind speed of 3 – 4 mph (let’s call it 3.5).

The device is 16′ high, and the blades start at 4′ of the ground; the blades are 4′ in diameter, meaning that the swept area (4 *12 = 48 feet²)

What he’s not saying is the power output, so let’s do the math.

Let’s reimagine the swept area of this rectangle as a circle, so we can find its radius and apply the wind power formula to it.

48 = πr², or r~=4

Now the formula: electric power is P = π/2 * radius² * velocity³ * air density ρ (usually 1.2) * efficiency factor (usually 40%), or P = o.oo4 KW, or 4W.  This means you’d need 40 – 50 of these to power your home refrigerator.  Nobody’s saying you can’t do it, but it would be a fabulously unappealing endeavor.