Small Wind Turbine?

I often get asked why I don’t add a wind turbine to my off-grid home, or get asked for advice on small wind turbines for people hoping to generate energy when solar isn’t cutting it (like in Finnish winter).

Unless you have ideal situations (constant wind, no turbulence, high enough, open fields, etc.) you’ll be very disappointed with small wind turbines.

You’re dealing with two fundamental issues:
– The Betz Limit
– The Power in Wind equation

The Betz Limit is basically a theoretical number of the maximum efficiency you can possibly get. At most, only 59.3% of the kinetic wind energy can be used to spin the turbine and generate electricity. Remember this is a theoretical limit; in practice, you’re going to be closer to 40%.

The Power in Wind equation is given as:

P = 1/2 x ρ x A x V³

With:
P = power in Watts
ρ = air density (kg/m³, at about 1.2 at sea level)
A = Swept area of the blades (m²)
V = Velocity of the wind

So, no matter how good your turbine is, you will get in practice at most 40% of the wind energy converted to electricity. To capture the wind energy in the first place, you have two variables to increase (one in your control, the other not): swept area and wind velocity. The smaller you make the turbine, the faster you need to spin to make any meaningful energy. The only variable you control is the swept area, which means making the blades as big as possible.

Note that the velocity is cubed in that equation, so you’ll generate much, much less power at low wind speeds.

In other words, small wind turbines don’t work except in ideal situations because physics. That’s why commercial wind turbines are huge.

Let’s add a practical example calculation. Let’s assume we have a constant 10mph (4.5 m/s, 16km/h) wind and let’s take a ‘small’ wind turbine with a blade length of 2 meters, swept area becomes r² x pi = 12.5 m². Putting the numbers in the formula this gives:

P = 1/2 x 1.2 x 12.5 x 4.53 = 683.5W –> this is the theoretical available wind power.

Now, the actual efficiency μ is somewhere in the region of 30%. In every case, even a magical turbine, gives you an absolute maximum efficiency of 59.3% – the Betz limit. Let’s assume we have the highest real efficiency of the very best turbines – 40%.

This means that our small turbine has a maximum output of around 274W.

Let’s double the blade length to 4m. Thanks to the exponential in the area calculation, we get a swept area of 50m². Keeping everything else the same, we get a theoretical max power of 2734W, and a realistic output of 1100W. So, by doubling the blade length, we get a 4x power increase.

Now let’s increase the wind speed slightly. Assume we have a decent pole to put it on, and put it where we get a 15mph wind (6.7m/s, 24km/h). For our small turbine, we now get a theoretical power output of 2256W, or 902W realistic. For our larger turbine, we get a theoretical power of 9023W, or 3609W realistic. So by just having an additional 2m/s wind speed, we increase the output by a factor of 3.

Now, to put this into perspective: one of the smallest commercial wind turbines you can get today has a blade length of 7.5 meters. A typical 1MW turbine sits around a blade length of 30 meters.