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Does Wind Turbine Blade Length Really Matter?

Courtesy of Orenda Energy Solutions Ltd.

Simply put: Longer wind turbine blade length means greater power production. Blades capture the wind which forces the rotation of the rotor; longer blades means more area for the wind to push against, which means greater force and rotational power.

However, how much difference does blade length make overall, in comparison to other factors?

There is a standard formula that can be used to apply the aerodynamic performance of the blade to the wind speed and the size of the blades. To calculate the amount of energy contained within the wind in a given area we start with the basic energy formula:

Energy = (1/2) x mass x velocity2

Air has a density of 1.23 kg/m3 so to determine the mass hitting our blades in any given second we can use the formula:

Mass/sec = velocity (meters/sec) x area (square meters) x density (kg/cubic meter)

Mass/sec = V x pi x blade length in meters2 x 1.23 kg/m3

Mass/sec = V x L2 x 3.86

Substituting this back into our original Energy formula we get:

Energy/Sec (Watts) = (1/2) x (V x L2 x 3.86) x V2 = (1.93) x (L2 ) x (V3)

A quick sample calculation of the total power that would theoretically be available in the swept area of a 51kW turbine with 9.2 meter wind turbine blade length and wind at 10 meters/second would be:

Watts = 1.93 x (9.22) x (103) = 1.93 x 84.64 x 1000 = 163,355

However, there is no way we can harvest all of the energy out of the wind. Why? The way we harvest energy from the wind is by slowing the wind down and removing some of its kinetic energy. Were we to remove too much of the energy, the wind on the downwind side of the rotor blade would be so slow that it wouldn’t move out of the way fast enough to make room for the incoming air – it would then begin to compress in front of the blades and blow off to the sides rather than through the turbine blades – essentially hitting a wall of stalled air. The theoretical limit of power that can be removed is called the Betz Limit and is around 59% of the available energy.
This would give us:

Betz limited power = 163,355 x .59 = 96,379 W

Of course, the blade efficiency, generator efficiency, friction losses, and electrical losses mean we can actually operate right now with somewhere between 50% and 60% of that theoretical maximum efficiency – leading us to right around 51,000 watts of power out of a 9.2 meter blade wind turbine system with 10m/s wind – which is exactly what the Orenda Skye™ 51kW system generates with a 9.2 meter wind turbine blade length.

One thing you may notice from the power output formula above is the relationship of swept area of the blades vs. wind speed. If you look closely, you’ll see that swept area has a square factor, while wind velocity has a cubed factor. This squared vs. cubed relationship is one of the reasons investigating the wind speed thoroughly at a proposed wind turbine location is of such importance. For example, doubling the blade length from 9.2m to 18.4m only increases the swept area by a factor of 4, from 265m2 to 1063m2, while doubling the wind speed from 10m/s to 20m/s increases power output multiplier by a factor of 8, from 1000 to 8000.

Therefore, one can easily conclude that finding a location with twice the wind pays off far better than buying a wind turbine with twice the blade length.