Q&A: How would you calculate the theoretical power output of a Savonius wind turbine?

wind turbine blades

How would you calculate the theoretical power output of a Savonius wind turbine?
I built a small scale Savonius style wind turbine for a project. I can easily measure the power it puts out in a wind tunnel using a wattmeter, but how would I calculate the theoretical maximum power output? I want to use these two values to find the turbine's efficiency. Thanks!

Best answer:

Answer by gatorbait
According to measurements done in a wind channel3, the maximum power of a 1-barrel Savonius rotor can be calculated with the following formula:
Pmax = 0,18 · H · D · v³ [W]
If we take into consideration all the efficiencies of the system (rotor approx. 50%, transmission device approx. 90%, car alternator approx. 50%), the maximum power of a 1-barrel Savonius wind generator will be (H·D = 0,94 m²):
Pmax = 0,08 · v³ [W]
Note: to get the power in watts [W], the wind speed v has to be introduced in meters per second [m/s] and the height H and the diameter D in meters [m].
The following table shows the maximum power and the optimal rotation speed of a Savonius wind generator for different wind speeds:

Ref: http://www.amics21.com/laveritat/savonius_generator_english.pdf

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One Response to Q&A: How would you calculate the theoretical power output of a Savonius wind turbine?

  1. Rudydoo

    Hey Drew, Gatorbait is on the right track, but the formulas in Mr. Voneshen’s publication cannot be used for a savonius turbine.

    First, the actual formula originally derived by Albert Betz was this:

    P = .5 X rho X A X V^3

    P is power in watts
    rho is the air density in kg / cubic meter
    A is the swept area in square meters
    V is the velocity in m/s, which is cubed to get the final power.

    This is the actual formula to find theoretical power available in a moving column of air. There are lots of hybrid formulas, such as the one Gatorbait references. Mr. Voneschen’s instructions use one that takes air density at sea level times one half, then converts it to a constant to adjust for the fact that he is using Diameter instead of swept Area. That’s fine, as long as you are using a horizontal turbine. With a vertical, or savonius, the diameter means nothing, because the area can be changed dramatically with a taller or shorter barrel. It is the area of the rotor that the wind sees that must be used for power calculations. Once Mr. Voneschen finishes his discussion, showing a diagram of a horizontal turbine, he then goes on to show you how to build a vertical one, so the hybrid formula no longer applies.

    The other problem is the efficiency he is using. The best modern turbines that science can build today run in the 25 to 35 % efficiency range, and they are all horizontal. Albert Betz correctly calculated that the best ideal efficiency any turbine could ever reach is a theoretical limit of 59%. The horizontal types have horrible efficiencies, generally in the 5 to 8 % range. The reason for this is that most of the torque developed by the downwind blade is used to push the upwind blade back into positon, so very little is left to actually push the generator. It is this reason that no commercial applications of these devices are built today. I think Savonius rotors are neat, as do most of creation, but besides turning a wind chime in the garden, or running a small pond pump, they can’t really do anything for us. In Mr. Voneschen’s instructions, he is using 50% as the “rough” efficiency of the home made barrel rotor. Even the very best horizontal units today do not come close to this level of efficiency, a good quality well engineered savonius rotor won’t be within one tenth of this level.

    We’ve been powering our home for 11 years now with the wind and sun, and the last 5 years or so I’ve been teaching renewable energy seminars in the local schools. In my experience, there are two things in vast supply when you get into wind power, wind, and missinformation. My suggestion is to go to the source and don’t waste your time asking questions to hacks like me online. When your turbine is finished, if you can get it to run well in a wind tunnel, get some good watt readings, then go to the American Wind Energy Associations website and do your calculations for theoretical power available, and it will be simple math to come up with your efficiency. Don’t be dissapointed by the results, if you can reach 3 or 4 %, you’re doing really well. Take care Drew, Rudydoo

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