As part of my ongoing survey of all things related to sustainable design (or renewable energy or simply “green” ) I have started to take a look at wind energy. Almost immediately I was confronted with Betz’ law which sets a limit on the efficiency of a wind turbine to about 59%. In other words, I won’t be able to collect and convert the kinetic energy of the wind at a rate better than 59%. When pondering the Betz’ law a few things struck me:
- Elegant- The derivation is fairly straightforward. The further removed I get from my academic skills the more my head starts to throb when I look at derivations but this one didn’t hurt! It even makes me think if ever there was something I could derive this might have been it. Too late, oh well….
- Dependencies: After a quick scan of the derivation it started to sink in that this efficiency was dependent on nothing. NOTHING! Come on… Carnot gave us the wiggle room of source and sink temperatures allowing us to reach for higher efficiencies, but with Betz there is nothing. Speaking of Carnot efficiency and extreme temperatures reminds me of an awful Keanu Reeves movie that still haunts me today. I can’t remember what it is called but after looking at IMDB I think it might have been Chain Reaction, which ironically is about a green alternative energy project. They were no doubt working on a revolutionary energy supply, but based on my recollection it looked like a large cylindrical propane tank with clear vinyl tubes coming in and out all over the place. I recall them discussing the temperatures they were pumping through this contraption and thinking that their real claim to fame was developing the tube that could withstand this temperature.
- What about fans?-After the shock of the Betz’ limit wore off I started to think about axial fans. I expected to find an elegant derivation for a fan but so far haven’t seen one. I wonder if fans are covered by the same limit?