Hi Dave,

Warning: the following material contains geekiness which may be shocking to some.

The graph is the result of a self-education I gave myself on a subject called blade-element theory. If you read this page, you will get more of the context in which I created it:

http://www.sparweb.ca/1_Blades/Aero.htmlOnce I started making turbines, I found that I didn't really know what matched the power in of the rotor to the power out of the generator. Threads on Fieldlines written by the late Flux were very valuable to get me started, and I wanted to know more. I wasn't actually starting from scratch. In my day job, I'm an aeronautical engineer. I had been taught quite a bit of aerodynamics in school, so I had a lot to build upon. What I didn't have was a way to get a hold of a rotor that takes power OUT of the wind. All you get as an aero engineer is the mechanics of aircraft propellers that put power INTO the wind to create thrust. There are some crucial differences that made it hard to just open an aircraft textbook and point at an equation or a graph. If you take the graph of aircraft propeller performance, and try to plot a wind turbine rotor on it, usually you are below the x-axis and to the left of the y-axis, guessing how to extrapolate the lines in a region they weren't meant to. So I kept looking.

I found a number of excellent technical papers on the NREL website, which were written to teach the theory of WT rotor blade performance. Then the coin dropped. I was able to use what I'd learned before and write out the equations of propeller performance start to finish. I could take the input parameters of blade length, chord, twist, and so on and turn it into a performance curve for varying wind speeds and shaft speeds. I could control the mathematical model like the TSR is fixed, or the RPM is fixed.

This was the most useful result of that work. You can find this graph in lots of wind turbine textbooks, but I hadn't found any that did the full derivation before I did it for myself using those NREL papers.

It was RW Hamming who said

*"the purpose of computing is insight, not numbers"*. When I started plotting this graph, I finally had my moment of insight. The graph actually looks like the lift-curve of an aerofoil, which you might recognize, being a pilot yourself, but facing to the left not the right. On it you can see where the peak power of the rotor is, where it stalls, where it spins so fast it generates no more power... the perfect graph for power-matching with generators.

Power matching is where the black lines on the upper graph come in. The black line in the middle isn't a generator's power curve, it's the connection of peak power points of the rotor as the wind speed increases. If you were to build a generator whose shaft input power follows that curve, you would have built the "perfect" matching generator for those rotor blades.