Despite many setbacks, I've never given up on making a computer program that can predict the performance of a set of prop blades for any given set of dimensions, wind speeds, and rotational speeds. I suppose it's not important to most, because building your own windmill blades isn't really a mystery any more. Certainly Hugh Piggott has done a lot for hobbyists, including myself, to make it easy to find a set of parameters that work and are easy to make.

For me, using a "plug and chug" spreadsheet isn't enough, but trying to make my own analysis has always proved too daunting and I would give up. Last year, my interest was re-ignited by Jim Overington in New Zealand, with whom I had a stimulating exchange of e-mails and spreadsheets that came close to making the proverbial better mousetrap. The project wasn't finished, however, partly due to being away for holidays and also due to a disagreement on how to use airfoil data. While Jim preferred using numerically generated airfoil lift/drag plots, I insisted on using data from the old NACA wind tunnel tests. Due to these exchanges, I suddenly realized that my previous explorations of aerodynamic analysis failed because I didn't take into account the Reynolds Number that scales airfoil lift and drag up and down with size. A horrible error and it was making my previous results worthless. Scale models of larger things simply cannot get the same coefficient of lift as their full-size counterparts, and by using airfoils designed for airplanes, there is a huge penalty to pay.

Cracking open a book called "Airplane Aerodynamics" by Domasch, Sherby, and Connolly, I found an excellent and clear analysis of an aircraft propeller using a method called "blade element analysis". They took into account all sorts of important details in their analysis, all of which are also important considerations in wind turbine props, too. The biggest blockade to using their analysis at face value was the fact that aircraft propellers ADD power into the wind, accelerating the air, while wind turbines SUBTRACT power from the wind, slowing it down. The directions of some arrows on the diagram are reversed, and of course, the lift on the aircraft prop is on the front, while it's on the back of a wind turbine blade. I re-drew the diagram for the wind turbine case. Once that was done I could step through the algebra and discovered than any differences in the direction of the arrows would eventually be cancelled out and only a few "-" signs were necessary here and there to make it work correctly.

When the wind passes through the disk of a wind turbine, some of the kinetic energy in the wind is taken out. With less kinetic energy, the air streaming out the back of the wind turbine is slower. At the disk itself, then, the speed of the wind is half of that difference. Before I understood this, any time I did TSR calculations, I just assumed that the prop would see the same wind speed. This isn't true! The wind is slowed down slightly, making the TSR of the prop slightly higher than you would think. Often a prop turning at a seeming TSR=6 will actually be experiencing TSR=7 or even =8, right at the blades.

Hugh Piggott takes this fact carefully into account in his "blade design" spreadsheet. That must be why his blades work so well, so often, even for novice builders. Hugh's spreadsheet goes even further and makes sure that there is enough chord for the diameter and speed that the user desires. Without enough blade chord there would not be enough surface area for the lift to act upon to produce the torque. It is calculated in a quick and efficient way, too. Now that I've done the work myself I commend him for the thought and effort that was put into it.

Going through this process, I discovered to my horror that my 8-ft diameter blades were given the wrong twist! They were given too much twist and have the wrong angle of attack. I'd intended to have TSR=7, but actually they are more like TSR=4! I did not follow the Hugh Piggott guidelines and so I get what I deserve. I am glad that I did not repeat the error on the next blades, where matching the generator will be much more difficult.

I've finally reached the point that I can do just a bit more than Hugh's spreadsheet. With one program, I can match the generator's power curve to a prop for any TSR, diameter, chord, twist, and airfoil, in any wind speed. Here is an example:

Diameter = 8 feet Chord = 7 inches (root) Taper = 50% (tip) TSR = 7.0 Airfoil = NACA3415 Angle of Attack = 5 deg Material = wood Blades = 3 Altitude = 3000 feet

This graph has several lines plotted. The red lines are power. The lower red line is the power that can be developed in 30 kph wind when the prop is allowed to turn at different RPM's. The peak power of 330 Watts in 30 kph wind happens at 315 RPM. This means it has a peak Cp of 0.22, at TSR=4.8

I repeated the same analysis at 45 and 60 kph winds and plotted graphs for each. Then I went hunting for the peak values at many other wind speeds and plotted them as the blue line.

Any time that I find the peak Cp for a real prop, then remove the factors accounting for Reynolds number, the peak Cp shoots back up to nearly 59%. Now I can see that the small scale and slow speed of small wind turbines is the key factor preventing high performance. Larger wind turbines gain an advantage simply through their larger geometry.

The way this is plotted, it can be adjusted until it agrees with the plot of the generator's load and speed. In this example below, on the left you can see that the generator's load curve is just a bit less than that of the blades, making it a good match to the blades. It is very hard to make a generator this perfect (it's only a made-up example in this case). Beside it are generator and blade curves that do NOT match. That set-up will run too slow in low winds, and run away in strong ones.

There is one very important conclusion to be drawn from this: The selection of the blade's airfoil can become important, if the matching of the blade and generator are to be close. There are several classes of airfoils that are designed to sustain their good lift and low drag properties even at low Reynolds Numbers. After all this work it is now clear how valuable they can be. I have now come full circle. At the top of this article, I mentioned a disagreement between myself and Jim Overington about the true value of the airfoil selection. At the time, I downplayed it. It now should rise in importance in my mind, and I also owe Mr. Overington a debt for pointing it out.