Hi Kitestrings,
In answer to your previous question, about prop matching, the details are important as you can see. One thing that helps the mental block is to convert the tip-speed ratio into angle of attack of the blade tip. Then it gets easier to see what's really happening to the blades (from stall to runaway) which I find easier to picture in my mind.
Take an airfoil profile whose angle of attack at stall is 15 degrees. Let's use it on a wind turbine whose TSR is 7:
TSR comes from the ratio of blade turning velocity to incoming wind velocity, Vr/Vw=X
Draw that as a triangle, and each is one side of the triangle, and the relative wind is the hypotenuse.
In other words...
if X=3 then for wind=10mph a 6' blade will turn 70 RPM
if X=7 then for wind=10mph a 6' blade will turn 160 RPM
if X=14 then for wind=10mph a 6' blade will turn 320 RPM
While doing trigonometry, we have the ratio we need to find the angle of the incoming wind:
atan(1/X) = atan(1/7) = 8.1 degrees
Okay, the blade is
designed to work at TSR=7 or 8 degrees angle of attack, but if it runs unloaded, the thing spins too fast...
atan(1/X) = atan(1/14) = 4 degrees
And if the generator load is too great, then it's forced to turn slower...
atan(1/X) = atan(1/3) = 18.4 degrees
That angle is greater than the airfoil's stall angle, and the blade will be stalled.
The stall actually starts near the root and works its way out so this blade is deeply stalled when forced to turn so slowly.
You want to match a generator to the blade in this example? Then pick a point, say... 200 RPM and Dave's generator can generate 200W without and 250W with capacitors.
The output comes from a mechanical efficiency of the generator of roughly 50%
NOT KIDDING DAVE so need to have 400-500W mechanical input on the shaft.
If the blades run at a Cp of about 0.30 (you'd be doing well) then the incoming wind power needs to be between 1330-1670W.
With blade radius 6 feet as said before, diameter is 12 feet. The wind through the swept area needs a velocity of 13-14 mph.
Check the TSR with that wind speed, radius and RPM... X=6.4 which is not bad at all. We have a match. With or without capacitors doesn't matter much.
Walk a little further up the power curve....
350 RPM: 350W without capacitors, 700W with them
mech efficiency will be less, 40% so we need 875/1750W shaft power, respectively.
Same blades so same Cp: 2900W/5830W wind power through the disk
wind velocity through that swept area has to be 17mph without / 22 mph with capacitors
That means the TSR that it will run at is actually X=8 without caps or X=7 with them
Not bad at all.
Hard to extrapolate from the data at hand, but you can see the TSR getting higher as the wind speed gets stronger and the turbine turns faster. This is where the matching comes in and apparently Dave's got a scheme that improves this match by keeping the TSR down closer to the design speed in higher winds.