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I liked the concise complete presentation of blade design Formulas as given under “workshop" at this site. And this below is from another list. I found this interesting to understand how the twist of propellers (water or wind or aircraft) is determined.

Offered by Mike.

I noticed mention of the quietness of the whisper 175 in a recent message. I don't know how many folks are carving their own blades, but years of experience in aircraft prop design have shown that the noise comes from curving vortices left by the blade tips. The pressure on one surface of the airfoil is greater than on the other, and the result is a spanwise flow of air around the tip from the high pressure to the low pressure zone. This turbulence causes noise. The greater the loading of the prop surface. Horsepower generated (in the case of windchargers) or horsepower absorbed (in the case of aircraft) the greater the flow around the tip. This is power lost, drag. The result of this is that the last bit of blade is doing nothing to contribute to power output on a windcharger blade, or thrust generated on an aircraft blade. This phenomenon is easily observable when a helicopter lifts off. As the pilot operates the collective, rolls on more pitch, the noise level increases tremendously. A chopper in hover makes a lotta racket. It is also pretty obvious when you hear a high powered aircraft take off. Blade loading is pretty directly linked to noise level, thus oversize blades will do a great deal to reduce load. Obviously if a wind charger is RPM regulated by loading the generator it will always be noisy. The old Jacobs chargers with their mechanical blade governors weren't especially noisy.

Model aircraft builders are it would seem always at the bleeding edge of aviation. Check out some of their websites if you're curious about the latest and greatest ideas. These guys have for many years been modifying their prop designs, the result being the highly efficient double and triple pitch props. Aircraft props are described by pitch in inches and diameter. Pitch in inches is simply the distance a prop would theoretically screw itself through a solid. It is derived from the angle of the prop at any given point and the circumference at that same point. If for example your diameter at some point on your prop is 24", and the angle of the blade were 45 degrees (unlikely) the pitch would tan (45) * circumference. Tangent of 45 degrees is 1, and the circumference

(PI * 24) = 75.39 1*75.39 = 75.39 (pitch in inches)

If the angle were 20 degrees tangent would be .3639 and the pitch in inches would be 27.44. Obviously using this formula in reverse allows you to get the correct angle at any point on a blade to make it operate properly along it's length. This is how twist is calculated. If you are optimizing for a wind speed of 10 mph you must translate that into inches per minute and calculate pitch accordingly.

10 mph = 52800 feet per hour = 880 feet per minute = 10560 inches per minute.

If you then decide you want a prop RPM of 900 you divide by that figure and the resulting geometric pitch is 11.73 inches of pitch. The issue of sound reduction was where I was headed if I remember correctly. Since your outer 3 or 4 inches of blade are doing nothing anyway due to the spanwise flow, the dodge modelers have used is to reduce pitch in this area. If you reduce the pitch here to where the tips are not trying to develop power, then the spanwise flow diffuses over the trailing edge as there is no pressure differential between top and bottom of the blade at this point to keep spanwise flow going. The result of this is improved efficiency and quietness. The same technique more or less is used on some aircraft wings and does the same thing as the little winglet you see on some aircraft. One would expect that reduced pitch would reduce the power produced by a blade, or the thrust if we were talking about aircraft, but this is not the case. The efficiency actually improves.

If you are interested in spreadsheets which cover pitch as related to wind speed and RPM, and spreadsheets that will allow you to calculate the blade angle at intervals along it's length for a given pitch, I have downloadable spreadsheets on one of my web pages. It should be noted that these spreadsheets are set up for aircraft propellers, though they can be easily modified to give the results we want for windcharger props. The pitch/angle chart and the airspeed/RPM/pitch chart were originally made up for windchargers. Nothing is locked. To get the desired results simply change the row and column figures to reflect the RPM and airspeed you are designing for if they are not shown. Excel format.

Stone Tool