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5 Watts for $25 Generator Calculations
Some aspects of the generator have already been determined. A preliminary budget was made and $8 was allotted for magnets (assumed purchased in large quantities). Sixteen magnets for $8 works out to be $0.50 each and the largest magnet I found in that price range was a 1" x 1" x 1/8" thick N42 neodymium magnet. It was decided that the magnet faces would be 3/8" apart to make room for a 1/4" thick stator and allow 1/16" per side for clearance. And, as shown elsewhere, a back plate of almost 0.10" thick was chosen leading to a magnetic field strength of about 0.42 T between the magnets where the stator would be located.
Two parameters to be established are number of turns of wire and wire diameter per leg of the generator. To get those parameters, the cutin speed (speed where the generator starts producing power) and coil resistance are required. The approach taken here is to overlay the generator power curve (the "consumed" line in the figure below) on a plot of the turbine power curves at various wind speeds. Then choose a cutin speed and coil resistance such that the generator power curve passes through the peaks of the turbine power curves; some compromise is usually required. In this case a cutin speed of 136 RPM and a resistance of 45 Ohms was chosen.
Two parameters to be established are number of turns of wire and wire diameter per leg of the generator. To get those parameters, the cutin speed (speed where the generator starts producing power) and coil resistance are required. The approach taken here is to overlay the generator power curve (the "consumed" line in the figure below) on a plot of the turbine power curves at various wind speeds. Then choose a cutin speed and coil resistance such that the generator power curve passes through the peaks of the turbine power curves; some compromise is usually required. In this case a cutin speed of 136 RPM and a resistance of 45 Ohms was chosen.
genpowercalcs.xlsx  
File Size:  118 kb 
File Type:  xlsx 
Power Curves
Many assumptions were made about the turbine, but one has to start someplace. It was assumed that the turbine would be a drag type. The relationship between speed and tubine power was assumed to be an inverted parabola with a peak at tip speed ratio (TSR) of 0.6 and a maximum TSR of 1.2. The peak efficiency was assumed to be 26%. Given this information, an equation can be written for turbine efficiency as a function of TSR. The plot shown above was generated by taking a particular RPM and windspeed, calculating the TSR and coresponding efficiency. The power available in the wind at that wind speed was multiplied by the efficiency to arrive at a power developed by the turbine.
To get the generator power curve, the battery voltage plus diode voltage drops was divided by the cutin speed to get a voltage vs. speed ratio. A given RPM was multiplied by this ratio to find the voltage developed by the generator. If it was greater than the battery and diode drops, the difference in voltages was divided by the resistance to determine the current developed. The generator voltage multiplied by the current gives the power required to drive the generator (consumed). The battery voltage multiplied by the current gives the useful power produced (delivered).
To determine the operating speed of the turbine, find the intersection of the turbine power curve and the generator "consumed" power. Then read straight down to the "delivered" curve to get how much power is actually sent to a battery.
To get the generator power curve, the battery voltage plus diode voltage drops was divided by the cutin speed to get a voltage vs. speed ratio. A given RPM was multiplied by this ratio to find the voltage developed by the generator. If it was greater than the battery and diode drops, the difference in voltages was divided by the resistance to determine the current developed. The generator voltage multiplied by the current gives the power required to drive the generator (consumed). The battery voltage multiplied by the current gives the useful power produced (delivered).
To determine the operating speed of the turbine, find the intersection of the turbine power curve and the generator "consumed" power. Then read straight down to the "delivered" curve to get how much power is actually sent to a battery.
Please Note: Information displayed on this web site in text and/or video form is for documentation purposes only. Nothing presented here should be considered professional advice or instruction. The visitor should follow safe procedures in their own projects and check all information for accuracy. Caleb Engineering, LLC is not responsible for any losses that may result from errors, misprints or display of improper procedure.