From my own scrap yard of math with many thinks to others on this board and beyond.
Its just a beginning
Wind Turbine
and
Generator
Formulas
for
Dummies
To find Voltage
N x A x R x B x P = V of each coil
N = number of turns of wire
A = area of one magnet in square meters (square inch x .000645 = sq meters)
R = revolutions per second ( 60 =1, 120 =2, 180 =3, 240 =4, etc..)
B = strength of magnet in Tesla (gauss / 10000) ( Neo in .5 - .7 est)
P = Number of magnetic poles
Three phase wire set ups
Multiply coil output by;
1.732 to get voltage output in Star
1.000 to get voltage output in Delta
To convert AC output to DC output
Multiply AC output by 1.4 to get DC voltage and then subtract 1.4v for bridge rectifier loss (real world equation seem to be more like ACv x 1.25 to 1.3 = DCv). Loss increases as voltage output increases.
Total equation (three phase star setup)
N x A x R x B x P = V x coils per phase = phase V x 1.732 = AC stator output x 1.3 or ( 1.4 then - 1.4v) = DC voltage est. output of generator
How much power is in the wind?
P = .5 * AD * (D^2 * .7854) * V^3
P = .5 * AD * A * V^3
P = .5 * AD * (sq. feet * .0929) * V^3
Where:
P = power in watts
AD = air density (RHO)( typically 1.22 at sea level )
D = Diameter of prop ( in meters )
V = Velocity of the wind ( in meters/sec )
A = swept area in square meters
Then (P) has to be Multiplied by blade eff. and generator eff. to get estimated useable wind power. P * BE * GE = WW
where;
BE = blade eff.
GE = generator eff.
WW = Windmill watts
If you know what your alternator/generator will do in watts, this one will help determine the size prop you will need to run it....
D = (P / ( Cp * rho / 2 * Pi / 4 * V^3 )) ^ 0.5
Where
D = Diameter of prop in meters
P = power in watts
Cp = overall efficiency ( typically .15 to .20)
rho = air density ( 1.22 at sea level )
V = velocity of the wind in meters/second
If you have a prop you plan to use, this one will determine the power output you can expect...
P = Cp * rho / 2 * Pi /4 * D^2 * V^3
To find the TSR ( tip speed ratio ) of a prop at a given output...
TSR = rpm * Pi * D / 60 / V
To calculate the rpm at a given TSR...
rpm = 60 * V * tsr / ( Pi * D )
Good idea
Adding a capacitor in line after the rectifier bridge to store power spikes so the battery has the opportunity to absorb the power made from the generator better.
Centrifugal Force:
.000341 * W * R * n^2
Where:
W = weight of outer ring
R = Radius in feet
n = RPM
Other formules to find wire turns per phase
17,000 x (System voltage + 1.4v) / (desired cut in speed RPM) / (strength of flux in Tesla) / (total area of magnet faces in square inches) = turns per phase