Concerning Efficiency

[PHinker]

I've been dinking with the various formula for calculating the amount of power extractable from the wind.  I've seen various folks post tables where they have a column for efficiency and was wondering what formula is used.

Windstuff Ed sometimes uses 0.00508 * Sa * V where 0.00508 is constant, Sa appears to be swept area (in square feet), and V is windspeed (in mph) cubed.  The formula I've been using from the AWEA site is :

P = 0.5 * rho * A * Cp * V^3 * Ng * Nb

P = power in watts

rho = air density (1.225 kg/m^3 at sea level, about 1.0583 where I am in Colorado)

A = rotor swept area in square meters

Cp = Coefficient of blade performance (.59 {Betz limit}, .35 is good)

V = wind speed in m/s (mph/2.24 = m/s)

Ng = generator efficiency (50% for a car alternator, 80% or more for a good pmg)

Nb = gearbox/bearing efficiency (varies, 95% is good)

So it seems that the theoretical peak would be something like:

P = 0.5 * rho * A * .59 * V^3 * .80 * .95

So for a 1 meter machine in a 30 mph wind the limit would be on the order of

910 watts using the above.  Using Ed's formula, it comes out around 970 watts so my guess is Ed's constant is assuming a different value for rho.

Is this what people use for calculating efficiency?  Thanks

[Flux]

The AWEA formula is fine, I suspect Ed's is the same if converted to metric.

The only real variable is Cp. Rho does change with altitude but not much.

Don't get too hung up on these formulae. Car alternators are not likely to be 50% efficient over much of the range. Even good alternators in the size you are talking about are not likely to hold 80% over much of the range if at all especially at 12v.

What is even worse is the fact that if you hold the alternator efficiency up you will reduce your chances of keeping the rotor on optimum tsr and Cp will likely fall to the point where the overall efficiency is worse unless you use an electronic speed load tracking system.

It is usually better to trade electrical efficiency to keep the rotor out of stall.

The difference between Ed's formula and the other one is neither here nor there when you consider the other variables.

Flux