Lithan said:

**WOOOT Read since87's post REAL REAL slow this time, and I can understand the HOW. But I still want to know the WHY. Can you maybe drop me some hints as to what books/chapters in books I'd find this stuff in? I've got a high school physics and I can probably get a college physics year one book. Or anything I could grab at the library. **

My textbook for this stuff was

Engineering Circuit Analysis.
I'm not sure how easy it'll be to get at a public library. Any book on basic electronics is likely to cover this stuff though.

What we're discussing here is a simple voltage divider composed of a voltage source (+12V to Ground) and two resistors. (A fan and a rheostat) All three are connected in a series loop.

The equation to calculate the voltage where the two resistors connect together is:

Vr1 = Vin * ( R1 / (R1 + R2) )

Where:

Vin is the voltage of our voltage source. (12V)

R1 is the resistor connected to ground.

R2 is the resistor connected to +12V.

Vr1 is the voltage drop across R1.

A brushless DC fan doesn't actually behave like a resistor, but it's a close enough approximation to get decent numbers. To get the "resistance" of the fan just use Ohms law:

V = I * R or R = V/I

So:

The fan's "resistance" = 12V / (The fan's current draw at 12V)

We'll call the fan resistance R1. At this point we know Vin and R1 of the voltage divider equation. We can either select a value for R2 and calculate Vr1 with the basic voltage divider equation:

Vr1 = Vin * ( R1 / (R1 + R2) )

Or we can select the voltage we want across the fan ( Vr1 ) and use the following version of the same equation to calculate a rheostat setting that gives us the desired voltage.

R2 = ( Vin * R1 ) / Vr1 - R1

To get the equation:

Prheo-max = Pfan12 / 4

I used a shortcut called

The Maximum Power Theorem. Simply stated this theorem says that the rheostat will be dissipating the most power when its resistance is the same as the fan resistance.

Knowing that the maximum power draw of the rheostat would be when both resistances were equal, I used the following equation relating voltage and resistance to power:

P = V^2 / R

Suppose the fan resistance is 10 Ohms. With the fan running at 12V:

P = 12^2 / 10 = 14.4 Watts.

Now suppose we put another 10 Ohms in series representing the rheostat:

P = 12^2 / 20 = 7.2 Watts.

But of those 7.2 Watts, half are being dissipated in the fan, and half are being dissipated in the rheostat. The maximum dissipation in the rheostat is 3.6 Watts.

So the maximum power dissipation in the rheostat is 1/4 of the dissipation of the fan when it is running at 12V.

Lithan said:

**With two fans MORE voltage must get to the fans or else they will dip below startup voltage and NOT spin. This is bad. So you get a weaker Rheo which at its highest resistance still does not resist current enough to stall the fans.**

It would be more accurate to say that, "Two fans in parallel will draw twice the current of a single fan for a given voltage. To get the same voltage across two fans requires the resistance to be half that of the single fan case."

Aside from that nit picking, yep you've got it.