I've been doing some mathematical modeling of faraday disk dynamos using equations found here:

http://www.geocities.com/CapeCanaveral/Hangar/5307/Principles.htm. The results are rather interesting. However, a certain assumption is made:

I have read that drawing current in opposite directions on the disk or drawing current from the entire circumference equally will reduce/eliminate the back-torque on the motor. Has anyone been able to verify if this is true or not, and under what condition this works?

There appears to be an optimized value for generator speed that creates the highest net output power. There are several variables to consider in the equations I saw:

B = Field Strength on the disk

R = Resistence of the disk/brushes

r = Radius of the disk

f = Rotational speed of the disk

m = mass of the disk (proportional to (r^2))

T = back-torque ratio on the motor from induction

Through testing different values I discovered the following:

1) The maximum net power gain (maxgain, or output power minus input power) depends on: B, R, and m only (also T)

2) B, R, and m have an exponential relationship to maxgain (R=3rd power, B=6th power, m=2nd power) such that maxgain = (B^6)/[(R^3)*(m^2)]*(1-T)

3) For any given B and r, there is an optimal f, and the system has a COP of 1.5 at this level (ignoring backtorque) regardless of the other variables (although input/output power may change, it maintains the same ratio)

4) If you double r with B constant, then f = f * 4, and maxgain remains the same (no advantage)

5) If you double B with r constant, then f = f * 4, and maxgain is multiplied by 64x (advantageous)

What this really means is that you don't have to increase the radius of the disk to achieve the optimal power output. Even with a small disk, you can get the optimal power output by increasing rotational speed. Of course, there are practical limitations, so you might want to go with a bigger disk to decrease the rotational speed. You can increase net output power by reducing the mass of the disk while maintaining the same radius, or reducing the resistence of the disk/brushes (can also cover a larger % of the disk surface, which should reduce T and R as well). However, the largest gains will be made from increasing the strength of the magnetic field around the disk. If using permanent magnets, then B is relatively constant. What would be better perhaps is to use a solenoid; it won't demagnetize, you can control the magnetic field strength, and you get an exponential (current^6) increase in power (I think).

What are realistic values for these variables? (I am guessing):

B = 0.3 tesla (rare earth magnets sufrace gauss can be 0.4-0.5 tesla, with a small distance to the disk); higher value possible with coils

R = 0.010 ohms (disk surface + brush resistence; good estimate for 1 brush? Multiple or wider brushes in parallel should reduce this)

r = 0.1 meters (any value really, but we will say 0.1 meters (about 4 inch radius))

m = 1.64 kg (if disk is 1/4 inch thick and made of copper; ~2e-4 m3 of copper at 8230 kg/m3. A thinner disk will be lighter of course)

T = 0.5 (full edge coverage is said to reduce this to ~0.25; we will assume only half the surface is covered with brushes)

f = 0.291 rotations/sec (solved from program)

[Program Output]

Rotations/sec: 0.291

Backtorque: 3.76095586728108E-04

Current: 0.2742610386942

Efficiency: 3.00141330911077

NetPowerGain: 1.25483259804341E-04

PowerInput: 2.50612326923767E-04

PowerOutput: 7.52191173456216E-04

Voltage: 0.002742610386942

Extra power produced is negligable. However, if you cover the disk completely with contacts, reduce the thickness to 1/16 inch, and use higher grade materials, then:

B = 0.5

R = 0.001

r = 0.1

m = 0.41

T = 0.2

f = 51.76

Rotations/sec: 51.7579999999701

Backtorque: 132.197950536826

Current: 813.01276292819

Efficiency: 1.87498931555775

NetPowerGain: 176.261925203708

PowerInput: 352.529876943596

PowerOutput: 660.989752684129

Voltage: 0.81301276292819

You would gain 176 watts of extra power despite the backtorque, making the system over-unity. Hopefully there are no errors in my math. Would anyone like to verify it?