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Re: [TCML] Break rate continued



Hi Andrew,

It's good you want to calc the data yourself. Ok, examples are always best and were talking a rotary so let me use 4 electrodes on a disc rotating at 3600rpm and passing through 1 stationary gap. Lets assume a 12kV 30mA supply and a cap size of .01uF:

Presentations per revolution (PPR) is 4
BPS = (ppr x rpm)/60 = (4 x 3600)/60 = 240
Firing rate = 1/BPS = 1/240 = 4.167ms
1 time constant = Supply Impedance x Cp = (Vout/Iout) x .01uF = (12kV/30mA) x .01uF = 0.004s = 4ms
Full charge time = 5 x 1 time constant = 5 x .004 = 0.02s = 20ms
Time constant at gap conduction = (Firing rate / Full charge time) x 5 = (4.167ms / 20ms) x 5 = 1.04175s Effective cap voltage at presentation (Vc) = Vp x (1 - e^(-firing rate/1 time constant)) = 16.968kV x (1-2.7182818^(-4.167ms/4ms) = 10.981kV Percent cap is charged to Vp = 1-((Vp-Vc)/Vp) = 1-((16.968kV-10.981kV)/16.968kV) = 64.71% Effective primary energy (eJ) = 0.5 x (Cp x Vc^2) = 0.5 x (.01uF x 10.981kV^2) = 0.6j Power across gap over 1s (not including losses) = eJ x BPS = 0.6 x 240 = 144 Watt-seconds

Some of those equations may wrap around by the time it gets to the list. Anyway, try setting that up in a spreadsheet like Excel or whatever, then vary input values (cap, transformer, electrodes, rpm, etc.).

Note that this cap would do better with a 60mA supply.
These are just some basic calcs that are helpful when looking at a rotary.

Take care,
Bart


Andrew Robinson wrote:
Thanks for all your answers. Thats kinda what I figured but wanted to be sure. I dusted off the old calc and physics books to see if I could find some help. Does anyone remember the old capacitor charging calculations. They solved for charge as a function of time. Doing the differential equation I come out with:

q(t) = CE(1-e^(-t/RC)) where RC is the time constant tau. I think this is in reference to DC circuits though. I'm pretty sure the reactance and frequency play a role in the charging time. Since im guessing this equation is incorrect can you point me towards the correct equation to calculate the time it takes to charge the capacitor. From there I can determine the correct break rate for the RSG as suggested. I saw the JAVA calculator but im not crazy about using calculators like that. I really prefer to do the math myself so I understand the concepts behind it, not just plug in some numbers, shoot off to my local hardware store, and say hey look what I can do lol. Im not saying anything bad about the calculators out there. I think they are great! Great way to check your work. Just not my style.

Regards,
Andrew Robinson
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