# [TCML] Break rate continued

bartb bartb at classictesla.com
Fri Apr 17 19:42:50 MDT 2009

```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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>
```