Lower voltage, bigger cap? 0.5CV^2 & Resonant Charging.

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Sent: 	Saturday, December 13, 1997 10:58 PM
To: 	tesla list
Subject: 	Lower voltage, bigger cap?  0.5CV^2 & Resonant Charging.

I am working on an 8" coil setup, and I have a few questions about
resonant charging and voltage levels vs. required capacitance.

I will be using only 9kV 60mA transformers (up to four of them) because
this was, at the start of my project 4 weeks ago, the only size
transformer I had available to me.  The other day, I went over to Gary
Lau's house, and was pretty impressed to see 45" discharges coming from
his system powered by only one 15kV 60mA transformer.  His system seems
to be very well optimized.

I thought for a while about why he is getting a foot more spark that I
am, at roughly the same power (~1 kVA) level.  I will admit here that my
project is in it's infancy (4th week) and A LOT of areas need
improvements, but something else came to mind: 0.5*C*V^2.  Upon examining
the relative energies in our two coils, I came up with a ratio.  Not
knowing actual gap & cap votlages, I used the main gap setting to find an
approximate firing voltage using the CRC spark gap tables, thus the
energy rating (joules) is probably not accurate (but this is not
important here):

Gary's coil (15kV xformer, 0.3" gap):  0.5 * 0.01uF * (10900)^2 = 0.594 J

My coil:    (9kV xformer, 0.18" gap):  0.5 * 0.02uF * (6750)^2  = 0.456 J

The ratio is: 0.594/0.456 = 1.3

If I divide Gary's coil performance of 45" by 1.3, I get 34.6", which,
curiously, is just about what my coil puts out at 120VAC input (36" max
to date -at- 130VAC in).

Does this suggest that since my transformer voltage is lower, I have to
make up for this by using a lot more primary tank capacitance- like
0.04uF or so? Sure looks that way to me.  With a large toroid, I could
still tune the coil with this much cap, and the energy figure would be
more like this:

0.5 * 0.04 * (6750)^2 = 0.911 J   ...will this give me 6 foot sparks?
Hmmm.

One last question- is there any advantage to matching a neon transformer
to the cap (to resonate) vs. using even more transformer power?  My
0.02uF cap is just about resonant with my 9kV 60mA transformer, but it
seems like if I add another transformer I could charge the cap faster and
hopefully get a two breaks per half cycle instead of one.  In reality,
when I add the second transformer spark length does indeed increase
considerably; from about 20" to 34-36".  So, if I increase my capacitance
to 0.04uF, I should be able to take advantage of using all four of my
transformers, right?

Sorry that was kind of long winded.