Although spark length is really directly related to power, not
potential, it does require a high potential to begin the ionization
process, so the basic idea is to apply the equation for potential
in an air coil inductor:
It seems to require "both" power "and" potential for the optimal
sparks. There are very high voltage coils that perform poorly and
there are very powerful coils that perform poorly. But high voltage
powerful coils do very well. This problem shows in ScanTesla's
streamer length predictions if one uses parameters that are not
"typical". The program does do it fairly well now in most cases by
combining power and potential together to come up with leader length
and strike distance. It is not perfect yet or anything, but there
are no giant obvious errors now. I also have plenty of fudge
factors to fix the remaining small errors :o))
.......
The rate change of current, dI/dt really depends on a number of
efficiency factors such as spark gap resistance, primary connection
resistance, etc. We use 4 AWG welding cable with copper battery
lugs for our primary connections (inside tygon tubing) and use 3/4
- 1 inch dia. copper pipes for our sparkgap thus keeping the
switching (dI/dt) value high as possible in current and fast as
possible in quenching time of the sparkgap). High current (the dI)
and fast speed (the dt) is important.
From the old post at:
http://www.pupman.com/listarchives/2006/Aug/msg00201.html
At t~0:
dI(t)/dt = Vfire x SQRT(Cp / Lp) x 1 / SQRT(Cp x Lp) x COS(t /
SQRT( Cp x LP))
If t ~~= 0 and with some simplification we get:
dI(t)/dt = Vfire / Lp
dI/dt is really almost totally "independent" of losses!!! What
losses do is "eat up all the power" before it turns into streamers
by destroying the primary system's "Q".
Qp = SQRT(Lp / Cp) / R
R (losses) kill primary "Q", not primary dI/dt.
It is very interesting to note that the Q numbers for the SISG PIRANHA are:
Qp = SQRT(15e-6 / 165e-9) / 0.16 = 59.6
However, if it used a conventional gap where R = 3.0 ohms:
Qp = SQRT(15e-6 / 165e-9) / 3 = 3.17
It would not even run "at all" with conventional spark gaps!! Thus
my warning to "don't even try" to use that topology without SISG spark gaps!!
http://drsstc.com/~piranha/PIRANHA/PIRANHA.pdf
....
Assuming the average coil's efficiency around 70%, then the sec
voltage equation becomes:
Vsec = Vpri x 70% x SQR (Lsec/Lpri)
I've used antenna current x field measuring systems developed by
Terry Fritz (our super-duper moderator) and this equation is very close ---
usually within a few percent so it really does work.
Glad to know that number works for someone else too!!!! It is hard
to get independent verification of such things!
...
Cheers,
Terry
Happy coiling,
Dr. Resonance