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0.5*C*V*V vaild? (Was Output Voltages and Voltage/Length)


From:  D.C. Cox [SMTP:DR.RESONANCE-at-next-wave-dot-net]
Sent:  Saturday, February 07, 1998 12:46 PM
To:  Tesla List
Subject:  Re: 0.5*C*V*V vaild?  (Was Output Voltages and Voltage/Length)

to: Mark

I concur with your accessment of the value of the energy equation and its
relationship to Tesla coil potential.  We measured 985 kV with a 9 ft.
spark (108 inches) which equates to approx 9 kV/linear inch.  Our break
rate was 400 bps.  These measurements also were accurate for a system
operating at 180 bps with a synchronous gap -- output was 510 kV in pulsed
mode and spark output was 5 ft. in typical Tesla running mode.  Although I
have great respect for the Corum's mathematical work I have yet to actually
see a measured system producing more than the energy equation would
dictate.  We still use 8.6 kV per linear inch as a reasonably accurate
measurement of Tesla output potential in most small and medium size systems
with spark lengths under 15 feet in length.



----------
> From: Tesla List <tesla-at-pupman-dot-com>
> To: 'Tesla List' <tesla-at-pupman-dot-com>
> Subject: 0.5*C*V*V vaild?  (Was Output Voltages and Voltage/Length)
> Date: Saturday, February 07, 1998 12:53 AM
> 
> 
> ----------
> From:  Mark S. Rzeszotarski, Ph.D. [SMTP:msr7-at-po.cwru.edu]
> Sent:  Friday, February 06, 1998 1:23 AM
> To:  Tesla List
> Subject:  Re: Is 0.5*C*V*V vaild?  (Was Output Voltages and
Voltage/Length)
> 
> Hello All,
>         I have stayed out of this voltage/length discussion until now,
but
> have really enjoyed the dialogue!
>         I have done considerable modelling of tesla coils and helical
> resonators, examining the theoretical voltage rise under non-breakout
> conditions.  I have also built a series of tesla coils with back-to-back
> LED's placed every 2 inches along the length of the coil with various H/D
> configurations to examine the voltage rise in these rather heavily damped
> coil systems.  Several observations are notable:
> 1.  The voltage distribution goes from a minimum at the base to a maximum
at
> the top when tuned to the quarter wavelength of the coil system, even in
a
> damped coil system.
> 2.  Adding a toroid or sphere to the top tends to linearize the voltage
rise
> somewhat, so that the turn-to-turn voltage stress is lessened especially
> near the top of the coil.
> 3.  If you want accurate measurements of the voltage at the top of the
coil,
> your probe better have very little capacitance.  I can visually affect
the
> LED voltage distribution of a coil from 6 feet away by waving a hand. 
This
> is in a heavily loaded, lossy coil system.  Measurements with a vector
> impedance meter on a coil without LED's demonstrate that the impedance is
> affected by moving about at distances of greater that 12 feet for a 16
inch
> tall by 4 inch diameter coil.  Typical oscilloscope probes have 10-30 pF
of
> capacitance, which greatly affects the readings unless you have a huge
coil
> system with a Csec of perhaps 10-20 times this or more.
> 4.  The Corum brothers suggest that the voltage rise in a helical
resonator
> can be rather astronomical.  I disagree.  My measurements of the maximum
> possible voltage at the toroid tend to agree with the equation:
> Vsec(max) = Vpri x SQRT(Cpri/Csec), or the equivalent:
> Vsec(max) = Vpri x SQRT(Lsec/Lpri), which is essentially the lumped
circuit
> model.
>         There is an interplay of energy storage between the capacitance
(1/2
> Csec V^2) and the inductance (L dIsec/dt), (as well as an interplay
between
> the primary and secondary systems while the spark gap is conducting).
> Trying to quantitate coil energy is fruitless, since it is a dynamic
system.
> In addition, when the sparks break out, the corona field around the
toroid
> adds significant capacitance to the system, thereby lowering the resonant
> frequency, (as well as adding another unknown capacitance quantity).  The
> intensity of the sparks depends on the available energy stored in the
> secondary during ringdown and the resonant frequency.
> Oscilloscope traces of firing coils demonstrate that the coil rings down
> completely between eack primary spark.  If the resonant frequency is low,
> this ringdown takes longer, and the spark ion paths persist a bit longer
so
> that they can be re-used during successive discharges, thereby
lengthening
> the spark.
>         I feel that any quantitation of voltage/length for a tesla coil
> should include specification of the number of breaks per second as well
as
> the resonant frequency, since these factors also play an important role
in
> determining what happens.  If you really need an equation, I suggest 8400
> volts/inch for a tesla coil.  Anything higher than this is speculative at
best.
> Regards,
> Mark S. Rzeszotarski, Ph.D.
>