Tesla Coil Optimun Parameters (was Wire length,resonance, Q)

From:  terryf-at-verinet-dot-com [SMTP:terryf-at-verinet-dot-com]
Sent:  Thursday, May 28, 1998 11:53 AM
To:  tesla-at-pupman-dot-com
Subject:  Re: Tesla Coil Optimun Parameters (was Wire length,resonance,  Q)

        As one who lives in both the theoretical and practical world of
Tesla coils, I must disagree.  

First your statement "Tesla coil design is empirical meaning both theory and
test results are required."  My dictionary defines empirical as "relying or
based solely on experiment and observation rather than on scientific

Empirical observations are collected and charted as a predictor when one has
no idea as to the underlying principles involved.  I submit that there a few
things we cannot predict about Tesla coils by calculation based on
principles.  The few remaining "mysteries" are being solved very quickly and
will soon be understood.  The following is a list of what can be found by
calculation or computer simulation to very good accuracy.

Primary coil inductance. - Wheeler's formula is based on empirical data but
modern computer simulations can find the same numbers using known principles
Secondary coil inductance. - Wheeler's formula is based on empirical data
but modern computer simulations can find the same numbers using known principles
Secondary coil self capacitance. - Oops! That one is still based on
empirical data :-)  I bet it won't be for long.
Coupling coefficient. - This solution has not yet been publicly released.
Primary resonant frequency.
Secondary resonant frequency.
All neon transformer and control circuit parameters.
All primary currents and voltages as a function of time.
All secondary currents and voltages as a function of time.
Basic spark gap operation.
Electrostatic fields and breakdown. - Can be modeled by computer although
few coilers do.

Here are the remaining things to be discovered:

The exact nature of the self capacitance.  This will be solved soon.
Spark gap quenching principles. - This is probably months away from being
The exact nature of how the output sparks affect the system.
The impedance that Tesla coils need to drive to get good sparks.
The dynamic impedance of the output sparks.

        We are very close to being able to design Tesla coils "on paper" to
produce the sparks we want efficiently.  I believe, within a year or so, the
last remaining problems will be pretty much solved.  When they are, a
computer could build and test more coils overnight virtually than we all
could build in our lifetimes.  BTW my latest models use 14th order
differential equations.  Of course, the computer does all the work but those
equations could be printed out with a few days work and a ream of paper. :-)

        I certainly do not mean to disregard the excellent work you and
others have done in collecting Tesla coil data.  For a long time it was all
we had.  However, the "era of mystery" surrounding Tesla coils is quickly
coming to an end.  We have, after all, been working on it for almost 100
years now!

BTW  Now that the theory of standing waves (1/4 waves) in Tesla coils is
falling apart.  I couldn't help noticing that your series of books are the
only ones I have that don't have 1/4 wave theory all through them.  I'll
keep yours! :-)
        I hate to think how many countless days have gone into trying to
figure out why Tesla coils don't match those theories well.  I, like most
others on this list, struggled for years on standing wave theory and never
could figure out why it never was quite right for Tesla coils.  At least
Tesla, who started it, had the same fun we all did with it. :-)  


        Terry Fritz


>From:  John H. Couture [SMTP:couturejh-at-worldnet.att-dot-net]
>  Jim, All -
>  Determining the optimum parameters for a Tesla coil is certainly a
>challenge. But why do it the hard (or impossible) way? The Corum's in their
>writings have shown the fourth order differential equations for Tesla coils.
>But this is a long way from ending up with a spark length output.
>  Tesla coil design is empirical meaning both theory and test results are
>required. We have the theoretical equations and can find the empirical
>equations based on tests. Why not set up some typical TC input parameters
>and do the calcs that will end up with a spark length. When the coils are
>built and tested if the spark length is different then change the empirical
>equations and calcs.
>  All complex engineering projects are done this way, including the design
>of locomotives, steamships, aircraft, space shuttles, etc. If enough coilers
>work on this type of empirical design program (manual or computer) and build
>and test enough coils we would soon have an acceptible method of determining
>the TC optimun parameters. Computer programs like the JHCTES are a start in
>this direction.
>  John Couture
>At 10:00 PM 5/25/98 -0500, you wrote:
>>From:  Jim Lux [SMTP:jimlux-at-earthlink-dot-net]
>>Sent:  Monday, May 25, 1998 10:39 AM
>>To:  Tesla List
>>Subject:  Re: Wire length,resonance, and Q (fwd)
>>>  > Going forward;
>>> > This thread is always interesting when it comes up from time to time.
>>The big
>>> > question which I keep asking myself is, "What are the optimum
>>parameters?" as
>>> > John hinted towards. I wonder if there is really is an optimum. It
>>appears that
>>> > each coils optimum setting is unique to the geometry, size, power
>>levels, ground
>>> > plane, and a host of other variables.
>>> > 
>>> They are pretty conflicting: A high secondary reactance to yield a 
>>> high voltage, a low secondary reactance to yield a high current. 
>>> Using a large top C removes the burden of the low reactance 
>>> requirement from the resonator itself. However, Vout can only reach 
>>> what Es and top C will allow.
>>Of course, "optimum" implies that there is some attribute (or combination
>>of attributes) that one wants to maximize (or minimize). Just what might
>>that be? Given most comments, I suspect that what people want out of their
>>coils is long sparks.  
>-----------------------------  Big snip
>>My gut feel is that the dimensions of a typical coil are so tiny compared
>>to a wavelength, that the lumped approximation should be more accurate.
>>This is good, because it means we can do the calculations of leader growth,
>>etc, using a fairly straightforward set of differential equations, which
>>can be numerically integrated.