RE: Spheres vs Toroids

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Godfrey Loudner" <ggreen-at-gwtc-dot-net> 


The empirical formulas are good enough for most tesla coils. Provided that
the
tesla coil components are up the standards specified by the formulas, you
can
expect good results with a little tuning. For coilers who want to see long
and
bright steamers, the use of advanced mathematics and long decimal expansions
is
totally unnecessary. The use of heavy mathematics offers the chance for a
deep
understanding of what is going on with tesla coils. If everything about the
macroscopic world of electricity and magnetism is hidden in Maxwell's
equations,
then a theoretical understanding of tesla coils might be possible. But one
obstruction to this dream is the high technical nature of the associated
mathematical problems. Finding exact formulas for everything in tesla coil
theory is
probably a practical impossibility. Probably what is needed is a high flying
statistical approach such as a Monte Carlo approach. A good statistical
model for a
tesla coil just might be possible. Suppose one had a proposed statistical
model,
then the accuracy of the model could be tested with long decimal expansions
derived
from known exact formulas. Computing Pi to 200 million places is used to
test the
reliability of advanced computers. Because of the complexities of computing
Pi,
any defect in software or hardware should surface. For the application of
calculus
to tesla coils, it is assumed that they are continuous in nature. Actually
they
are discrete. Then the tesla coils analyzed on paper do not exist. But the
assumption is that the early digits can be seen in experiments and will
match
the results of experiments. The further digits are physically meaningless
and
cannot be observed in experiments. So if we say that top load has a self
capacitance of 1/2^(1/2) pf, that is exact for that tesla coil on paper. But
only
the early digits of 1/2^(1/2) are presumed to be significant for the tesla
coil
that was constructed out of real materials. For those of us who tesla coil
on
paper, exact results are a coveted treasure. Of course, we know that the
exact
results are in reality only approximations to the real thing.

Godfrey Loudner


 >Hi All,
 >With most real world measuring devices only accurate to 3-5 digits, what is
 >the value of 20+digit accuracy in the calculation?

 >Matt D.