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spark length, bps, power, new formulas



Hello coilers,

I've been working on a more inclusive formula that attempts to predict
the spark length for a well built coil when the power input and bps are
known.  My original formula below was designed for coils running at
120 bps:


     Spark length (inches) = 1.8*sqrt power input (wallplug watts)


In my work, I've found that coils generally become less "efficient" as
the break rate is increased.  To allow for this, I now made a new
formula which takes bps into account.  (I'm defining efficiency here 
as the ratio of power input to spark length, which is of course not a 
true engineering definition.) 


     Spark length = 5.8*sqrt power input / 4th root of the bps


Again the units are inches and watts.  This formula may work well
for a range of bps's from 120 to 480 bps.  It may work for break rates
outside that range perhaps.  The 4th root can be found easily by 
pressing the sqrt button twice on a normal calculator.  It would appear
that doubling the break rate gives only about 1/2 the benefit that
doubling the bang size gives, and the formula takes this into account.

In a related issue, I suspect that spark length does not exactly follow
the square law for spark length vs input power.  This may cause the
formulas above to underestimate the spark lengths of very large coils.
In an attempt to correct for this, I made another formula that takes into
account the power input and bps, and provides a sliding correction as
the coil size increases:


  Spark length = (3.9*16th root of the power input*sqrt power input) /
  4th root of the bps.


Again the units are in inches and watts, and the range is from 120 to
480 bps.

It must be realized that async rotaries give a true break rate that is
lower than the calculated bps, because all the gap presentations do
not actually fire.  The 16th root can be found by pressing the sqrt
button 4 times on an ordinary calculator.  The MS Windows program
also contains a calculator that will find these n th roots directly.

A similar result can be obtained by making a table of various factors
for different sized coils which can be used in conjunction with the
original simpler formulas, but I prefer the idea of a single formula that
can handle the calcs for all coils.  Thus, I used the multi-root approach.
The use of these roots may cause a certain "non-linearity" in the 
results, but should be basically OK.  I'm not a mathematician.  These 
formulas are all empirically derived from the analysis of my coils and
the coils of others.  In some cases, I did not have many data points to
work with.

The two newer formulas above have not been fully verified on my coils
because I do not have the room to build a large coil.  These formulas
should not be considered to be exact, but rather to be a guide for
predicting and understanding TC behavior.  In a worst case the final
formula may result in a 10% error, but should usually be accurate to
within 5% for a well designed and built coil.  Further experiments may
perhaps indicate a need to revise or improve the formulas.  A charging
efficiency of 84% is assumed for 120 bps.  Lossy gaps or other 
components, poor charging efficiency, or poor coil design may prevent
a coil from performing in accordance with the formulas.  Let me remind 
newbies that NST's can often draw much more than their rated input 
power.

These formulas do not consider the effects of wire size, types of gaps,
toroid size, primary surge impedance, etc.  For this reason, the
formulas are only a guide.  Many guidelines exist to help in the
selection and design of specific TC components, many of which I and 
others have discussed in prior postings.  For this reason, these formulas
are only a guide.

Comments?

Cheers,
John Freau