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# Re: Sparklength inquiry

```> Original Poster: "Barton B. Anderson" <mopar-at-uswest-dot-net>
>
> Following a Vs equation; Vs = sqrt(Cp/Cs), Vs =
> sqrt(Ls/Lp), Vs = sqrt(2J/Cs), etc..
> If the efficiency is computed (Vs * eff.), then the
> energy available for the arc channels in watt/seconds
> (I'll call it Es?) should be:
> Es = .5 * Cs * (Vs * eff.)^2 / 1000.
>
> With BPS added, the equation should be the Energy per
> break (I'll call it Ebps?:
> Ebps = Es * BPS
>
> If John Cortures emperical equation for sparklength
> (Vs/1000/65)^1.43 has Vs replaced for Ebps, the
> sparklength in inches is equated as:
> Sparklength = (Ebps/1000/65)^1.43
>
> I was just playing with numbers, but strangely enough,
> this method matched my coil to my surprise. I would be
> curious if this equation matches sparklength for other
> coils.

If this equation matched your coil performance, I would say
that it's largely due to chance.  The first two equations
Vs = sqrt(Cp/Cs) and Vs = sqrt(Ls/Lp), are incorrect.
They should read Vs/Vp = sqrt(Cp/Cs) and Vs/Vp = sqrt(Ls/Lp),
respectively.

Also, efficiency does not affect the relationship between
Es and Vs, and  Es = .5 * Cs * (Vs * eff.)^2 / 1000
should read simply Es = .5 * Cs * (Vs)^2.

The equation 'Ebps = Es * BPS' is also not valid, since Ebps
has units of energy, and the quantity Es * BPS is in watts.
Power and Energy are routinely confused, it seems.

Finally, the equation  (Vs/1000/65)^1.43  is incorrect
for Tesla Coils, since both Vs *and* BPS are first-order
contributors to the total spark length of a real coil.

Sorry to nit-pick so much!
--

-GL
www.lod-dot-org

```