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Re: TC RMS Conditions - was Voltage/Length etc. (fwd)





---------- Forwarded message ----------
Date: Sat, 14 Feb 1998 23:11:51 -0700
From: "D.C. Cox" <DR.RESONANCE-at-next-wave-dot-net>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: TC RMS Conditions - was Voltage/Length etc. (fwd)

to: Antonio Carlos

Is the spark equation "everything in the brackets raised to the 1.43
power"?  It didn't come across clearly on my e-mail.

DR.RESONANCE-at-next-wave-dot-net


----------
> From: Tesla List <tesla-at-pupman-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: Re: TC RMS Conditions - was Voltage/Length etc. (fwd)
> Date: Saturday, February 14, 1998 7:35 PM
> 
> 
> 
> ---------- Forwarded message ----------
> Date: Sat, 14 Feb 1998 00:12:57 -0800
> From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
> To: Tesla List <tesla-at-pupman-dot-com>
> Subject: Re: TC RMS Conditions - was Voltage/Length etc. (fwd)
> 
> John H. Couture wrote:
> 
> > This means that in the TC transformer the electrical
> > energy can be stored in the TC primary capacitor on a continuous basis
but
> > the energy in the secondary is released in short pulses of sparks on a
> > RANDOM basis . A drawing showing this condition is in several
publications
> > including my Tesla Coil Construction Guide.
> > 
> >   This type of electrical operation means that power can be magnified
by
> > changing the time intervals in the primary and secondary circuits .
This
> > type of power magnification occurs in many kinds of electrical devices.
> 
> I agree with this.
> 
> >   The Tesla coil primary energy (Jp) equations per break are:
> >      Joules = input watts (continuous)/breaks
> >      Jp = .5 Cp Vp^2 x eff
> > 
> >   The Tesla coil secondary energy (Js) equations are:
> >       Js = Jp/dt = sec  watts (instantaneous) x eff = Vs x Is = Is^2 x
Rs
> >       Js = ,5 Cs Vs^2 x eff
> 
> For an evaluation, I need to know what are dt, eff, Is, and Rs.
> 
> Some equations:
> The time T for complete energy transfer from the primary to the secondary
> tank can be computed (from a previous post), using a lumped model with
low
> k, as:
> 
>               0.5              1
> T~=--------------------------*----
>          1             1       fr
>     ---------- - -----------
>     (1-k)^0.5     (1+k)^0.5
> 
> Where k is the coupling coefficient and fr is the resonance frequency
(Hz).
> This is the ideal quenching time for the spark gap.
> The maximum output voltage would be (*1=primary; *2=secondary):
> V2max~=V1max*sqrt(L2/L1)*Factor
> or
> V2max~=V1max*sqrt(C1/C2)*Factor
> where Factor depends on the time constants L/R of both tanks, at the
resonance
> frequency (so include skin effect). For low k: 
> Factor~=e^(-T*(R1/L1+R2/L2)/4)
> This gives the efficiency of the coil. This factor is not simple to
evaluate, 
> since R1 includes a linear approximation of the spark gap, that is rather
nonlinear.
> The maximum voltage does not depend on the break rate.
> The maximum spark length depends, because power is needed to keep a hot
> spark channel. The coil must only generate enough voltage to keep the
current
> in the spark, and enough power to keep the spark hot.
> 
> >   The Tesla coil secondary voltage and spark length equation is:
> >        Spark inches = (KVs/65)^1.43
> 
> This equation can be used to determine how much voltage is required for a
> given spark length, but how to compute the power required to keep the
> spark channel?
> The maximum energy available at the secondary, T seconds after each break
is:
> E2max=0.5*C2*V2max^2
> and so the maximum power available to keep sparks, assuming breakout
> at the peak voltage, is:
> P2mean=E2max*Fb
> where Fb is the mean break frequency (the break rate is somewhat random,
> as you wrote).
> An useful empirical equation to obtain would be:
> Mean expected spark length=function of V2 and P2.
> Both parameters are important, since voltage alone produces thin, cold
sparks,
> and power alone without voltage results only in heat.
> 
> >   What is your explanation of how the energy and power is utilized in
the
> > Tesla coil, input watts to spark length?
> 
> See above.
> 
> Antonio Carlos M. de Queiroz
> mailto:acmq-at-compuland-dot-com.br
> http://www.coe.ufrj.br/~acmq
>