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

To: tesla-at-pupman-dot-com
Subject: Re: TC RMS Conditions - was Voltage/Length etc. (fwd)
From: Tesla List <mod1-at-pupman-dot-com>
Date: Sat, 14 Feb 1998 19:35:08 -0700 (MST)
Approved: mod1-at-pupman-dot-com


---------- 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