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TC RMS Conditions - was Voltage/Length etc. (fwd)
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From: John H. Couture [SMTP:couturejh-at-worldnet.att-dot-net]
Sent: Tuesday, February 17, 1998 2:59 PM
To: Tesla List
Subject: Re: TC RMS Conditions - was Voltage/Length etc. (fwd)
At 07:35 PM 2/14/98 -0700, you wrote:
>
>
>---------- 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:
---------------------------------------------- Big snip
>
>> 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.
-----------------------------------------------------
Finding the dt, eff, Is, and Rs is a problem and has to be estimated
using other information. I do not know how the three scientists made these
estimates. I show a graph in one of my books for the Rs parameter.
Apparently no else has done this before so comparisons cannot be made. The
graph was made using the equation
R = 6.283 x L/Q The Q factor is from Terman's Handbook.
JC
-------------------------------------------------
>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
--------------------------------------------
These two equations and others like it for Vs all give different answers
for the same coil. I show these equations in one of my books but was not
able to come up with the factors. To get around this problem I used
empirical data from real coil tests to make the JHCTES program.
JC
----------------------------------------------
>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.
>
------------------------------------------------------
Why don't you make a TC computer program using the above information?
JC
--------------------------------------------------------
>Antonio Carlos M. de Queiroz
>mailto:acmq-at-compuland-dot-com.br
>http://www.coe.ufrj.br/~acmq