[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: toroid question



Original poster: "Kurt Schraner by way of Terry Fritz <twftesla-at-qwest-dot-net>" <k.schraner-at-datacomm.ch>

Hi Godfrey,

in my opinion there is no need to deal with toroids, whose hole in the
center is <=zero, or very small, relative to the outer diameter. The
outer diameter is probably choosen in a relation to the size of the
secondary or to sparklength, in order to get a nice "shielding effect"
for corona (i remember John Freau proposing D.toroid=~"desired
sparklength"/2.5), or considering the whole TC in a Pspice-simulation
for output power and voltage. The diameter of the "cord" should be in a
relation to the secondary outbreak-voltage (remembering again John:
d.toroid = "desired sparklength"/10, as a start). But the ROC of the
torus will never be really perfect, even if having a spun toroid. And as
soon we get breakout, the toroid will no more be smooth anyway, 'cause
the streamers and sparks are like "needles", and the jon-cloud may be
adding capacitance. Personally i try to choose a ratio of diameters, -
not at all scientifically - , which gives me a good feeling about
proportions. And this is not one with zero inner hole radius, which
might typically be not much less than the cord radius.

Anyway i'm keen to see your approximation to the "true capacitance" of
an isolated toroid, probably with an estimation of accuracy. This seems
to me of great value, even, if after all, either we may find Bert Pool's
formula just good for our purpose or utilizing a more elaborate formula
in our calculations (i.e. spreadsheets).

Cheers,
         Kurt

Tesla list wrote:
> 
> Original poster: "Loudner, Godfrey by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <gloudner-at-SINTE.EDU>
> 
> Hi All
> 
> I did some calculations tonight to compare values of Bert Pool's formula and
> the exact formula for the capacitance of an isolated toroid. Let D and d
> denote the width and thickness respectively of a toroid. The results of some
> randomly chosen values are given below.
> 
> D = 1", d = 0.4", C(bert) = 1.06746pF, C(exact) = 1.18129pF
> 
> D = 5", d = 2",    C(bert) = 5.33731pF, C(exact) = 5.90647pF
> 
> D = 8", d = 3.5", C(bert) = 8.27814pF, C(exact) = 9.60177pF
> 
> D = 100", d = 8", C(bert) = 80.6557pF, C(exact) = 90.7548pF
> 
> Here are the values for a toroid that sold on ebay tonight for $175.
> 
> D = 16", d = 2",  C(bert) = 15.1408pF, C(exact) = 15.615pF
> 
> Bert Pool's formula is very good for some values of D and d. The idea of
> Bert's formula is to replace a toroid with a sphere of equal surface area.
> Then the capacitance of the sphere is tinkered up to agree with a table of
> measured values. A simple idea, but the result is quite powerful.
> 
> I've been playing with the exact formula. I'm not saying that C(exact)
> depends only on (D - d)/d, but the difficult factor of the formula does. The
> difficult part of the formula is an infinite series, and I have been trying
> to determine its rate of convergence. This means that I want to know the
> optimal number of terms, which have to be added to achieve a given accuracy.
> I was hoping to answer this question for all values of D and d such that (D
> - d)/d  is greater than 1 with an accuracy of 1 in 1,000,000. I have already
> derived an almost such formula for the number of terms, but it is definitely
> not optimal. Why add 15 terms when 5 will suffice. The problem seems to be
> very difficult. The mathematical difficulty comes from the situation when (D
> - d)/d is very close to 1 from above. The closer you get to a toroid with no
> hole in the center, the greater the mathematical difficulty. When you get to
> toroid with no hole in the center, the formula degenerates to 0 times
> infinity. The formula still holds the information about a toroid with no
> hole, but one has to find the limit of the formula as (D - d)/d approaches 1
> from above to cover the case D = 2d. I have not considered this problem yet.
> 
> This brings me to my question. Do coilers have any thoughts about the size
> of the hole in the center of a toroid? Do coilers want that hole to be small
> or large?
> 
> Eventually I want to provide an approximation formula that is more accurate
> than Bert's formula. But without using powerful mathematical techniques,
> Bert derived a pretty good formula. My hat is off to Bert Pool.
> 
> Godfrey Loudner
> 
>