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*To*: tesla-at-pupman-dot-com*Subject*: RE: Optimum toroid size*From*: paul-at-abelian.demon.co.uk (by way of Terry Fritz <twftesla-at-uswest-dot-net>)*Date*: Sat, 07 Oct 2000 12:09:45 -0600*Delivered-To*: fixup-tesla-at-pupman-dot-com-at-fixme

John H. Couture <couturejh-at-worldnet.att-dot-net> wrote: > Paul - > I did not intend to belittle your approach to finding a solution to > the optimum toroid problem. I was only trying to find some TC > parameter that could simplify the problem. No, on the contrary, I was pleasantly surprised that you were able to pick up on the suggestions and respond so quickly with such straightforward approximations for those potentialy messy Fc and Fb functions. You certainly illustrated the idea nicely. Forgive me for feeling the need to point out (in my previous post) that the energy J which appears in your formula is itself very dependent on the radius R, since the topload efficiency which you took as a fixed constant, contains a factor Csphere/(Csphere + Ccoil). Thus I would say that the extra little refinement which takes this into account, leading to the cubic R^3 + 0.36 Ccoil R^2 - 169 * Eff * J = 0 is justifiable to achieve a genuine optimisation of radius R. [Note that Eff * J in this formula is the net bang energy delivered to the total secondary capacitance, whereas in John's simpler formula the J is the net bang energy delivered to the top capacitance only.] My ulterior motive was to raise a plug for the Monte Carlo method of tackling optimisation problems such as this. For example, a direct solution of the above for R took 20 lines of code, and a Monte Carlo took 11. > The toroid does not have this [Fc and Fb linear in R] advantage so > the solution for optimum size will be more complicated. > Any suggestions? Here's my guess: Lets take Fb to be dependent on the radius of the toroid tube in the same way as a sphere, ie Fb = 65 * Rtube kV. Then for the capacitance, we can use one of the regular formulae - I'll borrow one from Matt Behrend's neat web page http://home.earthlink-dot-net/~electronxlc/tccalc.html Ctor = 1.4(1.2781 - Rtube/Rtor) sqrt( 4 * PI * Rtube(Rtor-Rtube)) Ctor in pF, Rtube is the toroid tube radius, Rtor is the overall toroid radius, both in inches. >From the energy equation, we have Eff * J = 0.5 * 10^-12 * (Ccoil + Ctor) * V^2 where the caps are in pF, J is input bang energy (Joules) and Eff the energy efficiency (factor) into the secondary capacitance. Then Fc = 10^3 * sqrt( 2 * Eff * J/(Ccoil + Ctor(Rtube, Rtor))) kV So we need to find Rtube and Rtor, such that Fc( Rtube, Rtor) = Fb( Rtube) and Fb( Rtube) is a maximum. with an additional proviso that Rtube and Rtor are physically realizable! Here's a little C code to solve the above problem, http://www.abelian.demon.co.uk/mc/optimum_toroid1.c Interestingly, the optimum toroid always comes out to be as fat as possible, ie the tube radius wants to be half the toroid radius, so that the hole in the middle just disappears - the toroid wants to be a sphere. > In the past coilers have found that increasing the toroid size > in tests would increase the output spark. This is often found. Does this imply that topload sizes as commonly used are, on the whole, generally below our proposed optimum size? If you run the above program, you'll see that the optimum toroid does come out rather bigger than what you might normally use, eg John's example, 900 watts, 120 bps, and say, 50% efficiency and 40pF coil capacitance, the optimisation gives 66 inch radius as best toroid radius. Thats one big fat 200pF toroid! (I suspect that Fb, borrowed from the sphere, is too conservative for the toroid, since its curvature in one dimension is at most half that of the other dimension - thus favouring the larger toroids too much. Fixing this would I'm sure bring the optimum toroid size down some. However, unless we can take the coil dimensions into account, I think we'll always come out with 'zero-middle' toroids.) Regards, -- Paul Nicholson, Manchester, UK. --

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