RE: Spheres vs Toroids

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "John H. Couture" <couturejh-at-mgte-dot-com> 


Paul -

As I recall the original question was whether the sphere or a toroid would
give the best spark output. I took this to mean that we would start with a
certain size Tesla coil including a secondary and a certain topload sphere.
The question would be can
we get a longer output spark if we used a toroid? What size and shape should
the Toroid be? I agree the ratio of secondary coil length to streamer length
is not important.

A few years ago (Oct 2000) we did discuss an optimum size toroid. This ended
up as a graph with two intersecting curves. One curve for the available
toroid energy and one for the toroid voltage. The intersection of the curves
was considered to indicate the optimum toroid.

However, one important parameter was left out and that was the toroid shape
and location necessary to protect the top secondary windings. This has to do
with the shape of the electric fields around both the toroid and the top of
the secondary coil. In the past this problem was considered solved by using
a toroid that had the major diameter equal to at least twice the secondary
coil diameter. This diameter size also assumed the bottom of the toroid
would be above the secondary top winding a distance equal to one third of
the secondary diameter. To my knowledge this design criteria has worked
reasonably well when it was followed.

 >From the above you can see that coilers did give the TC secondary topload
design problem considerable attention in spite of the fact it was based on
sketchy empirical data. The challenge now is to improve this design method
by digging deeper into electrical field theory something I would have to
leave to you and other coilers.

I don't see any problem in starting with the toroid and streamer length and
then building the TC to conform to these conditions. Whether you start with
the toroid or the TC you will still be confronted with those difficult to
coordinate E-fields that were mostly left out in the past discussions.

John Couture

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-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Friday, October 31, 2003 1:46 PM
To: tesla-at-pupman-dot-com
Subject: Re: Spheres vs Toroids


Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk>

John Couture wrote:

  > But how do you determine the optimum toroid size because for a
  > certain size sphere diameter there are many different sizes of
  > toroids that have the same capacitance?

Hi John, All,

This is a familiar old bone that you've brought out for us
to chew!

Why choose a toroid to match the C of a certain sized sphere?
I must have missed that bit of the thread.

But more generally, why choose the topload to match any
given C at all.   Let's be radical and not give a damn
about the topload capacitance.

Let's instead think about charge storage and the surrounding
field gradient.   You also mention protecting the top of the
secondary by putting a gentle field gradient in this area -
that's ok too, but that's a minor (secondary?) consideration.

The shape of the topload determines the shape of the surrounding
E-field, to a large extent.  You can imagine a tiny secondary
and huge topload if you like.

Now when breakout occurs, it will start from a point on the
topload (typically the rim of the toroid) at which the surface
field gradient is highest.  Streamers will then develop more
or less along the lines of steepest field gradient.

Now overall, the steepest *average* gradient between topload
and ground occurs along the line of the secondary, and lines
running vertical with it, under the shadow, so to speak of
the toroid.

But these regions are not those where the initial breakout
occurs (we hope).  Instead the breakout occurs on the rim,
and the steepest descent through the field when starting at
the rim takes you out and away from the toroid, largely
horizontal at first, then curving either up or down, whichever
offers the most temptingly steep path.

So the first duty of the topload is to set up a suitable
E field in the surroundings to offer a nice long horizontal
run for the streamers, and at the same time a good preference
for breakout on the rim.

That does imply that independently of any considerations of
secondary coil and resonance, the topload size and shape must
bear some fairly basic relationship to the size of streamers
desired.

We often hear of so-and-so coil producing umpteen feet of
streamer from a 3" long secondary.  But I'm venturing that
the important ratio is not coil length to streamers, but it
is instead toroid proportions to streamer length. With of
course the single proviso that the coil is hefty enough to
raise breakout in the first place.

As well as setting up a 'background' field conducive to
long streamer formation, the topload must also store enough
charge to support that process.  This also implies some
basic relation between toroid dimensions and intended
streamer length.

I think it would in fact be an interesting modelling
exercise for someone to compute the field shapes for
various toroid dimensions and heights above ground.
This could be done without any consideration of coil
or operating frequency - just static field plots from the
toroid above an earth plane.  Look for the shapes which
give the best 'downhill' run for the streamers through
the E-field.

If it worked out that there really was an optimum shape,
you would then be able to say that, for example to achieve
say 10 foot streamers, the best topload would be a toroid
of so-and-so width and chord, placed at such-and-such a height.

Then all you've have to do is to build a coil to drive it.
You'd also know the target topvolts, roughly, so you'd know
how much juice to put in.

So lets think of the topload as the most important component
in the system, the one to which every other component is
chosen to match.  And lets try choosing the topload shape
with a certain target length of streamer development in mind.

There's got to be some marrow in this bone somewhere...
--
Paul Nicholson
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