# Re: H/D ratio

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

Luke Galyan wrote:

> I found on the net in a few places stating that the maximum
> amount of inductance from a coil is when the height is the
> same as the diameter.

Hi Luke,

For a given length of wire the highest inductance occurs when
it is wound into a coil with h/d = 0.45, so the width of the
coil is a little over twice the height.

> why is this ratio not used for the tesla coil secondary to
> take advantage of a high inductance ratio...

It would be a good value to start with, for the above reason.
In addition, the self capacitance of these small h/d coils
has an effect on the current distribution within the coil, such
that the effective inductance at resonance can be quite a bit
higher than the low frequency inductance.

In practice though, the short lengths of these coils imposes
limits on the possible output voltage due to breakdown along
the secondary:  the developed top voltage divided by the length
of the coil comes out to just too many volts/cm.

> all the seems to be offered for a reason as to why they are
> that tall is, "well that's what works good."  Or "Everyone
> else's is that way so it's the best rule."

That's very true.  I'm afraid we don't have much theory to back
up the empirical experience that coilers use to choose coil
sizes and topload sizes.  Certain ranges of h/d seem to do ok
(quite a wide range in fact - we see good coils from about 2:1
up to 10:1 or more) and likewise, certain ranges of toroid
size and shape seem to be preferred.    These have been arrived
at by much trial and error by many coilers over many decades.

It's important to insist on the 'hows' and 'whys', but don't be
too disappointed if we can't come up with good answers.  And don't
be too perturbed if the opinions of experts are varied and don't
always agree.  It just shows that there's a long way to go with
our theoretical understanding of these things.

For example we cannot give good answers to the following...(for a
given application)... What is the best topload size?... What is
the best coil size?...how many turns?.. wire size?...break rate?..
and so on.  A pretty poor show, really.

> So why can no one offer solid reasons for even one secondary
> dimension?

The main difficulty, I think, comes from the fact that we don't
discharges.  We know we need a lot of voltage in order to force
the electric charge out into the air, but voltage by itself is
not enough.   We find that we also need a fair amount of charge
available at that voltage.  To borrow a military analogy: it's
no good having the world's best shock troops to break through
enemy lines if you haven't got a sufficient quantity of general
infantry to follow through and occupy the territory.  So there's
likely to be an optimum balance between voltage and charge but
we don't know what that is - and therefore we can't determine
the best topload size or shape.   If we could solve that, we
would be able to say "Use this toroid for best results at this
frequency and power level".  Having got the toroid size,
we would then have a better chance of saying what coil size was
best to power it. And then in turn, we could say something about
the required primary, and so on.  IMO, it all seems to follow on
from the central problem of spark interaction with the topload.

Luke, I hope this little note serves to indicate where the state-
of-the-art lies.  Coiling offers the enthusiast a great many
genuine opportunities for research and is great territory for
the amateur scientist.  Keep on asking those 'Hows' and 'Whys'
and treat the lack of good answers as inspiration to get involved
in some interesting and worthwhile investigations.
--
Paul Nicholson
--

```