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# Re: calculating safe primary turn-to-turn distance

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> From: Tesla list <tesla-at-pupman-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: calculating safe primary turn-to-turn distance
> Date: Friday, August 25, 2000 10:43 PM
>
> Original poster: "Stan" <sdarling-at-columbus.rr-dot-com>
>
> Greetings all,
>
> I have been curious since I started doing Tesla coils about this:  how
> does one calculate the minimum air distance of turn to turn spacing in a
> primary for a given voltage?  I'm not an EE so my common sense tells me
> that current always favors the path of least resistance and that even a
> tiny distance of air would have a much greater R than the adjacent half
> turn of Cu tubing. So if the adjacent turns weren't touching, why would
> it ever arc over through the air?  I suspect it has something to do with
> the inductance of the Cu tubing coil(s) ....

Exactly.. it's the inductance.  The inductance makes the voltage drop along
the tubing greater than would be expected from just the DC resistance. The
entire primary voltage is fairly evenly distributed along the length of the
winding. So, if you have 10 turns in the primary, and 10 kV on the primary,
then there is 1 kV/turn.  The peak voltage across the primary will be
somewhat higher than the peak voltage out of the transformer, by the way.

So, if you have a 15 kV NST driving the primary, (peak voltage of 21 kV),
and you allow a margin of 2:1 (for resonance effects), then the entire
primary will be seeing 40 kV or so (as will the capacitor, by the way).
With 10 turns, now you are talking about 4 kV/turn.

The next question is what is the breakdown strength of the gap between
turns.
The breakdown strength for air in a uniform field (not the case for
parallel wires) is about 31 kV/cm (70 kV/inch). There are basically two
situations you can consider: 1) Very small wires, compared to the distance
between them (say you wound your primary with #14 solid wire) and 2)
something like copper tubing, where the diameter of the tubing is
comparable to the spacing.

In the first case, the radius of the wire is going to determine when a
spark can start forming.   The rule of thumb here is that the field is
equal to the voltage over the radius.  If the field is greater than 70
kV/inch, it will break down.  As an example AWG 10 wire is 0.100" in
diameter, or .05" radius.  This works out to 3.5 kV for when corona will
start, and where corona starts, breakdown follows.  For our 10 turn example
above, you'd probably have a real problem.

In the second case, the radius of curvature is fairly large, compared to
the spacing, so it's more the "gap" that determines the breakdown strength.
If the diameter is much bigger than the spacing, just use the spacing to
calculate the field strength (i.e. approximate it as a uniform field).. If
you used 1" tubing with a 1/4" turn/turn spacing, then our 4 kV/turn
example above would have a field of 16 kV/inch, well below the air
breakdown of 70.

If the tubing diameter is smaller than the gap (or comparable), you want to
be a bit more conservative.  Here is an equation:

D is center to center spacing of cylinders
d is gap between cylinders
r is radius of cylinders

E = V * SQRT(D^2-4*r^2)/(2 * r * (D - r)*arccosh(D/2r))

If you don't want to fool with inverse hyperbolic functions, there is a
simpler form

> Feeling stupid in Ohio.

Not at all stupid... It IS non intutive...

>

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