# Re: Vtop vs coil length

```Hi Finn, Doc R., all,

on Sun, 06 Jun 1999 Finn wrote on pupman:
> Can anyone pls tell me how to calculate the
> voltege that a secondary is able to withstand.
> My present coil is 32 " long, and puts up with
> round 600 kV, but I am considering to exeed
> 1 MV on the next big coil I build.
My question is, how did you calculate the voltage? My way to do
this is via energy preservation. But this gives only a mamimum
value.

Formula is:
Eprim > Eself + Etop
1/2 * Cp * Up^2 > Eself + 1/2 * Ctop * Utop^2   (1)

The energy which is lost during the energy tranfer is neglected
here.

Problem is how much energy will be stored (='lost') in the
selfcapacitance of the coil. To calculate this, we have to take
into account the nonlinear voltage rise along the coil length
and the nonlinear selfcapacitance along the coil length (and
perhaps a phase angle?).

I think the worst case is an effective self capacitance (as
calculated via the Medhurst formula) and a linear voltage
distribution (which seems to be a good approximation for coils
with a not to small toroid, I think Terry measured this once)
so we can say the maximum energy 'lost' in the self capacitance
is
Eself = 1/2 * Cself * (Utop/2)^2                (2)

When we combine formula (1) and (2) we get
1/2*Cp*Up^2 > 1/2*Cself*(Utop/2)^2 + 1/2*Ctop*Utop^2

and therefore
Cp * Up^2 > (1/4*Cself + Ctop) * Utop^2

which gives finally
Utop < Up * sqr [ Cp / (1/4*Cself + Ctop) ]     (3)

Do you agree with my math here or did you calculate the voltage
in an other way?

For your present coil, I have found the following parameters

tank circuit:
Up = 20kV
Cp = 33nF

secondary:
250mm
N=807
0,95mm wire
winding length therefore about 79cm (my guess)
this works out to Cself=18.9pF (???)
(L=45.7mH, f0=171kHz, f=101kHz)

toroid:
seems to be 250mm ducting
If this is true, the mean diameter seems to be 72cm
together with the anti corona ring you have approx.
Ctop=35pF (???)

Im missing a 'specs-page' on your Website! ;-)

Throwing all the data into formula (3), we get
Utop= 20kV * sqr(33nF/(18.9/4+35)pF)
= 20kV * sqr(33000/39.7)
= 576kV
which is pretty close to the 600kV you mentioned
(going to peak values, I get Űtop=815kV).

I guess the major problem is a short between two secondary
windings at the lower end of the coil (as happened to Stefan
Bauer when I visited him three weeks ago).

As Martin Damev pointed out, the voltage rise is Pi/2 higher
here because of the sine wave voltage distribution along the
coil (worst case here, personally I think you can calculate
with a linear voltage rise if the topload is big enough).

This would give you a voltage between two turns of
dU=(Pi/2)*Utop/N

dU=(Pi/2)*576kV/807
=1.12kV per turn at the lower end of the coil.

>>From my memory (which is degrading from day to day)
I would say that most wires in the 0.5-2mm range are rated
2-3kV (single enameled, up to 7kV for triple enameled). As
you have two insulations between two turns, the insulation
should be good for at least 4kV interturn voltage. But
better check the insulation via its data sheet or an
destructive test (shunted xfmr, variac, two twisted wires)
and derate by factor 3 for RF (your test will be only
50Hz!) and factor 1.5 for safety reasons (totally factor ~4).
Perhaps you can perform the test with RF in a small tank
circuit, that would give more reliable results.

Doc R. wrote:
> It's more total spark length than voltage although they are
> related. Most secondaries with two internal disks can withstand
> up to length = total spark length / 3.   (or 3 times sec coil
> length for spark length).  This assumes a large toroid on top
> --- considerably less if smaller toroid is total spark length
> = 1.5 x sec coil length.  Beyond this and you start pushing the
> envelope and failure is sure to occur at some point.  For
> reference 1 MV is equal to a spark length of 9 ft. through
> normal air at STP (this measured across 1/2 inch dia rod gap).

I'm not sure if Doc R. really meant TC-discharges when he spoke
>from 9ft/1MV. The '1/2 inch dia rod gap' indicates more the
low frequency range (power line) 50/60Hz or even DC.
Doc. R, could you please comment this?

Doc R. also spoke from 'secondaries with two internal disks'.
Could you please comment what you mean in detail? An insulating
endcap glued onto the upper and lower end of the coil former to
seal the tube airtight? Or do you mean the disks AROUND the
secondary like RWStephens has made on his big coil to stop the
racing arcs (I think the URL is
http://www.pupman-dot-com/current/rstephens/mtc-a1.html)?

Summary:
--------
There seem to be two limiting factors:
a) voltage (insulation breakdown)
b) power = arc length (racing sparks)

Cheers, Stefan
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