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 

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 

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 
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 
on your website:

tank circuit:
 Up = 20kV
 Cp = 33nF

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

 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 Ūtop=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

In your case (current coil):
  =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 

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

Cheers, Stefan
     \_            _    _/\_________________________________
       \_______  _/ `--'                                    |
       (_(_|_)_)< `        Reply to: STK.TC-at-gmx-dot-net, please |
_   __/   |_|    \_      visit "Stefans Tesla coil pages"   |
 \_/  `   |_|     `    with lots of photographs, formulas   |
 _/    .__|_|__.     and technical infos around TCs at      |
/_______\-|-|-/___ http://privat.schlund.de/skluge/toc.htm _|

Dieses Dokument wurde elektronisch erstellt und ist auch ohne 
Umlaute gueltig.

Famous last words:  Oh, a Tesla coil - I heard you can touch
                    it without getting hurt --> Zzzzzapp ...