Estimating spark length voltage

[oneKone]

Hey,
A while ago (about 7 years) I read somewhere that a general rule of thumb for estimating a spark length is 1kv for 1mm. I've been blindly using this concept without actually looking into it. I've tried to find some answers but it seems my Google skills are not upto the task!

So basically the question is, is 1kv equal to 1mm or is this far from accurate....... I'm equating my 400mm spark length on my sstc is 400kv.

Cheers,
Chris

[Mads Barnkob]

The old 10 kV/cm rule does not apply here, I seem to recall that it is for DC current between pointy objects, the attached short description goes into further detail on the required breakdown voltage for different spark gap geometries.

Tesla coils does however operate quite differently. We charge up a topload, secondary top capacitance, with as many electrons as possible, before the voltage is high enough to break down the dialectric strength of atmospheric air. This can differ with temperature, moisture and pressure.

The topload voltage will always be the greatest just before there is a spark formed, as this is when the charge is at its highest, once the spark starts to grow it represents a larger and larger load to the topload and as current goes up while discharging the energy, the voltage drops significantly.

This is just a bold statement, that for a Tesla coil we are more in the league of 3 kV/cm for long sparks. Terry Fritz once made some measurements on this: https://deanostoybox.com/hot-streamer/TeslaCoils/MyPapers/planant/waveant3.html

Hydron also posted a lot of topload/breakout point current measurements, these numbers can be used to calculate the topload voltage: https://highvoltageforum.net/index.php?topic=117.msg735;topicseen#new

[Uspring]

The differences between DC and AC arcs are mainly 2: An AC arc can end in midair and it usually lasts much longer. The AC arc can grow over many cycles by current flowing back and forth along it, keeping it hot. So once a small arc has broke out, it will establish a conductive channel to its tip from where the arc can grow further. The arc channel won't be a perfect conductor, so the voltage at its tip will gradually decrease as it gets longer. This will basically limit its length. In principle arc length and voltage don't even have to be linearly related. Probably higher frequency arcs are also longer for a given voltage, since charges are more often pushed back and forth, making it hotter and more conductive.

If you're into math, you might want to read https://www.pupman.com/listarchives/2012/Oct/msg00125.html

A back of the envelope calculation based on Hydrons data seems to indicate a voltage of about 300kV for an arc length somewhat above 2 m, i.e. 1.5kV/cm.

[oneKone]

Cheers for the replies and the links. Looking forward to understanding further

[AndreiRS]

I couldn't get an arc from a mot with 2kv output, at something like 0.3 maybe 0.4mm. It depends a lot on air humidity.