# Re: Voltage/Length (fwd)

```

---------- Forwarded message ----------
Date: Sat, 17 Jan 1998 11:18:26 -0800
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Voltage/Length (fwd)

> ---------- Forwarded message ----------
> Date: Sat, 17 Jan 1998 11:05:59 -0600
> From: Jeff Larson <jflarson-at-starnetinc-dot-com>
> To: Tesla List <tesla-at-pupman-dot-com>
> Subject: Voltage/Length
>
> Does any one have the voltage per length approximation formula?  This
> would be used to approximate the voltage of a coil output based on the
> measured spark length.  I imagine the spark length would be dependent on
> the humidity regardless of the voltage?

For a uniform field (which a tesla coil discharging is definitely NOT), the
breakdown voltage is roughly 70 kV/inch, and for normal temperatures and
pressures and gaps, is inversely proportional to density.  When the field
gets non-uniform, the relationship gets a lot more obscure. You can
calculate, with a lot of work, the field between a spherical electrode and
a plane ground, or between two spheres (same calculation, actually). In
general, the E field around a sphere in free space (i.e. the sphere is many
sphere radiuses from any other object, conducting or not), is inversely
proportional to the distance from the center of the sphere:

E (Volts/meter) = Voltage on sphere / radius from center.

Pretty simple, huh... If the V/m gets over 30 kV/cm (approx) the air breaks
down, forming either corona, or a spark, depending on what is in the
vicinity.

The tricky part is when the field is non uniform, i.e. you have a small
electrode, relative to the voltage (i.e. V/rsphere >30 kV/cm). With enough
charge/current supplying the electrode, you'll get a streamer or leader
that heads out from the electrode, the end of which acts like yet another
little electrode, from which a leader heads out, etc., etc. until it gets
to the other side of the circuit, at which point the arc develops. Until
the spark gets somewhere, the current is just going to charge the ever
growing electrode, which conceptually looks like a telescoping metal tube.

This is how a voltage of, say, a megavolt, which could only jump 30 cm in a
uniform field ( 1000 kV/33 cm = 30 kV/cm), can actually jump many meters,
providing the current is there to support the growth of the spark channel.
This is also the process in lightning, since it manages to jump across a
space where the field is only about 1 kV/meter, at most.

So, the short answer to your question, there isn't any nice relationship
between voltage (particularly on a tesla coil) and spark length. For a
somewhat contrived case with a well defined field (i.e. between spheres
that are much larger than the gap) it is about 30 kV/cm for DC or low
frequency (e.g. 60 Hz) AC voltages from about 1-1000 kV.

with respect to humidity, it doesn't have much effect on the breakdown
voltage. In fact, water vapor has a higher breakdown voltage than air, so
the higher the humidity the higher the breakdown voltage; or stated another
way, the drier the air, the longer the sparks. The oft noted phenomenon of
static electricity effects working better on dry days has to do with the
absorption of the humidity by objects and making them slightly conductive
which bleeds off the typically very small charges involved.

```