# Re: Spark length dependence on air pressure.

• To: tesla@xxxxxxxxxx
• Subject: Re: Spark length dependence on air pressure.
• From: "Tesla list" <tesla@xxxxxxxxxx>
• Date: Wed, 15 Jun 2005 11:09:22 -0600
• Delivered-to: testla@pupman.com
• Delivered-to: tesla@pupman.com
• Old-return-path: <teslalist@twfpowerelectronics.com>
• Resent-date: Wed, 15 Jun 2005 11:09:37 -0600 (MDT)
• Resent-from: tesla@xxxxxxxxxx
• Resent-message-id: <wK_O8.A.Q9G.NDGsCB@poodle>
• Resent-sender: tesla-request@xxxxxxxxxx

`Original poster: Robert Clark <bobbygc2001@xxxxxxxxx>`

``` Thanks for the info. There were two reason for asking
this question. First, in regards to this list Mike
posted his experience creating a Tesla coil in vacuum
in the "Re: Towards the autonomous lifter -
electrostatic voltage generators" thread. He noted the
breakdown voltage was *less* in his vacuum chamber
than at normal pressure.
This is in keeping with Paschen's law which states
that the breakdown voltage decreases as the pressure
decreases down to a smallest value at which point the
required voltage starts increasing again. Look for

```EHD thrusters performance analysis.
http://www.blazelabs.com/l-perf.asp```

``` This graph gives the breakdown voltage in volts per
mil (a thousandth of an inch) according to pressure in
Torrs. There is a minor typo in the figure. In blue
are written some breakdown voltages at some
temperatures and pressures. Those should be given as
volts not kilovolts. For example, it's written in blue
that at standard temperature and pressure the
breakdown voltage is "75 KV." That should be 75 V at a
distance of 1 mil, or 75,000 V at 1 inch. This
corresponds to the well- known value of 75,000/2.5 =
30,000 per cm.```

``` However, the main reason for my question is in
regards to electrical propulsion methods. The "lifter"
needs high power to lift large payloads. At this point
we don't have power supplies light enough to lift
their own weight using the lifter propulsion.
Therefore what I was thinking was perhaps by creating
"sparks" many kilometers long this would provide a
means of sending the power to the craft intended to
reach orbit.
Note I'm thinking while the breakdown voltage at a
certain distance is related to the spark length they
are not exactly the same. For instance the Freau
equation for spark length is given in terms of power
(volts times amps) while the breakdown voltage is just
a voltage. For my purposes I'm thinking the spark
length is what I really need.```

` Here's a web page that describes Paschen's law:`

```Gaseous Breakdown & Paschen's Law.

``` The formula it gives for short distances for the
voltage breakdown is```

```V = 30pd + 1.35 kV, where d is in centimeters, and p
is in atmospheres.```

``` However, it gives a more accurate formula for longer
distances:```

```Breakdown voltage:
Vbreakdown = B * p * d / (C + ln( p * d))```

```where B = 365 Vcm^-1 Torr^-1 and C = 1.18, and d is in
centimeters and p in Torrs.```

``` My idea would be to locate a Tesla coil high in the
atmosphere such as by a high altitude balloon. The
power for the TC would come from a power line attached
to the balloon from the ground. Then the TC would
shoot power to the launch craft from the balloon.
Since they are high in the atmosphere the required
voltage would be much less.
I still need to know though how long the sparks could
be that would be created.```

`  Bob Clark`

`--- Tesla list <tesla@xxxxxxxxxx> wrote:`

```> Original poster: "Mike" <mikev@xxxxxxxxxxxxxxxx>
>
> Hi Bob,
>                I remember reading in the early days
> when they wanted to
> determine this answer, there was a difference from
> sharp pointed electrodes
> and round ball type, also the material made a small
> difference.
> Not knowing how you were going to use or apply the
> answer, I opted to pass
> this question to a friend of mine who specializes in
> atmospheric electricity
> at MIT. I also needed the breakdown at 15 Km so this
> reply was a two fold
> forwarded to him.
> Regards,
> Mike
> Hi Mike
> The equation is
>
> Eb   = 3 x 10^6 v/m    exp(-z/7)
>
> where z is height in km
> (7km is the density scale height of the atmosphere
> and density declines
> exponentially with altitude.)
>
> So at z=0   Eb = 3 x 10^6 v/m
> Mike wrote:
>
>  >Hi Earle,
>  >                  For a DC model, can you answer
> this question? I need to
>  >know for myself the breakdown voltage at 15 Km  (I
> think that is ~103 Torr)
>  >anyway so this is not a wasted effort. Is there a
> this?
>  >He wants the equation.
>  >Regards,
>  >Mike
>
> ----- Original Message -----
> From: "Tesla list" <tesla@xxxxxxxxxx>
> To: <tesla@xxxxxxxxxx>
> Sent: Monday, June 13, 2005 3:55 PM
> Subject: Spark length dependence on air pressure.
>
>
>  > Original poster: Robert Clark
> <bobbygc2001@xxxxxxxxx>
>  >
>  >   I've seen for example the Freau Equation for
>  > predicting spark length:
>  >
>  > Thoughts on spark length and the "Freau Equation"
>  >
>
http://www.pupman.com/listarchives/2001/June/msg00433.html
>  >
>  >   But since the breakdown voltage in air depends
> on air
>  > pressure (or is it really air density?), what is
> the
>  > equation showing the dependence on air pressure
> (or
>  > air density)?
>  >
>  >
>  >    Bob Clark
>  >
>  > _
>  >
>  >
>  >
>
>
>```

```
__________________________________
Discover Yahoo!
Have fun online with music videos, cool games, IM and more. Check it out!
http://discover.yahoo.com/online.html```