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Re: Spark length dependence on air pressure.

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 10:39 PM 6/14/2005, Tesla list wrote: 
Original poster: "Mike" <induction@xxxxxxxxxxx>

Hi Jim,
Being very interested in your numbers (halving at 18,000 feet) and the voltage breakdown, I asked my friend to expand and sent him a copy of your posting. Below is exchange:
Earle wrote: Halving is 1/2 E-folding is 1/e which is less than 1/2 (e=2.71???)
(e is the base for the Naperian logarithm.)

Yep.. 1/e is .367 (familiar as the voltage you get to after one RC time constant)



His 7.7 km number may be more accurate than my 7 km number.  Would need
to check.
Another complication is that pressure also depends on temperature, which
varies with height also, and so the pressure
falloff with height is slightly different than for density.  But density
is the more fundamental parameter for breakdown, because it controls the
mean free path of the electrons, and it is over these mean free paths
that they gain enough energy to ionize.

Excellent point. I did use pressure to get my 7.7 km, and he's right, density is the controlling thing. Assumed lapse rate (temperature profile as you change in altitude) also affects it, because you're basically integrating. I just used ICAO standard atmosphere.

Looking up in the table, it looks like density ratio of 0.5 is around 22000-23000 ft. (6500m?) Density ratio of 0.367 is around 31,000 ft (interpolating between my table which is in 5000 ft chunks) (9500 m?).(Found an online copy just now: http://naca.larc.nasa.gov/reports/1955/naca-report-1235/index.cgi?thumbnail1)

That chart gives 6600 m geopotential altitude for density ratio = 0.5 and 5400-5500 m for pressure ratio = 0.5
7700m for p/p0=1/e, 9300m for rho/rho0=1/e
which is consistent with my rough and ready interpolation.


I found this interesting formula:

H = 44.3308 - 42.2665*D^0.234969

H in km
D in kg/m^3

however, because it has only one term, it only works up to the tropopause, where the lapse rate changes.

Mike wrote:

Earle,
Is this 18,000 Ft. halving elevation a valid rule of thumb, also is what he says about 7.7 Km also true? I get confused because 18,000 feet is 5.864 Km, which is less that 7 Km, never mind his advised 7.7 Km halving height.

7.7km is the 1/e height for pressure (the exp(-z/k) needs the value for 1/e, not halving.)

I use the halving number because when I'm doing it in my head, I can do dividing by two much more easily.


Having an easy to remember number sure would make it easy to work with. Could you clarify or defend please?
Mike 

----- Original Message ----- From: "Tesla list" <tesla@xxxxxxxxxx>
To: <tesla@xxxxxxxxxx>
Sent: Tuesday, June 14, 2005 7:07 PM
Subject: Re: Spark length dependence on air pressure.


Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 11:02 AM 6/14/2005, you 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
benefit. Here is the answer to your message I had 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 link to reference on
this?
>He wants the equation.
>Regards,
>Mike


A handy way to remember this sort of thing is that the "halving" elevation is 18,000ft. At 18,000 ft you're at half sea level pressure. Another 18,000 and you're at 1/4th, etc.

7.7 km might be a bit closer to the real constant for the exp(-z/k) term.


The 3MV/m breakdown is for uniform field. Spheres and needles are much lower. 

----- 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