From: Bert Hickman
Date: Sun, 27 May 2001 15:20:49 -0500
Subject: Re: [TSSP] Genetic optimisation (New: temperature sensitivity!!)
Boris and all,
Much of Peek's work was confined to measurements between spheres,
concentric cylinders, and parallel conductors. Peek, and previous
researchers, found that the dielectric gradient strength of air is
apparently stronger at the surface of smaller diameter conductors than for
larger ones. Peek discovered that relatively simple formulas (called Peek's
Laws of Corona) could be used to express this effect:
Gv = Gw*(1 + 0.301/SQRT(r)) kV/cm (parallel wires, wide separation)
= 29.8*(1 + 0.301/SQRT(r)) kV/cm
Gv = Gc*(1 + 0.308/SQRT(r)) kV/cm (concentric cylinders, r = radius of
inner conductor)
= 31*(1 + 0.308/SQRT(r)) kV/cm
where:
Gv = voltage stress for initiation of visible corona
Gw = a constant for air for parallel wire (approximately 29.8 kV/cm at
STP per Peek)
Gc = a constant for air for concentric conductors (approximately 31
kV/cm at STP per Peek)
r = radius of the conductor
The concentric cylinder case is probably the most meaningful for us since
the results are closest to the nonuniform E-field surrounding the toploads.
As Boris indicates, the E-field at the surface necessary to initiate corona
begins to increase significantly as the conductor diameter gets smaller,
and even when r = 1 cm is actually about 30% greater than for larger
diameter conductors. This effect also holds for small spheres.
HOWEVER...
==========
Of potentially greater impact for us, Peek also looked at the (visual
corona) breakdown strength of air at 60 Hz as a function of temperature in
the range of 20 - 140 degrees Celsius for a polished copper tube inside a
brass cylinder. He found a significant decline as the temperature was
increased, even in this relatively low temperature range (compared to
temperatures required for thermal ionization). The root cause was lower
density at higher temperatures. This is quite likely the underlying reason
why reignition along the same channel occurs between successive breaks in
disruptive Tesla Coils!
Through a series of experiments, Peek found that the above formulas could
be appropriately modified to account for temperature and barometric
pressure effects. The modified form of the Corona Law for the concentric
cylinder case becomes:
Gv = Gc*D*(1 + 0.308/SQRT(r*D)) kV/cm (concentric cylinders, r =
radius of inner conductor)
The new term (D) is a factor which takes into consideration both
temperature and barometric pressure:
D = 3.92*b/(273 + T)
where:
T = Temperature in degrees Celsius
b = Barometric pressure in cm of Hg (nominally 76.0 cm at sea level)
For example, if we use a conductor with a radius of 10 cm with Peek's
adjusted formula above, we find that the estimated terminal voltage to
initiate breakout declines almost 20% at 100 degrees C, and almost 36% at
200 Degrees C:
V (25 degrees) ~ 340 kV
V (100 degrees) ~ 275 kV
V (200 degrees) ~ 219 kV
It's beginning to look as though we may have pinpointed the mechanism
underlying bang-to-bang leader growth at relatively low break rates! The
previous leader leaves behind a high temperature, lower density region
having lowered dielectric strength - the NEXT leader can reignite at a
significantly LOWER terminal potential, further extending the overall
leader length over a series of sequential "bangs"!
The above formulae were gleaned from F. W. Peek, "Dielectric Phenomena in
High Voltage Engineering", 3rd edition, McGraw-Hill, 1929, 410pp.
-- Bert --
--
Bert Hickman
Stoneridge Engineering
Email: bert.hickman@aquila.net
Web Site: http://www.teslamania.com
boris petkovic wrote:
>
> > Bert's 26kV/cm number is very good. When the
> > voltage on a sphere of 1cm
> > radius reaches 26kV it will arc outward. It is a
> > linear function so a 2cm
> > radius sphere is 52kV and a three is 78kV...
> ---
> Isolasted r=1cm sphere in space at standard
> atmospheric conditions wouldn't arc at that
> voltage,but with someone higher .
> For small radii objects breakout critical field isn't
> a linear function,but is given by empirical Peek's
> low.
> I'm pretty sure Bert knows exactly how formula goes (I
> don't by hart).
>
> Regards,
> Boris
>
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