Talk:Peek's law

Delta discrepancy in Peek's book
There's a slight discrepancy between Blaze lab's equation:


 * $$\mathrm{CIV} = m_0 E_i r_w \ln \left ( {d \over r_w} \right )$$


 * $$E_i = E_0 \delta \left ( 1 + {0.0301 \over \sqrt{\delta r_w} } \right )$$

and Peek's paper:


 * $$e_v = m_v g_v \delta r \ln \left ({S \over r} \right )$$
 * $$g_v = g_0 \delta \left ( 1 + {0.301 \over \sqrt{\delta r}} \right )$$

Notice the extra &delta; in the ev = equation. I think that's a mistake in Peek's paper, since the fully expanded formula he gives is:


 * $$g_v = 30\delta \left ( 1 + {0.301 \over \sqrt{\delta r_w} } \right )$$


 * $$e_v = g_v \delta r \ln \left ({S \over r} \right ) = g_0 \delta \left ( 1 + {0.301 \over \sqrt{\delta r_w} } \right ) r \ln \left ({S \over r} \right )$$ (kilovolts)

If the &delta; were inside gv, there would be &delta;2 on the far right side of the last equation. But then below that he uses:


 * $$e_v = m_v \delta g_v r \ln \left ({S \over r} \right )$$

So I don't get it. Maybe I just haven't read the paper enough. - Omegatron 23:00, August 6, 2005 (UTC)

Just noticed Peek uses 0.301 and blaze uses 0.0301. Maybe just a kV/cm vs V/m discrepancy? I want to use non-prefixed units for the version on this page. - Omegatron 23:06, August 6, 2005 (UTC)


 * I am aware of the discrepancy between my equation and the referred Peek's paper. As you noted, the other equation leads to a delta squared term, which is wrong. In my opinion its a mistake in Peek's paper.


 * Also, the equations on Blaze Labs use non prefixed SI units for all parameters, unlike Peek's original work. The difference between 0.301 and 0.0301 is not a discrepancy, but just the difference between Peek's kV/cm and Blaze Labs V/m.


 * 1kV=1000V
 * 1kV/cm = 1000V/100cm=0.1V/m
 * 1kV/cm= 0.1V/m
 * 0.301kV/cm= 0.0301V/m
 * 0.0301 or 0.301 are not kV/cm or V/m. the quantity is the square root of a length.Dvd7587 (talk) 20:39, 31 October 2012 (UTC)
 * Me too prefer non prefixed units.


 * User:Blaze Labs Research

Air density

 * $$\delta = {3.92 b \over 273 + t}$$

where
 * b = pressure in centimeters of mercury
 * t = temperature in celsius

At STP (760 mmHg and 25&deg;C):


 * $$\delta = 1 = {3.92\cdot76 \over 273 + 25}$$

S is the spacing between the wires r is the radius of the wires e_v is hte visual critical votlage observed voltage to neutral at which corona starts g_v is the visual critical gradient

Another version?
User:Light current added a different version. I think it is for a wire inside a cylinder, though:

Ec/d =31.53 +9.63/sqr(dr)

where:

E is inception field strength for corona in kV/cm,

r in dia of inner conductor in cm

d is the relative air density defined by:

d=p*293/760(273+t) =0.386p/(273+t)

where p is pressure and t is temperature

it's actually the same thing with slightly different contants and 31.53*0.301~9.63 — Preceding unsigned comment added by Dvd7587 (talk • contribs) 20:33, 31 October 2012 (UTC)

Equations
for working on peek's law and such:

http://sudy_zhenja.tripod.com/lifter_theory/toolbox.html

http://myst-technology.com/mysmartchannels/public/blog/50288

http://sudy_zhenja.tripod.com/lifter_theory/

How visible?
When it says visible corona, does it mean visible to the naked eye. also under what lighting conditions is it visible? IOW: does it need a darkened room


 * Not sure. Everyone references it as if it's the actual corona threshold, but then I noticed it is specifically called the visual threshold, ev in his paper, and e0 is the "disruptive" threshold, whatever that means.  More research is needed.  For now, just quote his terminology verbatim. - Omegatron 19:20, August 9, 2005 (UTC)

"Units, needs SI version yet"
Yeah. Well, there are several equations for different geometries, and I'm not sure which would be considered "Peek's law".

Then we have to convert everything to SI units and add "unit removers" since his equations are just empirical and don't follow dimensional analysis exactly.

Also, there are apparently newer, more accurate equations developed by Zaengl as discussed on Talk:Corona discharge, so I don't know what to do with all this. - Omegatron 19:20, August 9, 2005 (UTC)

Ambiguities
The article is ambiguous in two ways which hamper its usefulness. I found these when trying to work out a simple example. I have three suggestions: 1) Say what the units of "r" are. Not important in the logarithm ratio, but in the factor of r before it matters. 2) Clarify what is meant by "S". Is this the separation of the nearest surfaces, or the separation of the centers of the wires from each other (or from the center of the geometry?) Note that as the value of S/r falls through "1", the breakdown voltage becomes negative, which suggests to me that S is really 1/2 the distance between the wire centers, such that S=r corresponds to the wires just touching, giving a breakdown voltage of 0. 3) Work out a simple example. A basic rule of thumb I have heard forever is 10 kV / inch for arc breakdown.  I'm surprised to see 30 kV / cm as the baseline for corona.  But 30 kV / cm would work if the units of r are cm; then a VDG with a 1 m diameter sphere upper electrode would be expected to corona at 30 kV / cm * 50 cm = 1.5 MV, which is about right. Pqmos (talk) 20:26, 7 June 2012 (UTC)