In South Africa, the government stipulates that the maximum allowable
voltage for an electric fence is 10 000 volts. Given this fact, what
would be the minimum separation between a conductor (fence wire) and
ground (the support pole - made from metal) required to ensure that
there is no arcing (across the air gap).

There is obviously an insulator that separates the pole and wire - but
one can draw a straight line through the air between where the wire
leaves the insulator and the nearest point on the pole. This is the
gap where arcing would occur if the wire was too close to the pole.

I would imagine that the answer is dependant on a number of variables
: the humidity of the air, the type (perhaps shape) of pole, etc.
Please assume worst case scenarios for these factors.

Also is it safe to assume that the pole is at earth potential? It is
in contact with the ground, and the energizer is earthed to ground as
well, but the pole and the energizer may be kilometers apart.

simonberry-ga 
                

Qualitative answer to your interesting question is
-------------------
10,000 Volts = E4 V, will arc over 3 mm distance of dry air gap.

 Distance for other voltages is given in this table:
http://www.kronjaeger.com/hv-old/hv/tbl/measure.html

Here are few examples of arcing shown on this web site
http://www.kronjaeger.com/hv-old/hv/do/sparks/index.html

For more detailed answer we need to differentiate three kinds of electrical
------------------------
 problems caused by high voltage in the open air:

Tracking, Corona Discharge and Arcing   - They are defined here

http://www.ctrlsys.com/library/applications/electrical-2.php

Corona (partial discharge) is most frequent,and can be observed, and
heard, on humid days on the high voltage lines. It is causing a
cumulative damage to insulator surface and usually precedes the
insulator failure. For this reason high voltage lines are regularly
inspected and monitored. Even though corona on the high voltage lines
is often visible to the naked eye, special equipment was developed for
its monitoring, such as this

The Ultrawave 170 Corona Tracer from SDT  designed specifically for
electrical and insulation inspectors.
http://www.sdt.be/03applications/acorona.html

 Procedures for such regular inspections are described in this
Technical paper in  PDF format:
http://klabs.org/DEI/References/design_guidelines/test_series/np1415.pdf

Influences on the breakdown Voltage
-----------------------------------

The exact values of breakdown depends 

1) on air properties 
     (hot, humid, low pressure, ionized air will develop arc sooner) - and 

2) on the Electric Field gradient 
       (this is how shape of electrodes enters the equation).
        Sharp edges and points mean high gradient. 


3) on properties of the surface (hot, wet, rough surfaces will promote
discharge).

4) It also depends on history: Once the  spark jumps, or arc is ignited,
   air is ionized and subsequent electric conduction is easier. 

Examples - of several effects:
-----------------------------
Several such effects are illustrated by common fluorescent tubes
used at homes. Here high voltage pulse initiates the discharge, in
partial vacuum, and discharge  is then maintained by the ordinary
voltage.
Same effect (ionization making air conductive) also happens during the lightning:
http://teslamania.delete.org/frames/longarc.htm#Pos-Lightning1

Another effect illustrated by the fluorescent tubes is that high
voltage spike which usually starts the discharge, happens when current
is suddenly interrupted.
(In the fluorescent light fixture this is done intentionally, by
ballast and starter ,as described here
http://home.howstuffworks.com/fluorescent-lamp4.htm  )
but most often such sparking is undesired, e.g. the  one shown here
http://teslamania.delete.org/frames/longarc.htm#Disconnect
Note that electrodes in the fluorescent tubes are heated to
facilitated discharge. Hot surface is more ready to emit electrones,
which are then accelerated by the electric field. At the given voltage
(potential difference
between the electrodes, the intensity of the field (E or gradient =
Voltage/ distance) is influenced by the geometry.

Shape of the electrode - geometry
-------------------
Electric field and electrostatic potential between sharp electrodes is shown here
http://www.cimne.com/kratos/emant/examples1.asp

Distance from the energizer (sparks vs arc)
---------------------------
Before the first discharge, situation is governed by laws of electrostatics.
For this reason metal pole can be considered to be the 'ground'. After
the breakdown, either spark or arc develops, depending on available
current. This current may be influenced resistance between the post
and energizer - which depends on the distance between the source and
fence.

For many technical details on  breakdown, glow, arc, spark and corona,
you may consult a book
http://www.amazon.com/exec/obidos/tg/detail/-/3540194622/102-7109271-7049768

but first,  and before rating this answer, please, do ask for
clarification (RFC) if I omitted something.

Hedgie

---

Request for Answer Clarification by simonberry-ga on 24 May 2005 23:22 PDT

Thank you for your detailed answer.

You state that the distance is dependent on a number of factors (air
properties, electric field gradient, surface properties, history). Is 
there an equation that incorporates these factors?

Given that the distance is 3mm in dry air for a spherical object, how
could I determine the distance for, eg, a pointed object in humid air
? I don't have a feel for how severely the factors will effect the
arcing distance (i.e will it change to 2.9995mm or 0.5mm ?).

Also, I don't think I was clear on the earth potetial part of the
question. Where the energizer is connected to the fence, it is also
earthed to a spike in the ground. I think it is safe to assume that
the post will therefore be roughly at earth potetial at this point and
that the worst cast potential difference between the post and wire
will be 10 000 V.

However, at a point in the fence 2 km away, could it be possible that
the earth potetial is lower relative to the earth potetial at the
energizer position ? This will have the effect that the potential
between post and wire is (far) greater than 10 000V. (Conversely it
could also be far less...)

---

Clarification of Answer by hedgie-ga on 25 May 2005 06:23 PDT

simonberry-ga
                 Thank you for opportunity to clarify my answer before you rate it.

 I will start with he second part:

A) You question was quite clear:
"could it be possible that the earth potential [at the post] is lower
relative to the earth potential at the energizer position ?"

May be my answer was not. We need to consider two situations:
1) before arc starts -- there is tension - but is no current flowing
      similar to pulling on a rope, close to its strength. There is no motion.
2) after to arc develops - there is a current
      

  The voltage drop (from the stake at the generator to the post) is  i *R

  where R is resistance between the post and the stake. That can be
significant at 2km,
   from kilo-Ohms to Mega-Ohms (depending mostly on soil water content) 

BUT i=0   !!

   therefore voltage drop is 10,000 *0 =0  to 100,000 *0 =0 


  That what I meant by saying 'it an problem of electrostatics' 
  
 meaning : there is no current, therefore no drop.

B) Is there an equation?

    Yes. But they are not very useful for practical cases. 

  First, distance will go up, not down. In very humid air, it will
start arcing  at even larger separation at 10mm or even 20mm, not at
2.9995mm or 0.5mm.
  
  To get quantitative, you would have to defined situation exactly.
Not to say humid, but to say at 70% humidity, temperature 30 C ,
pressure ...

  I came across a chart which shows effect of humidity -and can dig it
up for you, again, but it will not really help you much, in my
opinion:
   
   100% humidity means precipitation. Big drops, little drops? water
films on the insulator?  ..

   there just to many variables in real weather.

   And, you can not say sharp, but give exact geometry. The equation
exist, which will calculate field around a given conductor setup - I
gave you a reference for an image of such a field arond a sharp point.
   It is a Partial Differential Equations - elliptic type - and in
some engineering problems they do solve it on big computers.
    
    But it is not practical for a small home project.  

   That why we invoked the corona discharge at the high voltage lines.
It shows that you cannot completely avoid discharge and arcing. There
is an engineering practice - and it may differ from climate to
climate. But you still get some arcing, at severe weather.

 You need some breakers and other safety devices, if you really want
to put it in place. It should not be  do-it-yourself project.

 Please do read the disclaimers at the bottom:

    Disclaimer: Answers and comments provided on Google Answers are
general information, and are not intended to substitute for informed
professional advice.

 Hedgie

I didn't get the exact answer I hope to get - but I did learn that the
answer was not as straightforward as I expected.