On 9/26/2011 3:45 PM, Jeff Liebermann wrote:
On Mon, 26 Sep 2011 12:04:21 -0700, Jim
wrote:

On 9/25/2011 7:06 PM, Jeff Liebermann wrote:
The end and
highest antennas were also grounded with a undersized #4 copper wire
running down the pole to a ground rod at the base. We didn't get any
lightning hits because there was an all metal forestry lookout at the
highest point on Santiago which took all the hits.

#4 is plenty big enough for lightning grounding. The current is high,
but the duration is short. You see larger lightning conductors for
mechanical reasons (e.g. where it might get damaged, or where it has to
move repeatedly).

One of the neighboring towers took a direct hit. The #6 AWG he was
using literally exploded, spraying melted copper everywhere and
blowing pieces of concrete block all over the building.

http://en.wikipedia.org/wiki/American_wire_gauge#Table_of_AWG_wire_sizes
Fusing current (32msec) for #4 is 34,000 Amps. The average lightning
hit is about 20,000A but can go up to 200,000A.


One might want to check a different source for fusing current. The
standard test lightning stroke has a 2 microsecond rise time (10% to
90%) and a 50 microsecond fall time (to 50%) typically represented by a
double exponential (1-exp(-t/a))*exp(-t/b), so when you used the
Onderdonk equation, you want to use a 50 microsecond pulse

In general, fusing goes as a function of the "action", I^2*time.

The equation from Onderdonk is usually used for this kind of thing (as
shown in the table you cited). Onderdonk's equation assumes a
rectangular current pulse, but that works for the most part and for
lightning, it would be a conservative estimate.

For a 50 microsecond pulse, the fusing current is 22 amps/cmil (vs .87
A/cmil for the 32 ms pulse)

AWG4 is 42kcmil, roughly, so the fusing current is well over 8000kA

Another approach to analysis might be to consider the energy dissipated
in that wire. It's a bit tricky, because as the wire heats up, the
resistance increases. (by a factor of 4 or 5 at the melting point, as I
recall)

But let's consider a meter of that wire which is 5.189mm in diameter.
it has a resistance of 0.82 milliohm (at 25C). Let's round up to 5
milliohms.

Let's say our lightning stroke has an RMS current of 50kA (peak current
would be higher), so we have (50E3)^2*5E-3 = 12.5 MW. But that lasts
for only 50E-6 seconds, so we deposit 12.5E6*50E-6 = 625 Joules into the
meter of wire.

That wire has 21 sq mm cross section so the one meter length is about
21E-6 cubic meters or 21 cc. Copper has density about 7 g/cc, so we've
got around 150 grams of copper there. At a specific heat of 0.385 J/g
every 58 Joules will raise the temperature 1 degree. Since we're
dumping in about 600 joules, that lightning stroke will raise the
temperature around 10 degrees.

In practice, a typical lightning strike has several strokes, so you
probably dump 4-6 times that amount of energy into the wire. But still,
you're talking maybe a 50-60 C temperature rise, which is LONG way from
the 1000 degree rise you need to melt the copper.


Your observation of total destruction of a copper conductor was probably
from some other mechanism. The electromagnetic forces are the best
candidate. I used to do some quarter shrinking, and a few thousand amps
in sub millisecond pulse would destroy a AWG10 coil from the magnetic
forces.

An unsupported turn of AWG 4 or 6 wire would probably be destroyed by a
20kA pulse with a rise time of 2 microseconds. The di/dt is 400E9 A/sec,
so the flux is pretty spectacular.

The other source of disaster in high power pulse discharges is if there
is a loose connection or a gap in the conductor. The several tens of
volt cathode drop in an arc at 20kA gets the peak power up pretty high,
and unlike in the example above where the 12MW is distributed over a
meter of length, you get that megawatt dissipated in a few cm, so the
energy density is much higher.


http://www.lightningsafety.com/nlsi_info/media.html
Other references offer averages from 5,000 to 50,000A. I would call
#4 marginal but probably adequate for California, which doesn't get
much lightning.