If you just use di/dt for calculating voltage drops on lightning
conductors you can get some very misleading answers. Sure if you have a
known rise time and inductance you can calculate a voltage, but that
doesn't convey much information. It isn't even the fast edges on the
lightning pulses that cause the most damage. Those can punch holes in
you coax jacket, but they won't melt the coax (unless it happens to be
in the center of an arc). The huge voltages cause big arcs, but most of
the damage is done by the energy contained within the wider pulses.
Those wider pulses may be up to 10 ms wide or more, at hundreds to tens
of thousands of amps.
So if you are trying to calculate voltages and currents on things you
need a tool that considers the whole waveform. Also you need to decide
what the source waveform should be. It will vary a lot at different
points on the tower and it will vary a lot between different types of
lightning strikes. Many times you will see references to a standard
lightning waveform, but that is for a specific purpose, usually cables
on a power pole or in a conduit or something like that, with different
levels for different conditions. A tower will be completely different.
It's out there in the open being hit directly so it is subject to the
entire wide variety of lightning waveforms that mother nature can
generate, and they are not nearly all the same. Even the max current
pulse that should be used is questionable. Current pulses up to 340,000
amps have been recorded. Those are apparently rare (recording is also
rare), but what number should you use a design criteria? I would think
it should be something more than a typical value. A tower will also
ring like a bell when hit with a strike. Not only do you get the
initial pulses but you get some sort of distorted damped sinusoid
To complicate the problem even more, you have to calculate the induced
currents. In a lightning strike these are NOT negligible. Just ask
anyone who has some long cables near a strike, or has a house
wired-intercom and lightning happens to hit near the house. Near the
tower, induced currents can be huge.
Once you analyze all this you can start to get a feeling of what is
really happening. It's not a trivial analysis. When you see cable
lightning currents calculated by very simple formulas, you can bet the
answers are completely worthless.
A couple of other points:
1. Obvious but worth stating: For the high frequency edges on lightning
strikes, inductance always dominates the calculations for conducted
currents. However, as stated above those aren't the currents that cause
the most damage. Also induced currents have to be added and those may
not take the same paths.
2. You can reduce conducted currents on a cable by coiling the cable to
make a choke, but it is a two edged sword. Reducing the currents
increases the voltage drop across the choke and it may increase
susceptibility to induced currents.
It is obvious that this gets very complicated when you try to calculate
anything. It would be really nice if everyone was able to optimize his
tower system by calculating the expected currents on things, but it just
isn't going to happen for the average guy, at least not with any
dependable accuracy. I'm afraid we are limited to the (hopefully)
overdesign by rules method.
Jim Lux wrote:
>>Having the cables exit the tower above ground is a really bad idea.
>>Voltage drop down the tower is very high during a strike. Anything
>>exiting the tower above ground will see a very large voltage impressed
>>on the cable at the point it exits the tower.
>But how high? And what needs to withstand that potential?
>The voltage would depend on whether resistance or inductance dominates.
>A 30kA strike on a 1 ohm tower would only be 30kV over the whole length
>of the tower.. call it on the order of 5kV over a 10 foot length out of
>a 60 foot tower.
>A 30kA strike with a rise time of 2 microseconds on a 20 microhenry
>tower (1 uH/meter) would result in a voltage across 10 feet of about
>3E-6*30E3/2E-6 or 45kV.. so for the direct strike scenario, the
>That translates into very
>>high currents on the cable. Those currents go toward the shack instead
>>of into the ground at the tower base.
>If the cable has a low enough impedance relative to the path through the
>Considering the example above, where the di/dt makes the voltage 45kV.
>If the cable path has some extra inductance (say by coiling the coax a
>few times), you could make the path along the coax very much higher
>impedance than through the tower, so the majority of the current might
>flow through the tower. Using 30kA as your stroke current, say you
>wanted to limit the current through the jacket to 1kA (peak).. you'd
>need the coax path to have 30 times the inductance of 10 feet of tower.
>12 turns, one inch apart on a 12" diameter form would be about 28 uH.
>12 turns, 1/2inch apart on a 8" form is 23 uH. The former is about 10
>times the inductance of the tower to ground from 10 feet up (I'd guess
>the tower is <3uH) (I used Wheeler's approximation for inductance)
>I chose 1kA as a round number, and on the assumption that the fusing
>current of the jacket is quite a bit greater than the AWG13 center
>conductor of a RG-213 style cable. 16 AWG wire has a fusing current of
>about 100-150 A steady state. AWG13 is twice the area and fusing current
>runs roughly as the area (for small changes in area). This is also a
>short pulse at 1kA (lasting, say, 50 microseconds)
>So, at least the coax won't melt, and if the voltage is 45kV across
>those 12 turns, it's about 3kV/turn. If the turns are spaced a bit
>apart, it won't arc over.
>>1. The cable at the point of exit, looses its mutual inductance with the
>>tower which increases the currents on the cable.
>But, one can fairly easily increase the inductance of the cable, which
>would reduce the current. So I think that effect is a wash.
>>3. The cable is now more suceptible to direct strikes.
>Yes, but it's probably well below the top of the tower, so the tower
>provides some protection (whether you use the rolling ball or cone of
>protection idea, either way, a cable coming off at 10ft on a 60 ft tower
>would have to go fairly far to be a "good" lightning target)
>>4. The cable is also more susceptible to induced currents due to the
>>large loop area.
>That is, I think, the biggest problem.
>>5. There are no good points.
>Not having to dig a trench, not hitting your head on the cable when you
>walk under it, etc.
>There are places where mechanical constraints force doing things like
>this. On commercial installations, they'll have a cable tray from tower
>to building, and presumably, that tray carries a lot of the lightning
>Several folks (N6RK does this, I think) have array setups where the
>feedline is open wire line carried across a field at some feet above the
>field (so that animals can graze underneath)
>VOA's big curtain array in Delano,CA is fed by open wire line supported
>well off the ground. It might be interesting to look at what sorts of
>lightning protection strategies they use. (Although.. they have a big
>enough budget to take a "if it doesn't hurt, why not do it" approach)
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