Monday Mar. 2, 2015

Today we will be discussing lightning (return stroke) currents.  Today we'll look at what current properties or parameters are of most interest (from a lightning damage or protection point of view) and look at ways of directly measuring lightning currents.   In the next lecture we'll look at how return stroke currents can be determined from remote measurements of lightning electromagnetic fields.

The outline below was on one side of a class handout.  We'll cover everything with the exception of 2(d), currents measured in lightning strikes to aircraft.

Links to all but references 3, 4, and 5 can be found at the end of today's notes.  Many of these studies are still the source of some of the best lightning return stroke current data available.  Table 2.1, for example, in M.A. Uman's 2008 book "The Art and Science of Lightning Protection" is largely adapted from Reference #3.



The CN Tower, shown above at left, was completed in 1976 and was, at the time, the tallest free standing structure on earth.  It is still the tallest structure in the Western Hemisphere.  From left to right in the right figure are the Burj Khalifa in Dubai and now the tallest structure on earth, the CN Tower (Toronto) and the Willis (Sears) Tower in Chicago.


Now a quick look at the engineering parameters and examples of situations where they are important. 

Peak current is of interest when lightning strikes an object that presents a resistive load to the lightning current.  M.A. Uman uses the example of a phase conductor on a power line in his book on lightning protection.  When lightning strikes a power line, pulses of current will travel outward away from the strike point much as a signal travels along a transmission line.  Power lines, apparently, have a characteristic impedance of about 500 ohms.

A 1st return stroke has an average peak current of about 30,000 Amps.  Assume that the current divides in half as it moves away from the strike point as shown above.  This will produce an over-voltage of 15,000 Amps x 500 ohms = 7.5 MVolts. 

An electric field of about 3 MV/m breaks down air.  A 7.5 MVolt over-voltage thus could be high enough to spark across to a ground wire or to one of the other power lines.  This produces a "fault" and would most likely cause a circuit breaker to trip and stop the flow of current.

Lightning rods on the house sketched below are connected to ground rods that are driven into the soil. 


Depending on the soil type and moisture content, the ground resistance can range from a few 10s of ohms to a few 100s of ohms.  A peak current of 30,000 Amps would produce a voltage of 750,000 volts across 25 ohms and 7.5 MVolts across 250 ohm. 

The latter value almost certainly would be enough to spark across to nearby plumbing or some other part of the structure .  The lightning rod should be electrically connected (bonded) to a nearby water pipe to prevent this kind of occurrence.  When everything is electrically connected, the whole structure would "float" up to 7.5 MVolts, but there won't won't be any potential differences or arcing through or between different parts of the structure.

The peak value of the return stroke current derivative is of interest if lightning strikes something with an inductive impedance. 

The straight,  down conductor, in the sketch above has an impedance, L, of roughly 1 microHenry per meter.  Lightning return strokes (both 1st and subsequent strokes) have peak current derivatives values of about 100 kA/μsec or about 1011 A/sec.
The voltage produced here will be L x dI/dt = 1011 A/sec x 10-6 H = 100,000 volts for every meter of the down conductor.

The lightning dI/dt will produce a time varying magnetic field that can couple into nearby electronics (loops are of primary concern).

A current moving along a long vertical conductor as shown above will generate an azimuthal magnetic field, B.  Faraday's law of induction states that an electromotive force (EMF) or potential difference (ΔV) will be induced across the open ends of a nearby circuit when the magnetic flux through the crossectional area of the circuit changes with time.  In the simplest case B might be uniform across the area of the circuit.  Then ΔV will just be equal to the area of the circuit times dB/dt.  The time derivative of B in turn depends on the time rate of change of the current, dI/dt. 


The time integral of the return stroke current gives the total charge transferred during the strike.  This apparently determines (and this is something I don't really understand) whether the lightning current will burn through a sheet of metal (such as a metal roof or the thin metal skin of an airplane).


The lightning will burn through the metal sheet unless heat can be carried away from the strike point quickly enough.   Not as much charge would be needed to burn through thin sheets because they won't be able to dissipate heat as quickly as thicker sheets.  Here it is the continuing currents that are of concern because that is where most of the charge transfer occurs.  I like to think of the lightning strike resembling an arc welder in this kind of a situation. 


The last parameter of interest is called the action integral


The instantaneous power dissipated by a resistive load is


so the energy deposited is R times the action integral

This will cause heating or even vaporization of materials with low electrical conductivity that are struck by lightning.  Lightning can vaporize the sap in a tree, for example, and cause the tree to explode.

Some of the earliest estimates of return stroke peak currents come from measurements of the residual magnetism in nephelitic basalt (whatever that is) near trees that were struck by lightning (within centimeters of the tree perhaps).  The data were published by Pockels in 1897 & 1898 (the publications would be interesting to look at, but they are in German).

Pockels had determined, in laboratory experiments, that the magnetization of the basalt depended on the peak current value alone and wasn't affected by the shape of the current waveform or its duration. 

The sketch below shows a klydonograph.  A high voltage will produce a Lichtenberg figure on the film. 



The diameter of the pattern depends on the peak voltage which can then be related to peak current if the impedance of the arrangement is known. 



Different patterns are produced depending on the polarity of the applied voltage.  Here's an informative web site with some interesting historical background on Lichtenberg figures.

A Lichtenberg figure like pattern is often burned into the grass on golf courses when lightning strikes the flag on a green.  You'll find a particularly good example from a strike in Tucson here.  Similar burn patterns are, apparently, sometimes seen on lightning strike victims.

"Magnetic links" have been used extensively by the electric power industry to estimate peak currents in lightning strikes to power lines.

A magnetizable material is positioned perpendicularly to a straight conductor.  The strength of the magnetization in the link can be related to the peak current in the conductor.  Often two or more links are mounted with different orientations and at different distances from the conductor.

An inexpensive version of a magnetic link was at one time used at the Kennedy Space Center to estimate peak currents in certain launch facilities.  A strike to a launch complex would probably require time consuming and expensive testing to ensure the facility hadn't been damaged and was still fully operational. 



A loop of prerecorded magnetic tape (on a plastic support and sealed inside a length of  PVC pipe) was positioned perpendicularly to conductors that might carry large amplitude lightning currents.  A portion of the signal on the tape would be erased by the magnetic fields produced by lightning currents.  The magnetic tape wouldn't be removed and analyzed unless the photo bulb had flashed, indicating that a lightning strike had occurred.

A wire loop placed close to a straight conductor (the vertical conductor could be the lightning channel itself) can be used to determine the current derivative.


The output voltage across the open ends of the loop will be proportional to dI/dt.


This is the principle behind a Rogowski Coil used to measure time varying currents moving through a conductor.  Multiple loops of wire on a toroidal support surround the conductor.  The output voltage ΔV will be N times the expression above (N is the number of loops in the Rogowski coil)


The multiple loops of wire increases the inductance which limits the high frequency response of a sensor like this.

A sketch of a faster dI/dt sensor is shown below.

The induced voltage is measured across the gap on the inside surface of the sensor.  Sensors like this are used to measure lightning dI/dt signals and also are used in nuclear electromagnetic pulse testing.

Breaking the current conductor and adding an in-line resistive element is perhaps a more obvious way of measuring lightning currents.

Ideally then you would measure a voltage across the "shunt" that is simply R times I (R is the resistance of the shunt and I is the lightning current).  Very low resitance values (on the order of a milliohm) are needed because peak lightning current amplitudes are large. 

As the picture above shows however, measuring the voltage across the shunt introduces a loop circuit.  The lightning will produce a time varying magnetic field that will couple into the loop.  This will add an L dI/dt term to the output voltage.  Even if L is small, the lightning peak dI/dt can be very large.

The problem with induced voltages in the measuring circuit can be avoided if a coaxial shunt design is used.


Here's a crossectional view.  The resistive element has a cylindrical shape and the measuring circuit is inside the cylinder where the magnetic field is zero (B fields from currents flowing in the right and left hand sides of the cylinder point in opposite directions and cancel).  The measuring instrumentation is placed in the metal enclosure (rectangular or cylindrical), a Faraday cage, at the top part of the figure.  Signals could then be sent out on fiber optics cables to a nearby trailer for recording. Current is shown flowing through one side of the diagram.  In reality it flows through all sides.

We rushed through this last figure in the last minute or two of class so I will copy it over to the Wednesday, Mar. 4 notes and we will start class there.


Numbered references cited at the beginning of today's notes (full citations can be found in the Articles folder)

1.  McEachron, K.B., "Lightning to the Empire State Building,"

2.  Berger, K., "Novel Observations on Lightning Discharges: Results of Research on Mount San Salvatore,"

3.  Berger, K., R.B. Anderson, and H. Kroninger, "Parameters of Lightning Flashes,"

4.  Anderson, R.B., and A.J. Eriksson, "Lightning Parameters for Engineering Application,"

5.  Garbagnati, E., F. Marinoni, G.B. LoPiparo, "Parameters of Lightning Currents.  Interpretation of the Results Obtained in Italy,"

6.  Hussein, A.M., W. Janischewskyj, J.-S. Chang, V. Shostak, W.A. Chisolm, P. Dzurevych, and Z.-I. Kawasaki,"Simultaneous Measurement of Lightning Parameters for Strokes to the Toronto Canadian National Tower,"

7.  Leteinturier, C., J. Hamelin, and A. Eybert-Berard, "Submicrosecond Characteristics of Lightning Return-Stroke Currents," 

8.  Fisher, R.J., G.H. Schnetzer, R. Thottappillil, V.A. Rakov, M.A. Uman, and J.D. Goldberg, "Parameters of Triggered-Lightning Flashes in Florida and Alabama,"

 Again, the links above will take you online e-journal copies (usually PDF files) of the article that have been accessed via the UA Library; they may not be available to you if you try from an off-campus computer.