# After a lightning strike into the ground

From the series of articles "Lightning protection for beginners".

After this TV program of the "News" even pop stars could not compete with the popularity of high-voltage engineers. Everyone wanted to know whether it was true that after a lightning strike a Chinese citizen fell to the ground, quickly jumped up, dusted himself down, and was about to move on, but the second lightning knocked him down again and again without fatality. There are a lot of similar stories. Popular books and magazines will tell you about the mass lightning strike of football players at the stadium, passengers at the bus stop and almost the whole herd of cows in the pasture. These are terrible stories. A dozen of people in hospitals. But a hospital  is better than a cemetery. Maybe the danger of lightning has been greatly exaggerated, if a person is able to sustain its direct effect? But who said that the impact is direct? Most often it is not so.

A lightning strike is accompanied by a strong electric shock. Even the average strength of lightning is close to 30 000 A, and the strength of the most powerful lightning is almost an order of magnitude greater. Finally, the current spreads in the ground around the whole Earth's volume. Any lightning rod should be necessarily grounded. To do this, a ground electrode system is mounted at the lightning rod. It is formed by one or more underground grounding electrodes, vertical or horizontal. The current gets into the ground from metal electrodes, where, as in any conductor, Ohm's law is valid. Multiplication of current to resistance gives voltage, in this case, voltage on the ground electrode:

The expression seems to be familiar, but it's still not quite so, because we are talking about voltage in the ground, which is considered to be zero. It is grounded in order to avoid voltage. And then it turns on its head, and not in a figurative sense, but literally. The voltage affects a person through legs, that normally and firmly stand on the ground. This requires an explanation. We need to start with the most simple. If soil is considered to be a good conductor? The answer seems obvious - of course it is good, if electrical and safety experts are always talking about grounding. In science and technology the experts are used to the specific assessments. The words of many-few, good-bad do not explain anything in fact. The quality of conductors is estimated by their resistance. A good soil has resistance close to 100 ohm * m - a billion times greater than that of black steel! The comparison is more than convincing. It helps to a very large  volume over which the lightning current is spreading.

I don't want the reader to catch me on a qualitative description and therefore I go straight to the quantitative estimatations. To do this, it is useful to take advantage of another option from the school physics, instead of using the usual voltage. I am talking about the strength of the electric field. It is voltage drop value in some environment per a unit of length, for example, the voltage drop in the ground over a length of 1 m. By the way the length of 1 m is an approximate step length of an adult. You remember that intensity is measured in volts per meter. If the electric field E in the groundgr is equal to 1 V / m, there will be voltage between human feet on the length of l = 1 m.

Time to estimate the electric field of the lightning current in the ground. Let's imagine that it hit the lightning rod, the ground electrode of which is in the form of a hemisphere with a diameter d = 0,5 m (a pot or a cauldron for pilaf of a medium size) and is buried into the ground, as shown in Fig. 1. Lightning current IM will symmetrically drain from the surface of a metal hemisphere, where its density will be

For a lightning current of medium strength of 30 000 A in our case jM ≈ 7,6 × 104 A / m2. Then complete analogy with Ohm's law. To get intensity in the ground Egr, it is necessary to multiply the current density on the soil resistivity ρ.

Even if we focus on the highly conductive ground (ρ ≈ 100 Ohm * m), we get a very impressive value of 7.6 million V / m. The voltage on the step length of 1 m will be nearly eight million volts. It is hard to imagine that that Chinese was able to sustain that without harm to health. Most likely, the second lightning would not be required.

The value obtained here is called by the specialists step voltage (or voltage of step). It is important to understand how it changes in the vicinity of lightning impact point. If the ground is the same everywhere, everything will be determined by lightning current density. With the distance from the hemispherical ground electrode, the surface through which the current flows because of the symmetry force will remain hemispherical and its radius r will continuously increase. However, it will increase the hemispherical surface area, "filled with" current and, accordingly, reduce its density.

The electric field strength will also begin to decline rapidly

At the distance r = 10 m from the initial millions in our example only less than 5000 V / m will remain. It is significant, but as a rule, not fatal, because the time of high voltage operation, as well as the duration of the lightning current is hardly greater than 0.1 millisecond. High-voltage trip can easily knock down, but a human will most likely have the strength to get up.

If the reader is not bored with figures and he got to this line, it will be more easy to understand where the old recommendation of not to hide from the storm under the big trees came from. Due to the considerable height a lightning strike into them is most likely. After the strike, the current will flow through the root system of a tree like through the ground electrode. The electric field is especially great close to the roots. It is clear that it is not recommended to stand here, to sit and lie down too, especially because the person is twice longer than his step length.

If you come back to the figures, it must be admitted that they are not exaggerated at all. Even a lightning current of 100 000 A cannot be called a rare thing, and soil resistivity can be ten times greater than the used in the estimations. For this reason, life-threatening step voltage can be kept at a greater distance from the point of a lightning strike. Finally, it is necessary to take the shape of the ground electrode into account. All estimations above were made for a hemispherical ground electrode. Its electric field, as can be seen from the formulas given above, decreases very rapidly - in inverse proportion to the square of the distance. More often ground electrodes are mounted from extended buses or rods, hardly similar to a hemisphere. Their electric field decreases much more slowly. As a result, the radius of a dangerous meeting with lightning increases significantly, sometimes to many tens of meters. So, mass impact on people at the beach or on the football field are explained this way.

Шаговое напряжение, кВ- step voltage, kV

Грунт 1000 Ом м – Soil 1000 Ohm m

Ток молнии 100 кА – lightning current 100 kA

Удаление от заземлителя, м – distance from the ground electrode system, m

You see the results of the step voltage calculation for a typical grounding device that is recommended for lightning protection by the national regulation. It consists of a horizontal bus of 10 m and three vertical rods 5 m each - two at the edges of the bus and one in the middle. Soil resistivity 1000 Ohm * m (unmoistened sand), lightning current 100 kA. This is a powerful lightning - the current of 98% of lightning strikes is weaker. The figures in the diagram are impressive - hundreds of kilovolts directly at the ground electrode, more than 70 kV at the distance of 15 m and not less than 10 kV at the distance of 40 m.

When the Cathedral of Christ the Savior was being reconstructed in Moscow, the designers took into account that with its considerable height almost annual lightning strikes can be expected. It is possible that the strike will happen on a holiday, with a large crowd of people on the porch. To ensure the safety of the parishioners it was necessary to ensure spreading of the lightning current over a very extensive system of underground buses, thereby minimizing step voltages.

Strong electric field in the ground carries another nuisance. When the field strength rises to 1 MV / m, ionization begins in the ground. In certain conditions, this leads to an increase of the plasma channel, which slides along the surface of the ground, slightly burying into it. Channels (and there may be several channels as in this photo taken in the laboratory) can move from the injection point of the lightning current

to tens of meters. In fact, they should be considered as a continuation of lightning, not only in the air but along the ground surface. I must say that they are not becoming less dangerous, because the current in the channel is tens of percent of the lightning current and the temperature is certainly higher than 60000. I hope the reader will not need great imagination to imagine the consequences of contact of such a channel with the zone of fuel leakage at the oil loading rack or with an underground cable, for example, a phone cable or a cable controlling microelectronic system.

In the dry 2010 the Central Television aired a report from a completely burnt down village in Omsk region. The fire was caused by a lightning strike. The Moscow correspondent asked the village elderly ladies: "Why the fire was not doused?". They replied in unison; "We were scared - arrows of fire were crawling over the ground." Look at the picture again. Looks like arrows, you see? The elderly ladies were not afraid in vain. The electric field of the spark channel is not much different from the field of the metal buses. Approaching to them can be fatal.

It is enough to make sure how creative lightning is. You made a strong protection from above with the help of lightning rods, and it breaks to you workaround, paving its way along the ground surface. That's why almost all popular articles end with an appeal not to forget about the professionals. It is risky to make jokes with terrible natural phenomena and it is unacceptable to treat them carelessly.

E. M. Bazelyan, DEA, professor
Energy Institute named after G.M. Krzyzanowski, Moscow

We hope that in the future this site will perform the role of an elementary textbook for self-defense against lightning. We plan to continually post articles about the real dangers of lightning electricity and modern means of lightning protection here. They are designed to help to sort out the existing problems and to estimate the ways to solve it.