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I have this simple question, but I cannot find the answer.

I saw this video about a plane getting hit by lightning. In it, Captain Joe explains why people do not get electrocuted. This has a simple explanation, due to the Faraday cage effect produced by the fuselage. But another question come to my mind in that moment: why does the aluminum from the fuselage, that acts as a Faraday cage, not melt because of the extreme currents carried by the lightning?

After this, I thought about the following example: A thin metal (correctly grounded) lightning rod is almost intact after a strike, while a tree breaks in the middle and sometimes it even burns:

Tree burning after a lightning strike.

Clearly it has something to do with the resistivity of each material, much higher in the tree's wood.

It is also said in this article that the only dangerous zone a plane can get hit "is the radome (the nose cone), as it's the only part of a plane's shell that's not made of metal". So it clearly has something to do with the conductive properties of the fuselage.

So my question is basically this: why does a tree break and burn when struck by lightning but a lightning rod does not?

And, ultimately: why does a plane hit by lightning not melt with the hundreds of thousands Amperes going through the fuselage?

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    $\begingroup$ The trunk of a tree contains water. A lightning strike can heat some of that water to the point where the vapor pressure is high enough to split the wood (i.e., it causes a steam explosion.) The same thing can not happen in the aluminum skin of an airplane. Even if a lightning stroke was to deposit enough energy to cause some melting, that's all that would happen: the aluminum would merely melt. It would not explode. $\endgroup$ – Solomon Slow Nov 16 '17 at 13:50
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    $\begingroup$ @jameslarge I'm not sure melting is much better than exploding for a plane. $\endgroup$ – JAB Nov 16 '17 at 19:07
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    $\begingroup$ @JAB google for "aircraft lightning strike damage", click the "images" tab, judge for yourself. $\endgroup$ – Solomon Slow Nov 16 '17 at 20:08
  • $\begingroup$ First, what actually happens when a plane is struck by lightning? Is the path cloud -> plane -> ground? Or does the plane just equalise in potential to the surrounding cloud/air? $\endgroup$ – peterG Nov 16 '17 at 23:52
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    $\begingroup$ @jameslarge that should go in the answers box to be honest. $\endgroup$ – Tim Nov 18 '17 at 2:13
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The amount of heat generated by current flowing through a resistor (whether from lightning or more ordinary sources) is directly related to the power dissipated by the resistor, which is $$ P = I^2 R.$$ $R$ is small for objects made from good conductors, which many metals are, and large for objects that are made from bad conductors like plastic or wood. Since a lightning strike has a very short duration, the total heat generated during such a strike is not enough to melt metal, but enough to set wood aflame or melt plastic.

If you let the large currents from the lightning strike run through the metal for longer, it probably would also heat up gradually and eventually melt, but this would take longer than the time scale on which lightning occurs.

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    $\begingroup$ It might be worth pointing out that, for a lightning strike, the resistance of the last few feet probably has very little effect on current, so we can treat I as relatively constant. That makes your P=I^2R connection even more powerful. $\endgroup$ – Cort Ammon Nov 16 '17 at 15:34
  • $\begingroup$ This makes it valid. This answer is missing this very important detail; see the other answer for that. $\endgroup$ – user27542 Nov 17 '17 at 14:40
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The high electrical current in a lightning strike delivers heat energy along the full length of the lightning bolt. Part of that length is in the ionized air over the plane, part is the plane's fuselage, and part is the ionized air from the plane down to ground. The current is the same, but the heat generated is proportional to the electrical resistance of the path, and the aluminum of the plane (as well as the joints that hold the aluminum parts together) has very low electrical resistance. So, the air path gets very hot, while the aluminum path does not.

Trees and air have high electrical resistance, but (at breakdown) have a narrow conducting channel (ionized gas is 'Z-pinched' into a narrow channel, and the first woody parts that carbonize will hog all the current). So,

$$HeatPower = I^2 R = I^2 \rho * L/A$$

Heating per unit length of air is more than the aluminum plane because air has higher resistivity, even with comparable conduction cross-sectional area.

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A tree contains a lot of water which converts explosively into gas when the electrical current flows throughout the tree. Wood is also more combustible than metal, so it catches fire due to the extreme heat.

In an plane fuselage, the current flows harmlessly along the outside of the plane and back out. The plane is not grounded. The same way a car is isolated by having rubber tyres.

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    $\begingroup$ Isolated by tyres? The bolt just bored through miles of air, and it will stop because of rubber? Why not just ignore the tyre and jump through the air the remaining few inches? $\endgroup$ – JDługosz Nov 16 '17 at 21:11
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    $\begingroup$ @JDługosz: The lightning bolt goes wherever it wants, of course. But it doesn't particularly want to hit the car, because the tyres have prevented a countercharge from the ground from flowing up into the car's frame and attracting the lightning that's coming down. (No, that is not the explanation this answer seems to suggest). $\endgroup$ – Henning Makholm Nov 16 '17 at 23:52
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    $\begingroup$ lightning does strike cars. I can’t find anything on whether lightning is more or less likely to strike a car, per se, but have seen statements that height matters, and "good" vs "poor" conductors only matter in choosing between two close together targets. $\endgroup$ – JDługosz Nov 17 '17 at 0:03
  • $\begingroup$ @HenningMakholm youtu.be/9Du_w976s5Q $\endgroup$ – zane scheepers Nov 17 '17 at 0:15
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    $\begingroup$ Its not the rubber tires or that its grounded that protects you in a car. It is because the car is effectively a Faraday cage. $\endgroup$ – Kevin Milner Nov 17 '17 at 18:39

protected by Qmechanic Nov 17 '17 at 5:49

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