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First I am going to describe what many physics books and physicists say about lightning rods, and then I am going to present some more recent things I have read, and ask if anybody on this list knows more about the subject.
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I started looking into this when a roofing firm was telling me about the subcontractor they use to install lightning protection on houses and buildings they roof. The lightning protection firm says it is false that lightning rods prevent lightning, and it is also false that lightning rods attract lightning. The only thing lightning rods do is route the lightning though a safe path.
To me it seems inconsistent that the rods can route the lightning if they don't first attract the lightning.
* * * Another idea * * *
It appears there has been some legitimate research that lightning rods should not be sharp, but also not be "too dull." A sharp point is bad, a large conductive ball end is bad, but a radiused rod (perhaps a 2-cm diameter rod with rounded top) is best.
The experimental evidence is that sharp rods and radiused rods have been put on a mountain, and the only the radiused rods get strikes. The sharp rods do not get strikes.
The theoretical interpretation is that the electric field near the sharp point is higher than the field on the radiused rod *if* you are observing near the end of the rod. However, as you go up in the air above the radiused rod, the electric field becomes higher. Therefore, when the strike is about to occur, the ion path forms more easily over the blunt rod because the electric field is higher there. It might be that the corona discharge from the sharp rod puts so many ions in the air around the end of the rod that the ion density is high enough over a large enough area that the sharp rod essentially appears as a rounded ball due to the space charge.