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I want to know what the maximum possible angle is that a lightning bolt can take in the path of least resistance.

The idea behind this question is that because the lightning bolt must touch the ground, there shouldn't be an angle higher than X amount for it to accomplish this task. There should be some sort of equation that proves it is less efficient to travel upwards, 90 degrees or more, in order to find the path of least resistance.

For example: Say I have a lightning bolt that must hit the ground. This means that the "default" path of least resistance, provided there is nothing of a benefit or detriment in it's way, would be straight down. However, in the real world this is not the case as there is always something in the way. This means that it must arc to a mass which would allow it to travel faster than any other mass. Using these rules, there should be a way to prove that lightning cannot travel upwards, as losing distance is more detrimental than taking the path of a mass that is slightly less conductive, but closer to the ground.

Where is this point at which it is no longer efficient to travel through in order to accomplish it's task?

I have thought about it, but I'm not adequate enough in resistances, nor the math to prove it.

Fundamentally, the angle it takes must not be at the same altitude as another mass, so dependent on how far it must travel to hit the next mass and the curvature of the earth, it can't possibly be above "X" amount (Another example of this would be if you had the same situation as before, just with a mass that is less efficient on it's path down, and another mass to arc to which would be less resistant than the one directly below it).

The application of this is within a 3D world, but with no curvature (a game I'm making), so in my scenario it's important not to calculate Earth curvature; however, assume all other variables are the same as they would be on Earth. I'm trying to create "natural lightning," but without randomization through numbers, and instead by using the "air." This is what prompted this question, and I would really like to know what the circumstances would be on Earth.

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    $\begingroup$ I thought lightning often travelled upwards (from ground up) or sideways (between charged clouds)... $\endgroup$ – ZeroTheHero Feb 4 '17 at 17:31
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As I know, the lightning bolt does this differently, because it cannot predict what's on it's way, what it does is that it take a kind of optimization approach, it uses fractal as a way to look for the best path to get where it wants to go, and actually a similar approach is used by a fungi to look for its food, here is a video of this fungi creating paths from different feeding points (https://www.youtube.com/watch?v=GwKuFREOgmo)

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  • $\begingroup$ That's amazing, and helps a lot when you think about the fact that lightning would that also, however that does mean that lightning does not need to touch the ground, it could go everywhere as long as they were less resistant than the ground. I thought lightning was so powerful that it "predicted" the path of least resistance when it was charging to discharge correctly because of the sheer amount of static that happens to discharge, though. $\endgroup$ – user3097852 Feb 4 '17 at 17:27
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    $\begingroup$ yes, but it want to discharge in the ground as you can see from lightning pictures, the intensity is more high for the main path that goes directly to the ground. It really is a fascinating technique to look for the minimum path, and how that fungi use it so well, just fascinates me. $\endgroup$ – Ismasou Feb 5 '17 at 14:15

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