Note that I’m talking about the visual aspect of a lightning bolt: normal lightning bolts, according to a simple Google search, are only about an inch (3 cm) in diameter, but they appear much bigger from a distance thanks to the light they emit. Basically, I’m asking how big a lightning bolt appears to be to the naked eye, not how big a bolt actually is.
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5$\begingroup$ I mean, tbh, I fail to see how this isn’t physics. $\endgroup$– Godzilla LouiseMay 24 at 18:59
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1$\begingroup$ I can personally see lightning even without looking at the bolt directly, so the visual impression of a lightning bolt (as something that illuminates the entire landscape) is fairly wide, for all I can tell. I would say that it pretty much includes the full solid angle. $\endgroup$– FlatterMannMay 24 at 19:47
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5$\begingroup$ I don't think it makes sense to put a number on it. The closest lightning bolt I've ever seen (about 30m away,* Yikes!) seemed to occupy about the same visual angle as lightning bolts that I've seen from miles away. But of course, the actual flash is so brief, that mostly what I'm remembering are the afterimages of lightning bolts. I'm guessing that the extreme brightness of a bolt relative to the dark background might make its afterimage look about the same at any distance. $\endgroup$– Solomon SlowMay 25 at 13:37
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$\begingroup$ * I was indoors, looking out through a window when that one hit in the garden. $\endgroup$– Solomon SlowMay 25 at 13:38
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$\begingroup$ @GodzillaLouise and even if it would not be physics, it would be very interesting how that works. (But I would count any effects inside the body caused by the light under optics - physics.) $\endgroup$– Volker SiegelMay 26 at 13:35
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4 Answers
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Well, if all what you care is just the visual (subjective) perception of how wide a lightning bolt looks like, here we go. We take as an example lightning which very often hits CN Tower in Toronto:
According to the public data tower base is about $66.6~m$ wide.
Now we grab tower schematics -
and measuring its base in some image editing tool like GIMP,- gives us that tower "inverse DPI" resolution at base is $\approx 85 \text{cm/pixel} \tag 1$.
Now measure in the same image editing program the width of the tower place in pixels where lightning hits,- i.e., the width of the upper part of the antenna, multiply it with $DPI^{-1}$ in (1) and we get that the upper part where the lightning hits is about $2.5~m$ wide. Hence we conclude that visually the lightning bolt, which hit CN Tower and was taken in the given picture, must be at least $2.5m$ wide or greater (lower bound).
answered May 24 at 20:48
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41$\begingroup$ It's hard to tell how much of that is actual lighting bolt width and how much is a very bright light source being spread out by aberration in the camera lens then saturating a bunch of pixels. $\endgroup$– AXensenMay 24 at 21:38
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12$\begingroup$ Well, it's just a crude estimate here, you have to start from somewhere, especially when OP has asked "visual width" of the lightning bolt, not for actual dimensions. So it depends what "visual width" is for OP, it can be that saturation of pixels goes into that definition as well. Besides human eye also has same saturation effect on light receptors, but if we omit this factor (and maybe others), then not much "visual" things are left. $\endgroup$ May 24 at 22:04
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2$\begingroup$ The image is of some finite exposure time - the shutter wasn't opened for just some fraction of the flash so any motion of the bolt would exposure adjacient pixels and lead to an over estimate of the bolt diameter $\endgroup$– D DuckMay 25 at 19:30
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4$\begingroup$ @Peter_Cordes the natural lens of an eye scatters light more than glass does. A very bright flash will overload adjacent cones with small-angle scattered light. The older the eye the worse this gets (pre-cataract, and eventually full cataract). $\endgroup$– nigel222May 26 at 13:27
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3$\begingroup$ It would be interesting to see whether the results of this kind of analysis yield consistent results over different pictures of lightning. $\endgroup$ May 26 at 17:51
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There are a couple ways the answer could go.
The 1 inch diameter probably refers to plasma generated by the bolt. The air for some distance around it might be hot enough to glow.
Then there are visual effects. You can't see anything smaller than a receptor in your eye. This means anything smaller than about an arc minute appears to be an arc minute. You can see this in starlight. The actual angle of the disk is too small to resolve with a good telescope. You just see the minimum size your eye can resolve.
Your eyesight might not be perfect. A blurry image appear bigger. You might move your eyes during the stroke. This would make the bolt cover more receptors.
Photographs of lightning would be subject to the same considerations.
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$\begingroup$ Alright. In that case, let’s go with the first way the answer could go. Next, we use a photograph of Lightning for an example. The brightest parts of the bolt is what we’re looking for the diameter of. Any part that could be said as being part of the bolt but has a distinguishable color to it would not be included in our calculation. $\endgroup$ May 24 at 20:12
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5$\begingroup$ @GodzillaLouise - the problem with how big it appears visually is that it cannot necessarily be translated to a diameter in a consistent way; e.g, if you go by that method, a lighting bolt at some distance may give you a larger diameter than a nearby one. And the apparent size can vary during the same footage - see: youtube.com/watch?v=Y-LPERlRHYA $\endgroup$ May 25 at 3:34
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$\begingroup$ Also, add scattering of light by the natural lens of an eye. It's not as clear as glass even for a young person, and by the time we reach 65 many of us have pre-cataracts (noticeable cloudiness, and increased dazzle by bright lights). $\endgroup$– nigel222May 26 at 13:25
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2$\begingroup$ To put some concrete numbers to it, if "... anything smaller than about an arc minute appears to be an arc minute," then visually, a lightning bolt is indistinguishable from a cylinder that is 0.0003 times the distance to your eye. If it's 1km away from you, it will look to be 0.3m wide. If it's 10km away, it will look 3m wide. 100km away bolts will look 30m wide. (rough numbers, of course) $\endgroup$ May 26 at 14:00
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When I was a teenager I had a newspaper delivery round; one morning a storm broke as I was out delivering papers and a lightning bolt struck the ground just in front of me. It seemed to me to be about a 1 to 1.5 metres in diameter. The blast (there's not really any other word for it) was enough to throw me backwards off my bicycle. About 30 seconds later another bolt struck the ground across the road; it also seemed to be just as wide as the first.
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3$\begingroup$ @SolomonSlow - The bicycle frame may have helped reduce field gradients near him. $\endgroup$ May 25 at 14:21
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1$\begingroup$ D'oh! "Off my bicycle"...means...they must have been on a bicycle. I see that now. 😐 $\endgroup$ May 25 at 14:43
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2$\begingroup$ At about age 16 I saw a lighting bolt hit a tree about 5m away, a friend had just kicked a ball in that direction so it happened that about 5 of us were looking directly at it. My memory of it would suggest it was about 300mm in diameter, but this was so long ago ¯\_(ツ)_/¯ $\endgroup$ May 25 at 20:20
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7$\begingroup$ I love how each answer is 'well you can't really answer that' or "let's try to do math from these pictures' and wocky just says "when I was struck by lightning it looked about this big." $\endgroup$ May 25 at 21:56
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1$\begingroup$ @akostadinov - I don't recommend bicycling where lightning is about to strike. If lightning does strike near you, I recommend being lucky enough not to be electrocuted. $\endgroup$ May 26 at 4:13
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There are several contributing effects:
- The actual initial width of the plasma itself. This is surprisingly small - this paper indicates that peak optical output occurs at only ~3mm radius for the modeled 20kA stroke.
- The plasma expansion with time. As the return stroke starts, you get a column of very hot plasma in the air. This is obviously unstable, and rapidly radially expands. The plasma also rapidly cools... but doesn't do so instantly. Said paper indicates that even 50us into the return stroke there is still a fair amount of optical output, and the plasma has expanded significantly (to ~7mm radius). Unfortunately, figure 6d) stops at 50us.
- Diffraction limit. The human eye is ~3x worse than the theoretical maximum here, at somewhere around 60 arcseconds. This in turn works out to somewhere around 30cm at 1km.
- Dazzle and other effects. Lightning is bright [Citation Needed]. Our eyes are not perfect, and internal optical reflections happen. This is somewhat comparing apples to oranges here, but some empirical equations from laser dazzle are as follows. (These equations assume monochromatic light; lightning's optical spectrum isn't. Ditto, lightning is not a coherent source, and is a line rather than a point. Ditto, these equations are more designed for steady-state, whereas lightning isn't.) Said 20kA stroke has a peak optical power on the order of 4.3MW/m. Take a slice of this 3m long (diffraction-limited at 10km), and that's a peak optical output of ~10mW/m^2. Peak optical output seems to be in the blue region of the spectrum, so $V = 0.0647$ from their paper. Multiplying through, that's a MDE of ~660uW/cm^2. From the paper's table, this indicates this would be between 1-5 degrees radius of dazzle in full daylight, or >20 degrees of dazzle at dusk/dawn (the paper indicates 20 degrees of dazzle at ~450uW/cm^2). Note that even 1 degree radius of dazzle at 10km is an effective visible width of ~350 meters.
Again, note bunches of caveats.
