I’m not a physics major, but this is how I would reason: a regular human usually survives a lightning strike, IIRC. Why would fish be any different? It might hurt them but they have simpler nervous systems to boot. So my initial guess is that no fish at all is hurt, no more than they are fried by the sun unleashing gigawatts onto the ocean.
But that’s a cheap answer, perhaps. Let’s try another route. A human isn’t that big compared to a tuna fish, but is pretty big compared to things like trout or salmon. Let’s say we weigh 100x as much as those small fish.
Lightning is a one-shot packet of energy—like quickly blinking a flashlight. As the light spreads away from the flashlight, it begins to fade out. (Why isn’t the entire earth illuminated?) Well, there’s a fixed number of photons released, and the sphere/area they are spread over keeps getting bigger as they go—it increases as the square of how far away they are. It’s like gravity: you get an inverse square law. Squares increase pretty fast − 2^2 = 4, 3^2 = 9, 4^2 = 16 etc.
So if we humans are 2 feet around from the ‘epicenter’, how many units of 2 feet do we have to go to cut the strength by 1⁄100 and give the little fish a little fish-sized dose? Well, the square root of 100 is 10, so 10 2-feets is 20 feet.
In other words, by this reasoning, I’d expect even little fish to survive a lightning strike around 20 feet away. 20 feet is much smaller than an ocean.
This is all high-school physics at best; all you really have to do is think about why gravity follows an inverse square law, analogize a space-filling gravity to light, and guess some numbers in the best spirit of Fermi calculations.
Is this a correct model, though? My understanding is that the relevant figure is the potential difference between various points the creature’s body touches during the lightning strike. (Just like if a high voltage power transmission cable snaps and falls to the ground close to where you stand, you’re in much worse danger of electrocution if you stand so that one of your feet is closer than the other to a point where the cable touches the ground.)
Considering that the fish are usually elongated and the potential is (presumably?) distributed in a radially symmetrical way, they will be struck much worse if they happen to be swimming directly towards or away from the lightning strike point. [Edit: This is incorrect—please see the further discussion with Constant below.] Ignoring this and assuming spherical fish, the danger seems to be proportional to D*dV(r)/dr, where V(r) is the potential as a function of distance on the radial between the strike point and the current position of the fish, and D is the diameter of the fish. Now does anyone know what V(r) is supposed to look like?
Vladimir, I’m not sure about the orientation bit. Imagine constructing a sphere of fish around the lightning strike, so that the fish tile the sphere and are flat against the sphere (actually, hemisphere). Necessarily, all the electricity flows through the fish, because they completely tile the hemisphere. Now re-orient the fish without otherwise changing their location. Now, because the fish are thin, they no longer cover the sphere, and between them is a lot of seawater. So only a small fraction, now, of the electricity flows through the fish, and the rest passes by them in the seawater.
Meanwhile, of course, that small fraction of electricity is staying in the fish for much longer, because each unit of power is flowing the entire length of the fish, from head to tail, whereas when the fish are placed sideways relative to the flow of electricity, each unit of power is only flowing from one side to the other.
At first glance, it seems to cancel out.
Imagine the following: each fish is made out ten unit cubes placed next to each other. They can either be placed perpendicular to the flow of energy, so that each cube gets the energy that flows through one unit square. Or, they can be placed parallel to the flow of energy, so that they all share the energy from a single unit square, which flows through all of them one after the other.
It seems to come to the same thing.
But here’s one further complication: if the fish is a better conductor than the seawater, then the energy will tend to re-direct to seek out the fish (more electricity will flow through the better conductor, cet.par.), so that placing the fish parallel to the flow of energy rather than perpendicular to it will not entirely protect it from the neighboring energy. In short, if the fish is a better conductor than the seawater, then it is better for the fish to be oriented perpendicular to the flow of energy.
But, without going into details, I hastily extrapolate that if the fish is a poorer conductor than the seawater, then it is better for the fish to be oriented parallel to the flow of energy (i.e. facing the lighting strike point, or facing away).
But, without going into details, I hastily extrapolate that if the fish is a poorer conductor than the seawater, then it is better for the fish to be oriented parallel to the flow of energy (i.e. facing the lighting strike point, or facing away).
You are correct! I hastily analogized from the human step potential, ignoring the fact that fish, unlike humans, may well be much poorer conductors than the surrounding (or, in the human case, underlying) medium. Sadly, it seems the electrical engineering courses I took long ago haven’t left many surviving correct intuitions.
After a bit of googling about this question, I’m intrigued to find out that the problem of electrocuting fish has attracted considerable research attention. A prominent reference appears to be a paper titled Electrical stunning of fish: the relationship between the electrical field strength and water conductivity by two gentlemen named J. Lines and S. Kestin (available ungated here, and with a gruesome experimental section). Alas, the paper says, “No publications appear to be available which identify conductivity measurements of fish tissue at the frequencies being used.” It does however say that we might expect something in the hundreds or low thousands of uS/cm, whereas Wikipedia informs us that the conductivity of seawater is around 4.8 S/m, i.e. as much as 48,000 uS/cm.
So, yes, this was definitely a blunder on my part.
I’m sure it isn’t! But that’s the fun of Fermi problems: reaching not-wildly-incorrect solutions by way of absurdly simplified & wrong models.
For example, I feel sure that if my 20 foot answer is too little, the lethal radius would still be less than 1 larger order of magnitude (200 feet), and if it’s too much, that the lethal radius is still bigger than 1 smaller order (2 feet).
Oh, I like your Fermi model! (And also my above comment was horribly incorrect—see the subsequent discussion with Constant.)
What I was wondering however is whether it might be off too much even by Fermi problem standards, i.e. by multiple orders of magnitude. The trouble is that if the target creatures are vastly better or poorer conductors than the surrounding medium, this greatly influences how the flow of energy through and around them is distributed, possibly making the model based on uniform energy flow across all angles too inaccurate even for a Fermi calculation. (To give an extreme example, a metal wire connecting the poles of a battery draws nearly all energy flow in the circuit through itself, despite being a negligible part of the spatial cross-section.)
Or to put it more precisely, the way a human distorts the flow of electrical energy when surrounded by ground and air may well be extremely different, and possibly go in a totally different direction, from the way a fish distorts it when surrounded by seawater, so your generalization from humans to fish might be problematic.
My initial idea was to attempt another Fermi approach based on guesstimating V(r) and its derivative, but the poor conductivity of fish relative to seawater seems to complicate that one too.
I’m not a physics major, but this is how I would reason: a regular human usually survives a lightning strike, IIRC. Why would fish be any different? It might hurt them but they have simpler nervous systems to boot. So my initial guess is that no fish at all is hurt, no more than they are fried by the sun unleashing gigawatts onto the ocean.
But that’s a cheap answer, perhaps. Let’s try another route. A human isn’t that big compared to a tuna fish, but is pretty big compared to things like trout or salmon. Let’s say we weigh 100x as much as those small fish.
Lightning is a one-shot packet of energy—like quickly blinking a flashlight. As the light spreads away from the flashlight, it begins to fade out. (Why isn’t the entire earth illuminated?) Well, there’s a fixed number of photons released, and the sphere/area they are spread over keeps getting bigger as they go—it increases as the square of how far away they are. It’s like gravity: you get an inverse square law. Squares increase pretty fast − 2^2 = 4, 3^2 = 9, 4^2 = 16 etc.
So if we humans are 2 feet around from the ‘epicenter’, how many units of 2 feet do we have to go to cut the strength by 1⁄100 and give the little fish a little fish-sized dose? Well, the square root of 100 is 10, so 10 2-feets is 20 feet.
In other words, by this reasoning, I’d expect even little fish to survive a lightning strike around 20 feet away. 20 feet is much smaller than an ocean.
This is all high-school physics at best; all you really have to do is think about why gravity follows an inverse square law, analogize a space-filling gravity to light, and guess some numbers in the best spirit of Fermi calculations.
Is this a correct model, though? My understanding is that the relevant figure is the potential difference between various points the creature’s body touches during the lightning strike. (Just like if a high voltage power transmission cable snaps and falls to the ground close to where you stand, you’re in much worse danger of electrocution if you stand so that one of your feet is closer than the other to a point where the cable touches the ground.)
Considering that the fish are usually elongated and the potential is (presumably?) distributed in a radially symmetrical way, they will be struck much worse if they happen to be swimming directly towards or away from the lightning strike point. [Edit: This is incorrect—please see the further discussion with Constant below.] Ignoring this and assuming spherical fish, the danger seems to be proportional to D*dV(r)/dr, where V(r) is the potential as a function of distance on the radial between the strike point and the current position of the fish, and D is the diameter of the fish. Now does anyone know what V(r) is supposed to look like?
Vladimir, I’m not sure about the orientation bit. Imagine constructing a sphere of fish around the lightning strike, so that the fish tile the sphere and are flat against the sphere (actually, hemisphere). Necessarily, all the electricity flows through the fish, because they completely tile the hemisphere. Now re-orient the fish without otherwise changing their location. Now, because the fish are thin, they no longer cover the sphere, and between them is a lot of seawater. So only a small fraction, now, of the electricity flows through the fish, and the rest passes by them in the seawater.
Meanwhile, of course, that small fraction of electricity is staying in the fish for much longer, because each unit of power is flowing the entire length of the fish, from head to tail, whereas when the fish are placed sideways relative to the flow of electricity, each unit of power is only flowing from one side to the other.
At first glance, it seems to cancel out.
Imagine the following: each fish is made out ten unit cubes placed next to each other. They can either be placed perpendicular to the flow of energy, so that each cube gets the energy that flows through one unit square. Or, they can be placed parallel to the flow of energy, so that they all share the energy from a single unit square, which flows through all of them one after the other.
It seems to come to the same thing.
But here’s one further complication: if the fish is a better conductor than the seawater, then the energy will tend to re-direct to seek out the fish (more electricity will flow through the better conductor, cet.par.), so that placing the fish parallel to the flow of energy rather than perpendicular to it will not entirely protect it from the neighboring energy. In short, if the fish is a better conductor than the seawater, then it is better for the fish to be oriented perpendicular to the flow of energy.
But, without going into details, I hastily extrapolate that if the fish is a poorer conductor than the seawater, then it is better for the fish to be oriented parallel to the flow of energy (i.e. facing the lighting strike point, or facing away).
Constant:
You are correct! I hastily analogized from the human step potential, ignoring the fact that fish, unlike humans, may well be much poorer conductors than the surrounding (or, in the human case, underlying) medium. Sadly, it seems the electrical engineering courses I took long ago haven’t left many surviving correct intuitions.
After a bit of googling about this question, I’m intrigued to find out that the problem of electrocuting fish has attracted considerable research attention. A prominent reference appears to be a paper titled Electrical stunning of fish: the relationship between the electrical field strength and water conductivity by two gentlemen named J. Lines and S. Kestin (available ungated here, and with a gruesome experimental section). Alas, the paper says, “No publications appear to be available which identify conductivity measurements of fish tissue at the frequencies being used.” It does however say that we might expect something in the hundreds or low thousands of uS/cm, whereas Wikipedia informs us that the conductivity of seawater is around 4.8 S/m, i.e. as much as 48,000 uS/cm.
So, yes, this was definitely a blunder on my part.
I’m sure it isn’t! But that’s the fun of Fermi problems: reaching not-wildly-incorrect solutions by way of absurdly simplified & wrong models.
For example, I feel sure that if my 20 foot answer is too little, the lethal radius would still be less than 1 larger order of magnitude (200 feet), and if it’s too much, that the lethal radius is still bigger than 1 smaller order (2 feet).
Oh, I like your Fermi model! (And also my above comment was horribly incorrect—see the subsequent discussion with Constant.)
What I was wondering however is whether it might be off too much even by Fermi problem standards, i.e. by multiple orders of magnitude. The trouble is that if the target creatures are vastly better or poorer conductors than the surrounding medium, this greatly influences how the flow of energy through and around them is distributed, possibly making the model based on uniform energy flow across all angles too inaccurate even for a Fermi calculation. (To give an extreme example, a metal wire connecting the poles of a battery draws nearly all energy flow in the circuit through itself, despite being a negligible part of the spatial cross-section.)
Or to put it more precisely, the way a human distorts the flow of electrical energy when surrounded by ground and air may well be extremely different, and possibly go in a totally different direction, from the way a fish distorts it when surrounded by seawater, so your generalization from humans to fish might be problematic.
My initial idea was to attempt another Fermi approach based on guesstimating V(r) and its derivative, but the poor conductivity of fish relative to seawater seems to complicate that one too.