Recently one of my friends asked me about a device, about the size of a gas-mask filter, that claims to extract enough oxygen from water to allow you to breathe while submerged. He had some thoughts about the mechanical details and whether this device could outperform gills, but what he asked me was, essentially, this: if you had gills how big would they need to be? This is an interesting question1 and so I thought I’d share a detailed, sourced answer.
Let’s start with some basic fish biology drawn from Bone and Moore’s 2008 general ichthyology text, Biology of Fishes. A typical 1 kg fish has 18,000 square centimeters of gill lamellae. These gills extract 70-80% of the oxygen available in the water. This is such a big task that around 30% of the blood resistance in a fish’s circulatory system is in the gills2.
If we simply scaled this up to a 70 kg human3 we’d get 126 square meters of gill lamellae. This isn’t the number we want, though, since approximating a 70 kg human with a pile of seventy 1 kg fish isn’t accurate4. There are issues both of scaling efficiency (larger animals tend to need less oxygen per kilogram) and metabolic rate (humans are much more energy-hungry than fish on a kilo-per-kilo basis). What we actually want is a metabolic rate for our 1 kg average fish and a human metabolic rate5 so we can scale from there.
Clarke and Johnson (1999) estimated the metabolic scaling equation for teleost fish overall. Since teleost fish encompass more than 90% of all fish species a teleost fish equation is probably pretty close to a generalized fish equation. The equation from Clarke and Johnson is ln(metabolic rate as mmol of oxygen per hour) = 0.8(ln(body mass in grams)) – 5.43. A 1 kg fish would then need 1.101 mmol of oxygen per hour.
Ravussin et al. (1982) measured subjects of varying obesity and determined that non-obese subjects used 6,118 kJ a day for their resting metabolism. Leonard (2010) states that in humans 1 liter of oxygen is equal to 5 kcal of energy. Working through a lot of conversions (1 mol of oxygen is 1,000 mmol and is 22.4 liters at standard temperature and pressure, so that’s 44.64 mmol/liter, 5 kcal is 20.92 kJ so that’s 2.13 mmol/kJ, 6,118 kJ/day is 254.9 kJ/hr) we get 543.98 mmol of oxygen/hr. So, if an average, non-obese human needed to get by with gills we’d be looking at 889.4 square meters of gill lamellae just to meet basal metabolic needs.
Now, if you’re following all of this you may see a problem: that gill area/mass ratio is for a fish in total, not a fish that only rests. But we’ve calculated this for a human that only rests. Surely fish have some built-in safety factor which will help us out here. However, we exercise using mostly aerobic muscle activity, and fish exercise using mostly anaerobic muscular activity. Fish also use about 10% as much energy as land mammals in locomotion (both of these facts come from Bone & Moore, 2008). So whatever the safety factor a fish has to let it engage in fast movement that safety factor is going to be far too low for a human.
So what would 889.5 square meters of gill lamellae look like? This is hard to figure out. Gill lamellae are very small and tightly-packed, and so a lot of surface can fit in a small area. However, our average human now has gills 494 times larger than our 1 kg fish. Imagine a medium sized trout. Now imagine the gills – the full, feathery, red structures behind the operculum (gill cover). Now imagine basically 500 of those. If the trout had a mere cubic inch of gill our hypothetical human would need 0.29 cubic feet of gills. Of course, that much gill tissue would change the water flow through it in ways that would force changes in the gill dimensions as well, and so an actual cube of gill tissue would have dead spaces in it and would need even more tissue. Instead, the best design would probably be more like stacked wings of tissue, probably about the size of a person’s head. Remember, that’s a minimal gill that will let you breathe underwater but not really move around (or panic). If you were planning on living underwater, instead of just hopping into the water and drifting with the current, you’d need gills probably at least twenty times that size, since activity can easily use twenty times as much oxygen per minute as resting.
Sanity Check
These numbers appear strangely large. Would you really need gills twice the size of your torso to sustain you swimming around underwater? And it is possible I made an mathematical error. However, the sanity check suggests that this is probably about right.
First, that oxygen use rate is about 8 times higher for our hypothetical human than our fish on a kg-for-kg basis. (We’d need the exact weight of Ravussin et al.’s subjects to do better.) Since endotherms, like humans, tend to have metabolisms about ten times faster than ectotherms (like the vast majority of fish) we’re running clearly in the sanity zone on that one, perhaps even lowballing human oxygen needs (although large animals, like humans, are more efficient per kilogram than small ones, like our 1 kg fish).
Second, what’s a comparable animal? A great white shark is a large, endothermic fish. Its gills take up an area behind its head about as long as the head length. Great white sharks are also have lower body temperatures than humans (which reduces energy use) and are very streamlined, hydrodynamic swimmers, which means they use far less energy moving than humans do. (Humans, and all walking animals, use lots of energy in their limbs just holding themselves off the ground, while swimming animals can use all or almost all their energy moving themselves forward.)
Thirdly, what are swimming mammals doing? Not using gills. Water, under good conditions, only holds about 3% as much oxygen as air does. This means that gills should be larger than lungs for a given oxygen demand. If we ran the numbers based off of this we’d get gills that were 33 times larger than lungs. However, gills are more efficient than mammalian lungs (see the 70-80% oxygen capture rate quoted above) and so we can probably reduce the gill size by a factor of three. That would give us gills 11 times larger than lungs.
All in all, the gill sizes we’ve estimated seem reasonable, if extremely large.
Bone, Quentin;, and Richard H.; Moore. Biology of Fishes. Third Edit. New York, New York: Taylor & Francis, 2008.
Clarke, Andrew, and Nadine M. Johnston. “Scaling of Metabolic Rate with Body Mass and Temperature in Teleost Fish.” Journal of Animal Ecology 68, no. 5 (September 1, 1999): 893–905. https://doi.org/10.1046/j.1365-2656.1999.00337.x.
Leonard, William R. “Measuring Human Energy Expenditure and Metabolic Function: Basic Principles and Methods,” Journal of Anthropological Sciences 88, (2010): 221-230.
Ravussin, E., B. Burnand, Y. Schutz, and E. Jéquier. “Twenty-Four-Hour Energy Expenditure and Resting Metabolic Rate in Obese, Moderately Obese, and Control Subjects.” The American Journal of Clinical Nutrition 35, no. 3 (March 1, 1982): 566–73. https://doi.org/10.1093/ajcn/35.3.566.
- To people who like weird questions, at least
- If this isn’t straightforward to you, what this means is that roughly 30% of a fish’s heart strength is devoted just to pushing blood through the gills
- A number I chose for this example more or less at random, but which falls within the global range of variation for “average” humans.
- And would be pretty weird in real life
- If you aren’t following this just be aware that metabolic rate and oxygen demand are two measures of the same thing – you need oxygen for, and only for, the reactions that make up your metabolism.