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(Inspired by many other questions that I'm not going to try to list...)

According to most sources I've seen, a "typical adult human" burns around 10-15 kcal/min while doing "strenuous" exercise. (Some sources may go as high as 25 kcal/min. Also, the number can increase depending on mass, so let's say we're talking about someone who masses ~100 kg or less.) However, it seems to me that even a "full body workout", isn't really. (If nothing else, you're usually not using opposing muscles simultaneously.)

If I had some way of causing every cell in the body to spontaneously metabolize as quickly as possible, how much Power could this produce? (Mind that I'm talking about Power in the physics sense, not electricity. Also mind that I'm not asking about burning cells or matter-energy conversion, I'm asking about producing power via normal metabolic processes, i.e. without destroying the body in the process.)

For the purpose of this question, don't worry about waste products or waste heat. I'll ask about those separately. For now, just assume that they are all magically whisked away.

(Note: Yes, this is very similar to this question. Please don't close this as a duplicate, as a) it isn't quite the same, and b) that question doesn't answer this one.)

Matthew
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    The other question asks, verbatim: How much caloric energy can an average human put out?. You are asking how much power (energy over time) a human can produce, which is indeed present in answers to the other question. In light of this, how is this one not a duplicate? – The Square-Cube Law Jul 20 '20 at 14:44
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    It may be, but the other question *doesn't have an answer* to that, specifically; only citations of existing sources based on exercise. I'm asking what difference does it make if I'm not limited to exercise. Unless someone goes back and provides a useful answer to the other question, closing this as a duplicate would be completely unhelpful. – Matthew Jul 20 '20 at 14:46
  • Got it, and I'll take a shot at answering here. – The Square-Cube Law Jul 20 '20 at 14:49
  • What could differentiate that question from this one is: "... some way of causing every cell in the body to spontaneously metabolize as quickly as possible." The answers in the linked question address roughly what is physically possible for an average human, while forcing every cell to metabolize at the greatest rate possible is probably not physically possible. – BMF Jul 20 '20 at 14:50
  • However, I can't tell if this is what you're looking for based on context from your question and replies. Are you looking for how much power a human body's worth of cell mass could be created from metabolic processes? Or are you looking for the physically possible? – BMF Jul 20 '20 at 14:52
  • @BMF remember this question has this: For the purpose of this question, don't worry about waste products or waste heat – The Square-Cube Law Jul 20 '20 at 14:54
  • @BMF, yes, that (your first comment) is the key point why the existing answers to the other question aren't what I'm looking for. I'd wonder if it's possible to make an entire body metabolize simultaneously, but it occurs to me, this might actually happen if the body is trying to keep warm in very cold conditions. Anyway, feel free to assume I want the body to not kill itself in the process (though you can ignore waste products), but don't worry about what's causing this to happen. (Ultimately, the answer is "magic", but I'm trying to keep the magic grounded in science as much as possible.) – Matthew Jul 20 '20 at 14:58
  • Put differently, what I'm asking is roughly "what percent of cells are metabolizing during 'normal' exercise, and how much power could be produced if we could somehow increase that percentage?". (Well, I really only care about the second half of that.) – Matthew Jul 20 '20 at 15:00
  • All your living cells are metabolizing, what changes is the amount for each cell. your big issue is there are two major exercise regiments aerobic and anaerobic, and they effect the body in drastically different ways. – John Jul 20 '20 at 15:52
  • @John, right, sorry; I should have added 'as fast as possible' or something along those lines. Obviously, "more" metabolism happens if I'm shivering than if I'm sitting in a room that is at comfortable temperature, or if I'm exercising vs. just sitting, but you're also correct that "low activity" isn't the same as no activity. – Matthew Jul 20 '20 at 15:56
  • your best bet then is trying to find out total (not just mechanical) metabolic output during anaerobic exercise, which is basically as much as the body can put out safely. as a bonus there is plenty of data for it. I would suggest looking at caloric output since it will measure everything. giving us a time interval will help a lot as well – John Jul 20 '20 at 16:00
  • @John, you say that like such information is easy to find, but the best I've been able to turn up is 22 kcal/min. (I get buried in articles that don't give numbers.) But Madlozoz's answer suggests much higher than that is possible. Maybe you can share some links, or even give an answer? – Matthew Jul 20 '20 at 16:11
  • Again what time interval are we working with, seconds, minutes, milliseconds. – John Jul 20 '20 at 17:08
  • For most people, the longer term (minutes) time interval is dominated by the cardiovascular system providing oxygen. For shortest term (milliseconds), it is based on available stockpiles of ATP. – Cort Ammon Jul 20 '20 at 17:11
  • Not a dupe, but has some answers that might be relevant: https://worldbuilding.stackexchange.com/questions/628/explaining-where-energy-comes-from-to-power-magic – Telastyn Jul 21 '20 at 03:31
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    I wonder if there is a study of caloric output of people close to OD on ecstasy. That might be close to the maximum output of a human body (death from ecstasy is generally due to exhaustion and hyperthermia as far as I'm aware) – Curiosity Dec 14 '21 at 19:35

5 Answers5

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A zeroth order approximation from first principles

Let's try to arrive at a Fermi approximation of the maximum sustained primary energy production of the human body.

("Sustained" is important. The human body can output 2 kW or more of mechanical power, corresponding of about 7 kW primary energy production, for a brief period of time, using ATP and oxygen already stored in the muscles. Sprint runners use this mode of operation.)

Disregarding all the details which make the joy of biochemistry, the human body produces energy by burning glucose. The gross reaction is

$$\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 + 6\mathrm{O}_2 \rightarrow 6\mathrm{CO_2} + 6\mathrm{H_2O} + 2{,}880\ \text{kJ/mol}_{\text{glucose}}$$

The human heart pumps no more than about 2 $\times$ 100 mL of blood per beat, and the maximum heart rate is about 200 beats/minute, giving about 20 liters of blood per minute in the systemic circulation. One liter of fully oxygenated blood contains a little less than 0.3 grams of oxygen. All in all, you have no more than 6 grams of oxygen per minute to burn your glucose.

6 grams of oxygen is about 0.2 moles. Since you need 6 moles of oxygen to burn one mole of glucose, you cannot burn more than 0.03125 moles of glucose per minute; times 2,880 kJ/mol, we get a top theoretical energy prodution rate of

$$90\ \text{kJ/minute} = 21.5\ \text{kcal/minute}$$

That's about 1.5 kW, for those who care.

AlexP
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    Excellent answer. Would deserve a +2. – cmaster - reinstate monica Jul 20 '20 at 23:22
  • That meshes with my answer, since short burst exercise would involve some anaerobic output as well (no oxygen but also very inefficient). With sustained exercise oxygen exchange becomes the limiting factor. The average untrained healthy male can uptake oxygen at a max of about ~35–40 mL/(kg·min) top athlete max out at around 6.1±0.6 L/min sustained. – John Jul 21 '20 at 13:51
  • A similar approach is to use VO2 max. During a controled test, Rob Wadeell has been "burning" 4g of oxygen per minute (see https://en.wikipedia.org/wiki/VO2_max#Athletes ). That's unsuprisingly a lower value as you cannot have the maximum blood oxygenation at the same time than the maximum heart rate and oxygen burning – Madlozoz Jul 21 '20 at 15:18
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According to this link, cyclist Chris Hoy could blast 2500W of mechanical power during a short time.

Assuming a 30% muscular efficiency, that's 8333W metabolized.

Obviously, Hafþór Björnsson can do much better

This does not exactly answer your question, but that's a lower bound

Note: As your question implies some level of magic in the metabolism, I focused on the idea of the maximum Energy a human can make without destroying the body in the process. Of course, such an effort can not be sustained for many reasons.
You explicitaly told us not to care about overheating and waste management, but oxygen (as detailled by AlexP) and glucose flux are the next limitation in realistic biology

Madlozoz
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  • That would work out to 120 kcal/min, which is six times higher than the highest figure I've seen anywhere. I seem to recall some sources (I'll try to find the article again) citing ~1kW but also ~15-20 kcal/min, which is why I'm still scratching my head. Do you know any sources that can confirm that presumed 120 kcal/min? – Matthew Jul 20 '20 at 16:03
  • @Matthew Most of the time, cyclist boast about their sustained output (typically 400W). Chris Hoy number is about sprinting. And performed by a man whose only purpose in life is sprinting on a bike. Also, those Numbers (I mean 2500W) are mechanical output. When people talk about calories, they usually mean metabolism. Typically sustained metabolism – Madlozoz Jul 20 '20 at 16:10
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    @Matthew: By and large, short spurs of mechanical output power use the ATP and oxygen already available in the muscles, which get depleted pretty quickly, usually in less than a minute. It's a very limited metabolism -- basically just burning ATP to release energy. On the other hand, those 400 W of sustained mechanical output do correspond to a complete metabolic rate of about 20 kcal/minute. (Assuming a muscle efficiency of about 30%.) Note that the difference (about 900 W) is waste heat which the body needs to dissipate, which is not so easy at all without a very strong air current... – AlexP Jul 20 '20 at 16:22
  • @AlexP Matthew mentioned in the question that heat and toxine will be magically disposed of. So the sprinting figure can make sense (Assuming O2 also magically arrive to the muiscle) – Madlozoz Jul 20 '20 at 16:28
  • It cannot. Top athletes cannot sustain more than 300 to 400 W of mechanical output for any length of time. If top athletes cannot do it, I'm confident that the human circulatory system, liver, lungs etc. cannot sustain more. – AlexP Jul 20 '20 at 16:29
  • @alex to be fair we don't know how long it needs to be sustained, sprinters can output thousands of watts within a few seconds. – John Jul 20 '20 at 17:02
  • the 8333W number is way off. muscle can be as high as ~65% efficient in utilizing the energy it actually is given. – John Jul 20 '20 at 17:19
  • @john: "Muscle can be as high as ~65% efficient": That's... very unlikely. Exercise: calculate the temperature of the hot reservoir of a Carnot heat engine, knowing that the cold reservoir is at 37° C and the efficiency is 65%. Hint: 65% is a very high efficiency for converting chemical energy into mechanical energy; only some very large marine diesels come close. – AlexP Jul 20 '20 at 19:14
  • @AlexP it surprised me too, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3144848/ but even before that study 50% was known from several sources. – John Jul 20 '20 at 20:07
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    @John: Ah, that article makes it clear that it measures only the efficiency from ATP to mechanical output. That's OK. – AlexP Jul 20 '20 at 20:23
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    @AlexP Also note that human metabolism is not a heat engine. Nowhere in the process does it even try to convert heat into mechanical work. It directly turns the chemical energy into mechanical work + waste heat, keeping working temperatures down to around frosty 40°C, even in the case of a top athlete. A Carnot engine with a heat source at 40°C (athletes muscles) and a sink at 0°C (riding in winter) would have an efficiency around 13%. The athlete can do better than that, even in summer. – cmaster - reinstate monica Jul 20 '20 at 23:20
  • @AlexP what other efficiency do you think is relevant to muscle efficiency? – John Jul 21 '20 at 13:33
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I can make a very rough calculation assuming that the maximum heat loss for a body in water corresponds to a power of about 24 kW, and "immersing a person in iced water" is not enough to lower his temperature in case of severe TFMPH poisoning.

Therefore, the human body can produce at least 24 kW of heat.

TFMPH, as well as other proton translocators, causes exactly what you describe: "causing every cell in the body to spontaneously metabolize as quickly as possible" (it is used for this purpose in some highly illegal "weight loss" concoctions).

However, be advised that this results in death in a matter of minutes, because the organism literally cooks itself alive. You asked instead "without destroying the body in the process".

Also, this is not the same as producing useable energy (rather the opposite: all energy goes away as heat). The latter would require muscular activity, so you might maybe found some estimates in medical papers on malignant hyperthermia.

LSerni
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  • note the human body is also really inefficient at producing heat, compared to say generating mechanical force, so heat may not be the best measure. – John Jul 20 '20 at 16:07
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    @John, are you sure? Heat is the end result of entropy; what exactly happens to the energy that doesn't end up as heat? – Matthew Jul 20 '20 at 16:14
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    I think this is the most useful answer so far! This sounds plausible, I will definitely have to do more research here. Also, note that I said to not worry about the heat ; for my ultimate purposes (metabolism-powered magic), I can't totally hand-wave it away, but my working theory is that, depending on the application, I can convert ~80% of that into something "useful", or even simply dump most of it (as heat) somewhere else. This is the point at which my other question becomes important . – Matthew Jul 20 '20 at 16:25
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    @John: The human body is very much more "efficient" at producing heat than mechanical output; for each joule of mechanical output it produces at least 2 joules of heat. – AlexP Jul 20 '20 at 16:26
  • I am talking about purposefully generated heat, not waste heat, the metabolic heat production of a body is remarkably poor most of the energy is spent moving ions around creating potential energy that is never used. Yes eventually all that gets converted into waste heat, just not in a timely fashion. I realize I was not being clear. if you want energy fast the bodies heat production mechanism is not the best. – John Jul 20 '20 at 16:59
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    @John: I'm not sure that you understand how this energy thing works. "Creating potential energy that is never used" is not physically possible; and there is no difference between waste heat and "purposefully generated" heat. Heat is heat. – AlexP Jul 20 '20 at 18:53
  • @AlexP, never used to do work, image pumping water uphill then dumping it back into a river. There is a difference in the timing, if I fill a leaky basin it eventually releases the potential energy as heat but it does not do immediately but slowly as the water works its way back to equilibrium. or as a better analogy, charging a battery then just letting it sit and naturally discharge slowly, all the energy is converted to heat but not in a timely fashion. there is probably a better set of terms to describe the difference in heat production but I don't know it off the top of my head. – John Jul 20 '20 at 20:18
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For the purpose of this question, don't worry about waste products or waste heat. I'll ask about those separately.

I have no data on how fast human temperature can go up and down, only the anecdotal evidence that fast temperature changes due to fever (going either up due to sickness or down due to antipyretic) usually take no less than an hour to happen.

I do have a link to a question in chemistry.se stating that the specific heat for the human body is 3.5kJ/kgK. So for a 100kg person to go from 36C to 40C in 1h, that is an energy expenditure of 1,400kJ. Over 3,600 seconds, that is ~389 watts.

That is enough to power maybe a couple 60" TV's, or seven laptops. Not enough to power a coffee maker machine, though, so I wouldn't even bother. If I'm using magic to get energy from people I'd rather mix pyromancy with necromancy - completely burning a person yelds 1kWh/kg, which is 3,600,000 joules/Kg. If a 100kg person takes an hour to completely roast, that's 360,000,000 joules in one hour, so 100kW - three orders of magnitude more power!

To be clear: this is energy coming from all cells, just wasting energy generating heat. Muscles contracting can reach higher watt counts. See Madlozoz's answer.

The Square-Cube Law
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  • Interesting, but 15 kcal/min is already about 1,000 watts (note Madlozoz's comment!) ; we can probably get to at least 1,600 or so. You might be on the right track, though; I'm going to try to see if anyone has numbers for e.g. people in extreme cold. I hadn't thought of that when I asked the question. BTW, one of the reasons I'm sticking with metabolism as a power source is because I don't want overpowered magic . – Matthew Jul 20 '20 at 15:36
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    That's a first lower bond, but I metabolize MUCH more that 389 W while cycling. – Madlozoz Jul 20 '20 at 15:36
  • My prior comment notwithstanding, I think this is still interesting, because I don't think temperature increase due to fever is necessarily using muscles, which makes me suspect we can, at the very least, add those additional ~400W to the 1kW we get from exercise. If I had to guess, I'd guess the "right" answer is somewhere around 2-3kW, but it would be nice to have something backing that up. – Matthew Jul 20 '20 at 15:40
  • @Matthew according to Wikipedia human heat is generated not only in muscles but also in the brain and viscerae. It is a result of metabolism simply happening. One of my biology teachers in high school told me sodium pumps keep causing cells to use up energy constantly in mammals, being the mechanism through which we become homeothermic. – The Square-Cube Law Jul 20 '20 at 15:54
  • @Renan yeah mammals basically generate heat by running cellular pumps with holes in them so they don't actually do any work just generate heat. its a bit like running an electric motor attached to nothing. – John Jul 20 '20 at 15:58
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    The main problem with this answer is, that the body is nowhere near its limits when it increases its body temperature in response to an infect. Otherwise, you wouldn't need to wait for the temperature to rise, you'd recognize the starting fever from the increase in breathing and heart rate. They would need to rise to levels that a cyclist has during a race. But they do not. Feverish persons do not breathe recognizably faster than a person at rest, so they must be very far from top metabolism. – cmaster - reinstate monica Jul 20 '20 at 23:33
  • Performing an effective warm-up, or just any strenuous exercise can raise the body temperature to the same levels within minutes. Two minutes and you're sweating and shedding layers even outdoors in the winter. – Curiosity Dec 14 '21 at 19:54
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According to Stanford around 2000 watts in short bursts or 300-400 watts sustained.

This from studies interested in using metabolic energy to power implants, they wanted a baseline of how much energy was theoretically possible. Without knowing what time interval you want this is about the best you are going to get, how much energy the body can put out over minutes is drastically different than over seconds because they involve drastically different metabolic pathways and limiting factors.

John
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  • I also came on this Stanford page. But I realized they put on the same level the energy consumption (when they say "100W") and the mechanical output (when they say "300-400W"). In my opinion, this is just an electric engineer toying with the idea. He knows as much about human body than Alberto Contador about reverse electrowetting – Madlozoz Jul 21 '20 at 14:41
  • @Madlozoz I am confuses as to what you think the problem is, 100W was not consumption it was the resting output (which would be close to consumption) 3-400W is the sustained output during exercise. I have seen several BMR estimates that are near 100W , (80W for bed ridden patients) and sustained exercise estimate that are within their estimates if not a little higher. – John Jul 21 '20 at 16:53