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We know that humans are capable of incredible feats, as displayed by Olympic athletes. However, the superhuman heroes that appear in comic books and fantasy novels tend to not only be able to perform such feats, but to be able to sustain such action over a period of time. Not only that, but athletes tend to focus on just one sport or exercise, while these fantasy characters seem to do everything equally well.

So what would a such a superhuman look like assuming human biology? Would he have biceps so muscular they would be at risk of crushing his own head? Or would he really look like Captain America?

To prevent this question from being too darn broad, I'm going to specify what this person's limitations should be:

  1. Able to lift maybe 300-ish kg for several minutes before becoming fatigued.
  2. Capable of running at about 10 m/s at a sustained pace for over an hour.

I don't particularly care if its not realistically possible, I'm just interested in what such a person might look like, particularly his physique. If the above numbers are too over the top, feel free to use a lower number.

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  • $\begingroup$ In The Six Million Dollar Man and The Bionic Woman TV series, superhumans look like average people. $\endgroup$ – mouviciel Jan 21 '15 at 9:00
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    $\begingroup$ @mouviciel well, yeah. But I asked what would they look like assuming human biology was not wrung through the ringer. $\endgroup$ – Feaurie Vladskovitz Jan 21 '15 at 11:48
  • $\begingroup$ I would assume that they would have significantly denser muscles than a normal humans and much larger lung capacity as well as a very powerful heart. A size increase seems unavoidable. As an added benefit, this would give them a longer stride which would make running fast easier. $\endgroup$ – overactor Jan 21 '15 at 13:17
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    $\begingroup$ We're very far off from anyone being able to sustain 10 m/s for over an hour by the way. The world record for the one hour run is 21,285 m which corresponds to an average speed of 5.9125 m/s. The man who holds that record is 165 cm tall and weighs no more than 56 kg. Not exactly someone I'd expect to be able to lift 300-ish kg. $\endgroup$ – overactor Jan 21 '15 at 13:25
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As has been mentioned, they would need denser muscles to look even remotely human.

The world record for the one hour run is held by Haile Gebrselassie, a 65 kg man who managed to average a speed of 5.9125 m/s over an hour.

If we look at the weightlifting side of things, Eric Spoto weighs somewhere between 140 and 150 kg and managed to benchpress 327.5 kg without special equipment and has mananaged 4 reps with 294 kg.

What I'll do now is estimate how much more energy a man the weight of Eric Spoto would need compared to Haile Gebrselassie in order to run 10 m/s for an hour. I'm (falsely assuming that a 150 kg person generating enough energy would actually be able to perform the feats he can technically do. I'll justify this by handwaving and saying "denser muscles".

When exerting a constant force on a moving object, energy used is proportional to force exerted in the direction of the movement times the magnitude of the movement.

$$ E = F\times\Delta x $$

Since we can assume the speed is constant, there is no resulting force operating on our athlete. This means that the force the athlete is exerting has the same magnitude as the force he experiences by aerodynamic drag. according to this paper we can approximate the drag working on a human by:

$$ F = AV^{2} $$

With $A$ being the cross-sectional surface of the human.

Assuming that two humans are to scale versions of eachother, we can get the ratio between their cross-sectional surface as:

$$ \frac{A_{1}}{A_{2}} = (\frac{M_{1}}{M_{2}})^{\frac{2}{3}} $$

We can now reduce the ratio between energy consumed to known factors:

$$ \begin{align*} \frac{E_{1}}{E_{2}}& = \frac{F_{1}\times\Delta x_{1}}{F_{2}\times\Delta x_{2}} \\ & = \frac{A_{1}V^{2}_{1}\times V_{1}}{A_{2}V^{2}_{2}\times V_{2}} \textrm{ (Distance covered is proportional to speed)} \\ & = (\frac{M_{1}}{M_{2}})^{\frac{2}{3}} \times \frac{V^{3}_{1}}{V^{3}_{2}} \end{align*} $$

Filling this out with the values we have gives:

$$ (\frac{150kg}{65kg})^{\frac{2}{3}} \times \frac{(10m/s)^{3}}{(5.9125m/s)^{3}} = 8.4 $$

That's 8.4 times more energy needed than Haile Gebrselassie used to set his world record, assuming that the lost energy will be proportionally the same.

The good news is that this formula predicts that the required energy scales with "just" $(\frac{M_{1}}{M_{2}})^{\frac{2}{3}}$ this means that doubling the mass only increases the required energy by roughly 1.59 times. This supports that a taller man, bigger person could possibly achieve this. My guess would be that this person would need to be well over 2 meters (approaching the height of the tallest people who ever lived) and weigh at least 300 kg of mostly very dense muscle, eat like a horse and have a heart that's about 3 times bigger in length than a normal person.

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  • $\begingroup$ The guess I make at the end is not based on all that much and should be taken with quite a bit of salt. $\endgroup$ – overactor Jan 21 '15 at 15:25
  • $\begingroup$ It's nice to see some numbers for this! +1 $\endgroup$ – bowlturner Jan 21 '15 at 15:29
  • $\begingroup$ @Bowlturner, what I haven't done is look into what sort of lungs and heart we really need to deliver these amounts of energy to the muscles, that's why my last paragraph is just guesswork. I basically just scaled the volume of the heart proportionally to the amount of energy it needs to deliver per hour. I also suspect that my 300 kg pure muscle person is actually wasting mass, since at that point lifting 300 kg is getting a bit "easy". $\endgroup$ – overactor Jan 21 '15 at 15:33
  • $\begingroup$ So... This guy would look a bit like Letho from the Witcher 2? +1 for the awesome math btw. $\endgroup$ – Feaurie Vladskovitz Jan 22 '15 at 9:40
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My biggest guess would be that their muscles would be much denser than ours. Muscle density allows for more power in a small physical muscle. Orangutans, Apes, and Chimpanzees all have much denser muscles than humans. This is not to say they still won't be bulked up, but for them to still function without being muscle bound, the density would make a big difference.

The next would be a large 'powerful' chest because they would need a large powerful heart to keep moving the blood with enough quantity. Large lungs are needed to facilitate the rapid exchange of CO2 and O2. While they might be able to perform great feats of strength anaerobically (and the dense muscles could allow for longer than the rest of us), for something to be sustained for any length of time, (and not require a large time to recover) there needs to be the ability to send energy to the needed muscles and remove the waste products quickly and efficiently. This also suggests that they have high efficiency or extra large kidneys to help remove wastes.

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The superhuman would look a lot like a sled dog: http://www.outsideonline.com/fitness/endurance-training/It-s-the-Dog-in-You.html They can certainly do the running at ~20 mph for an hour or more. I don't know exactly how you would compare lifting, since dogs aren't built to do that, but they run like that while pulling a sled.

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According to Wikipedia, "The average horse can carry up to approximately 25% of its body weight." A large draft horse can weight over a ton, 2200 lbs or 1000 kg, so the most a horse can carry is about 550 lbs or 250 kg, close to what you specify.

But, a horse could only gallop at 10 m/s (22 mph or 36 kph) for maybe four or five miles, around 10 minutes (Again using Wikipedia).

However, humans are extremely efficient at running. Regular sized humans can even compete with horses in long-distance running.

Taking all this together, I see a human 8-10 ft tall (2.5 to 3 m) with muscle mass similar to a horse being able to accomplish the feats you describe.

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    $\begingroup$ The weight a horse can carry (20% is usually considered the upper limit among horse people) isn't a function of strength, but of the fact that the weight is carried in the middle of the spine, and can bounce around. Horses can pull quite a bit more, given a proper harness: en.wikipedia.org/wiki/Horse_pulling $\endgroup$ – jamesqf Jan 22 '15 at 6:33
  • $\begingroup$ 1/4 of body weight is the approximate limit also of what dogs can carry when backpacking. Very fit dogs can approach 1/2 their body weight in backpacking, but 1/4 to 1/3 is more realistic. $\endgroup$ – a CVn Jan 22 '15 at 11:41
  • $\begingroup$ @jamesqf True that you can pull more, but the question specified lifting specifically. Plus, I can lift at most around 30 lbs for a few minutes, 25% of my 120 lb weight, so it seemed a good rule of thumb. $\endgroup$ – 2012rcampion Jan 23 '15 at 23:37

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