So, this is a thing I never fully understood. There are a lot of reasons for a flying creature to be limited in mass (though I'm unsure if I'm familiar with all of them), from energy consumption to material strength. However, there seems to be an argument that goes along the lines that over a certain mass, no matter what, they can't generate enough power to counteract gravity.

What limitation could they exactly mean with that?

  • $\begingroup$ The design of the “wing” and its materials... $\endgroup$
    – Solar Mike
    Commented Sep 21, 2019 at 20:11

1 Answer 1


One of the physical limits to biological flight is muscle physiology.

Muscle force output is proportional to muscle physiological cross sectional area (PCSA) multiplied by its specific tension (Gans, 1982):

$$F = \text{PCSA} \times \text{Specific Tension}$$

PCSA is basically just the cross-sectional area of a muscle adjusted for its architecture. Pennate muscles have higher PCSA than parallel fibered muscles, because more fibers are packed into the area (at the cost of shorter functional distances). Specific tension is the force output per unit area. For a single species, specific tension is essentially constant.

So the way to make more force is to make more PCSA. But muscles don't scale only in area, they scale in volume as well. Increased volume increases mass as a cubic power, but muscle area only scales as a square power. So any increase in area that requires a volume increase (which is inevitable), will quickly outstrip any gains in force output.

Note that this doesn't mean that very large flying vertebrates were not possible: the largest pterosaurs (e.g., Quetzalcoatlus) had ~15 m wingspan and perhaps weighed 200 kg and the largest birds (e.g., Argentavis) had ~7 m wingspan with a mass over 50 kg. Both, however, were likely gliders.

Gans C. 1982. Fiber architecture and muscle function. Exerc Sport Sci Rev 10:160–207.

  • $\begingroup$ There's also the aerobic/anerobic issue. If you look at the largest flighted birds, they actually use powered flight for very short periods, usually to get airborne. Then they will soar (or like the albatross, use lift from ocean waves), which uses only a miniscule amount of muscle power for control. Just as humans in sailplanes or hang gliders can stay aloft for many hours in favorable conditions, if they're towed up or launch from a high place. $\endgroup$
    – jamesqf
    Commented Sep 22, 2019 at 4:17
  • $\begingroup$ Weird. Doesn't the square-cube law apply only when you scale an object in all three dimensions? $\endgroup$ Commented May 31, 2020 at 18:45
  • $\begingroup$ @Mephistopheles yes which is the problem the weight increases by the cube but the strength only increases by the square. so you reach a point were you can't add more strength without adding more weight than that strength can offset. And not just muscle, bone and connective tissue have the came problem. $\endgroup$
    – John
    Commented May 31, 2020 at 22:24
  • $\begingroup$ @John I know, but can't you just... make it thicker without changing the length of the fibers? $\endgroup$ Commented May 31, 2020 at 22:26
  • $\begingroup$ @Mephistopheles the issues is if you make the muscle thicker you make it more massive, you also have to make the ligaments thinker and more massive becasue they are taking the load, then you have to do it for the bones., ect, then you have to do it for the digestive system and cardiovascular system supplying those muscles, and the lungs, and the ect. it is like the worlds least favorable rocket equation. If you just make hte muscle thicker without changing anything else it just tears itself apart, (which can happen to bodybuilders that put on muscle too fast). $\endgroup$
    – John
    Commented May 31, 2020 at 22:31

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