# What is the maximum size of a flying creature?

Giant winged beasts such as the Roc and the western dragon feature strongly in mythology. Is there a maximum size on a biological winged flying creature? How would an atmosphere different from Earth's change such a limit?

• If I'm not mistaken, the largest flying creature to live on Earth was the Quetzalcoatlus Ptersaurous - en.wikipedia.org/wiki/Quetzalcoatlus – CoolCurry Oct 2 '14 at 3:21
• You need factors on this, there are so many possible answers. But for starters you can look at this question about dragons. Part of it includes if they can fly. In my answer, I did try to go into the mechanics of it, but again there are a lot of factors. Could you specify a few? (Body shape, wing shape, whether or not wings provide all lift, etc.) – DonyorM Oct 2 '14 at 3:23
• Well, Carl Sagan did speculate about balloon-creatures, which are physically possible on Earth too, and they can be massive, although they'd be pretty vulnerable to predators. I assume you're only interested in the heavier-than-air kinds though. – congusbongus Oct 2 '14 at 7:22
• Increase the atmospheric pressure to increase density of the atmosphere and the atmosphere has denser constiutents and almost any size of animal can fly. The limit is only the pressure to crush DNA. – user2617804 Oct 2 '14 at 7:28
• @CoolCurry Well, the Quetzalcoatlus had a ridiculously huge head and long neck but a relatively short and small body. While being as tall as a Giraffe when being on ground they only weighed about 200-250kg. Western dragons portrayed with their lizard like appearance probably weigh a couple of tons. – Otto Abnormalverbraucher Jun 26 '18 at 11:11

This depends on many factors. A scientific way, how to approach this problem, is called allometry. If we change some conditions, physical parameters more or less change with certain power of the change. For example according to Kleiber's law, the amount of food an animal needs is scaled as $M^{3/4}$ with its mass $M$. This means that if human of mass 100 kg needs 1 kg of food per day, mouse of mass 100 g will need $(0.1 / 100)^{3/4} \times 1\;\mathrm{kg} = 5.6\;\mathrm{g}$. This fits quite well.

Similar laws can be derived for the flight, which allows us to estimate, how difficult it would be to flight in a very thin atmosphere like Mars has, or a very thick atmosphere of Venus.

### Power to sustain flight

According to the book Modelling the Flying Bird by Pennycuick, the bird's flight induces velocity change on air. This velocity is approximately calculated as

$$v = \sqrt{\frac{2 M g}{ \pi B^2 \rho} }$$

Here $M$ is bird mass, $g = 9.81 \;\mathrm{ms}^{-2}$ is the gravitational acceleration of Earth, $B$ is the wingspan, $\rho$ is density of air and $\pi$ is mathematical constant pi. This is not the velocity of the bird, but the velocity change of air induced by the flight! It is only important to calculate the power $P$ needed to sustain the flight

$$P = M g v$$

These three laws should be enough to answer your question in almost any environment. You can calculate how much power you need for flight and how much power is approximately available from the food for animal of given size.

Let us try to calculate things for Quetzalcoatlus, the largest animal that ever flew. (Wingspan 10 m and mass 200 kg). According to the formula for velocities, v = 12.7 km/hour. Power necessary for that is approximately 7 kW, which is 10 horse powers. Given the animal is approximately of size of a horse, it seems reasonable and we see that the flight was probably quite a demanding task.

Let us try martial eagle (4.6 kg, wingspan 2 m). We get v = 10 km/hour and the required power would be 120 W. I do not have these information about eagles, but they seem reasonable to me. We can see that airplanes can flight with quite small wingspan, but only because they can use extremely large power output of their engines. Animals do not have that advantage and they need bigger wingspan. (This can become a problem, if a 20 ton animal required 100 m wingspan to get within reasonable power requirements - its wings are still from flesh and bones and it probably couldn't support the animal weight.)

### Dense atmospheres

We can also see that the flight on Venus (had it breathable atmosphere) would require 20x smaller power and much bigger animals could flight there. Maybe even more, because for very dense atmospheres, the Archimedes law will start reducing the animal mass, which will make the flight even easier. In very dense atmospheres, flight would be very similar to swimming and birds might be similar to fish.

• @Irigi I've tried to use your formulas to arrive at my own calculations but I don't arrive at the same numbers you have. I've plugged everything into a spreadsheet to calculate for me, but the numbers it spits out are quite different. Perhaps our units are different? For example, in the case of a Martial Eagle here is what I have: • Grav Constant: 9.81 ms^-2 • Air Density: 1.292 kg/m^3 • Mass: 4.6kg • Wingspan: 2m • Pie: 3.14159 I arrive at an induced velocity change of 2.36 (I presume that is km/hr?) and a power needed of 106.39w. As you can see this is different than your calcs. – n_bandit Apr 16 '18 at 16:33
• An interesting sidenote to your last sentence: There is a family of insects called the mymaridae, which consists of such tiny flying insects, air molecules in comparison are so large that some of them dont even have traditional wings anymore but rather limb-like extensions covered in bristles, with which they can swim through the air. Look up the Mymar or Arescon. – Otto Abnormalverbraucher Jun 26 '18 at 11:38
• What kind of "flying" are you referring to, soaring like a wandering albatross, hovering like a hummingbird, or gliding like a flying squirrel? – nalzok Jan 25 '19 at 11:47

I recall from long, long ago that someone had worked out that a length of about 5 meters was the upper limit (larger than that and either it couldn't fly or its wings would snap under their own weight).