What is the maximum size of a flying creature?

Question

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?

Answer 1

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.

Answer 2

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).

I did, however, dig up this article on dragon physics. There's also this article

Oh, and just so we can skip it all together, a hydrogen balloon is not terribly buoyant (look up how much helium it takes to lift a human). This post on the XKCD forums talks about it, if you're interested.

Answer 3

Gliding should be possible with much bigger sizes than a possibility to take off, land and live on the ground. During flight, the wings are supported by the air so need no bones and muscles strong enough to hold them stretched while standing in place. Like on a propeller plane, additional pair of much smaller wings may provide a propulsion if required. Also a plane needs most of its engine power during take off.

The creatures could take of from the land into the cruising altitude before being fully grown up.