How big would a dragon's wings need to be?

Question

I need to know how big the wings would be for a dragon of a particular size. The dragon is 20 foot long and weighs 6 tonnes. How wide and long would the wings need to be for it to fly?

Answer 1

It depends on some other factors, but the answer is: REALLY BIG

The equation we need is: $$ A = \frac{L}{0.5 v^2 \rho C_L} $$

Where $A$ is the area of the wing, $L$ is the mass of the dragon, $v$ is the velocity that the dragon needs to achieve flight, $\rho$ is the density of air, and $C_L$ is the lift coefficient (usually close to 1 for most flying creatures).

So if we make some assumptions

$L=6,000\,$kg, $v=7.0\,$m/s (about the same as T-rex), $\rho=1.225\,$kg/m^3, and $C_L=1$.

Then the wing area is about $200\,$m^2, or $100\,$m^2 per wing. Wings are usually at least twice as long as they are wide, so something like $6.9\,$m$\times14.5\,$m would be about right.

Note that this answer changes drastically with the velocity value, as the area is inversely proportional to the square of the velocity. So a dragon would need much larger wings if it needs to be able to take off without a running start or jumping from a high place.

Answer 2

My initial thought is that a a real life adult European style dragon would be much to heavy to fly no matter how large a wing span it might have. Most flying creatures have hollow bones, but dragons as they are usually depicted just look super heavy.

However let's look at at wingspan to weight ratios of some of the largest know flying creatures.

Teratornis a vulture like bird had a wingspan of about 12 feet and weighed about 33 pounds. That is works out to 2.75 pounds per foot of wingspan.

Quetzalcoatlus a pterodactyl like creature had a wingspan of about 36 feet and weighed about 500 pounds. That is works out to 13.9 pounds per foot of wingspan.

On of the heaviest extant flying birds is the Mute swan. The largest specimens come in at 32 pounds with a wing and of 7.8 feet. That is works out to 4.1 pounds per foot of wingspan.

The Kori bustard can weight up to 44 pounds and have a wingspan of 9 feet. That is works out to 4.8 pounds per foot of wingspan.

The Magnificent Argentine bird had a wingspan of 19 feet and a weight of 156 pounds. That is works out to 8.4 pounds per foot of wingspan.

This gives us a range from about 3 pounds per foot of wing span to 14 pounds per foot of wingspan.

Your dragon weights 12,000 pounds.

That works out to a wingspan of 4000 feet to 857 feet. Such a large wingspan does not seem feasible. A semi realistic wingspan of 300 feet the size of a football field would require a figure of 40 pounds per foot. Several times any real life example.