[...]

I would always start with Newton’s second law by translation calculations, but that’s nothing to blame you.

But anyway, I have some points to query:

1.) Toothless weight: You used 1,400 kg. That is in my opinion way to much. Okay, the volume of his whole body is around 2.05 cubic metres (calculated from a very exact 3D model). That would implify an average density of ~0.7 g/cm^3 which is around 30% lower than the density of a normal human body. But there are two things that make him even more lighter: The bones are hollow, a density of 0.2 g/cm^3 is on my opinion a value to start with. And the second thing is the organ where he stores the acetylen gas which have to be quite huge to store the amount of gas we’ve seen in several scenes. 200 litres should be enough.

Where are we now? At around 900 kg? But this is still so heavy, that he would never even be able to fly 10 metres. Do you know the ‘Quetzalcoatlus’? It was the largest pterosaurs ever existed. He lived in the Cretaceous. Paleontologist say that he probably weight 200 to 250 kg. Its wing area is around 40% small than Toothless’. That’s why I would say that Toothless won’t be able to fly like we’ve seen it in the movie when he would weight more than 600 kg.


2.) The lift coefficient: Your formula is correct, but you forgot one thing: It works only for static objects. But his wings are the wings of bats, not birds. They bloat while gliding (that’s one of the reasons why bats cannot glide really good). Without a correct streamline simulation this value is useless. It could be 1.6 or 1.2 or 0.5. That shall not mean that everything is incorrect, but you should also calculate everything with values with a variation of 50% from your one.


3.) Air resistance: Did I missed it? Because this is a very very VERY important coefficiant in any equation about the movement through a dense medium. You cannot just ignore it. It affects the speed, the stream of the air and creates turbulences.


4.) Turbulences and stuff: With this shape and at this speed you have to involve turbulent flows, reynold’s number and dynamic and kinematic viscosity. At least use an approximated value for it.

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Yay! A throwback for me, since I actually did this analysis near January of 2013. More than a year ago, that is.

But yes, you are right in all accounts; however, I also didn’t have any resource back then as to how I should calculate Toothless’s volume (since I didn’t really have a good model of him or the 3D chops to do it) so I basically said “screw it” and approached it in the vein of Fermi problems.

Here were my restrictions:

No calculus. Though I do introduce the concept of integration a bit, I didn’t actually want to do a full integral; I basically reduced it down to integration of a constant function (y = a), which is just multiplication. The reason why I set this was because, well, without models I couldn’t really do a great math.
No-flap flight. Though Toothless does flap wings, in plenty of shots he is seen basically horizontally cruising without flapping his wings for a good while. By assuming there is no flapping, I can get the maximum lift his body needs to generate by itself for horizontal cruising.
Screw air resistance. I knew that if anything, I was going to get an unrealistically high required airspeed (with respect to Hiccup’s safety, etc.) and air resistance would have only increased that required speed.
Screw turbulent flow. Because, well, I couldn’t really do the math.
I would actually love to see how this can be done with the actual math as opposed to my idiosyncratic approximation (which was done ONLY USING MY HIGH-SCHOOL PHYSICS KNOWLEDGE and some basic Wikipedia research).