Can Toothless Fly? |
Topic Started: 31 May 2014, 15:23 (3077 Views)
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Zer0x
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31 May 2014, 15:23
Post #1
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[b]Banhammerdragon [/b]
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More than one year ago TheCube42 posted on Tumbr a mathematically and physically proven article about the aerodynamics of Toothless while gliding. I discovered the post few days ago and found some discrepancies in his calculations.
I created this topic to talk about the the physics of Toothless and try to continue his work.
Here is the link to the original post:
http://thecube42.tumblr.com/post/557263 ... rodynamics
And here our little discussion:
Spoiler: click to toggle
My reply
[...]
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.
[...]
Spoiler: click to toggle 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).
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UNAMUSED
No, I'm serious....stop it..
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Hope_and_Heir
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31 May 2014, 15:26
Post #2
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[color=#B40431]Winner of Shnuckle's Oneshot Fanfiction Contest 2014 [/color]
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My. Head. It's. Spinning. Your intellect is too much for my brain to handle.
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'There Were Dragons When I Was A Boy…'
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HideousZippleback
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31 May 2014, 15:47
Post #3
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[color=blue]I'm just here for Snotlout. [/color]
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GAH... I don't understand any of it... My bran ain't made for this...
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BerserkDragon
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31 May 2014, 16:55
Post #4
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antisocial british nerd with a youtube channel
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I understand the gist of it, seen as I'm designing a glider, but I wouldn't of been able to do this myself
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Me? An otaku? Pfff.
Yes I do like dragons if you're wondering. Doesn't seem like it from my profile pic n signature, I know, but I do.
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chimuelo
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01 Jun 2014, 00:55
Post #5
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Blacksmith Apprentice
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Note to self: revisit this topic after I've taken fluid dynamics.
I just finished a basic dynamics class so I could understand most the set-up, but there's no way I could have pointed out all of Zer0x's criticism by myself!
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Zer0x
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01 Jun 2014, 14:58
Post #6
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[b]Banhammerdragon [/b]
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In the next days I will make a detailed sketch with all affecting forces.
I mentioned before that we have to know how fast Toothless can go. For that I use the maximum speed he could reach after a dive.
Here is the formula for the max. speed:
v=sqrt((2xmxg)/(pxAxc))
And here is the formula for the speed at any time while falling:
Don't ask me where it comes from. It needs more than 3 sheets of paper, 3 substitutions, separation of variables and a heavy integral.
m - mass (I used 130kg for it, if his is higher he will be faster)
g - acceleration (9.81 m/s^2)
p - density of the medium (air at level 0: 1.2041 kg/m^3)
A - area of the falling axis (according from the size of a 3D model it is around 0.8 m^2)
c - drag coefficient (without his wings he have a nearly ideal streamline shape (0.02), I used 0.06, that's a bit lower than an airplane)
v0 - speed at the start (mostly 0)
t - time
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UNAMUSED
No, I'm serious....stop it..
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Toothless123
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01 Jun 2014, 15:09
Post #7
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Night Fury
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- Zer0x
- 01 Jun 2014, 18:58
In the next days I will make a detailed sketch with all affecting forces.
I mentioned before that we have to know how fast Toothless can go. For that I use the maximum speed he could reach after a dive.
Here is the formula for the max. speed:
v=sqrt((2xmxg)/(pxAxc))
And here is the formula for the speed at any time while falling:
Don't ask me where it come from. It needs more than 3 sheets of paper, 3 substitutions, separation of variables and a heavy integral.
m - mass (I used 130kg for it, if his is higher he will be faster)
g - acceleration (9.81 m/s^2)
p - density of the medium (air at level 0: 1.2041 kg/m^3)
A - area of the falling axis (according from the size of a 3D model it is around 0.8 m^2)
c - drag coefficient (without his wings he have a nearly ideal streamline shape (0.02), I used 0.06, that's a bit lower than an airplane)
v0 - speed at the start (mostly 0)
t - time
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WasBornCrazy
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06 Jun 2014, 02:34
Post #8
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i dont think my avatar is working but ehh
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o.O
Intellect.
O.o
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i'm not very active anymore!! it's sad, but i'll come back sometimes to feel nostalgic ahaha
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Lageos
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06 Jun 2014, 09:24
Post #9
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Gronckle
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You said that the dragon's bones are hollow, I would beg to differ, the amount of abuse that dragons are able to take, is underrepresented, it most likely would be sold, seeing how much abuse toothless took in the first movie, plunging from the sky, twice, hitting sea-stacks, not to mention, they need to support their own weight! anyways, they are extremely durable creatures, so my guess is that they have solid bones.
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Dan_Oceans
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06 Jun 2014, 09:30
Post #10
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What do I put here again?
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okay so solid bones=more weight. That makes thing more difficult for dragons in terms of flying right?The force needed to propel Toothless increases and makes it hard for Toothless to stay in the air. But how much do the bones weigh? Is there a limit to the weight Toothless can have before he can fly?
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"can you hear the birds sing? saying go the f*** to sleep (to the sound of les mis)"
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