Sorry, Toothless, but Physics happened (Analysis)

[TheCube]

I guess this isn't fiction or literature of any sort (unless bad data and approximations count as fiction). I'm not sure if it's really considered fanwork, but I guess it is.

A couple of weeks ago, I was watching the TV show on my phone, and the intro sequence with the sonic boom brought up some interesting issues: if Hiccup is not wearing any protective goggles, how fast is Toothless REALLY flying in order to prevent Hiccup from getting blinded and plummeting Toothless down onto the ground or sea? Or, going even further, can he manage to fly at that kind of speed without falling?
Because I read some books about seeing flawed science in movies and games, I knew I could do something to figure that out; the result is me looking up stuff on Wikipedia for three hours in order to basically learn aerodynamics and make a nice guesstimate without doing something I have no idea how to do (i.e. multivariable calculus).

If you can just look at the problems and solve them yourself without looking at my answer (my answer is not the only answer, and it certainly isn't the exact answer), I salute you. I might get to explaining how I got the answers and how they are not the most accurate answers, but I don't know if I'll have time to write all that.

Both documents in the .zip file are also on my Google Drive as .pdf files for people who don't have Word 2007:
docs.google.com/file/d/0BzRfBXBdGXiCa21tZUpXcHB2Q0U/edit?usp=sharing
docs.google.com/file/d/0BzRfBXBdGXiCblh0dzdOUXYxSFU/edit

(Spoiler: Physics 1:0 Dragons )
If anyone else can think of other interesting physics/science problems in the world of HTTYD, post 'em down below and I might get to figure them out if I have time.

[iridescent]

This is very interesting. So according to your calculations, Toothless must fly at 105 kmph in order to stay aloft. However, I actually think Toothless' weight is a lot less than 1400 kg, since dragons must be built to be light for their size. Using an estimate of 500 kg instead, I get the final speed 63.2 kmph, which is still pretty fast.

What I think goes even more against physics is when Toothless simply floats in the air without flapping his wings. Like during the Romantic Flight scene in the film, among many others.

I know of a few more instances where physics is defied, and even when biology is defied, but, meh, whenever I'm into a story involving dragons, I don't take science very seriously.

Also, I'm very good at math, but I've never learned aerodynamics (although I'll try when I have time), so if you could translate the physics problems into pure math problems, then I'll most likely be able to solve them. I know multivariable calculus, linear algebra, and differential equations.

[TheCube]

If you know multivariable calculus, you should be able to just learn the lifting-line theory and its variables to a reasonable level. I am only a high school junior with a pretty good grasp of elementary calculus topics, which is why I was relegated to using the old thin-airfoil theory and basic calculus concepts... Again, I learned all of aerodynamics I know on Wikipedia.

My calculation assumes that Toothless's wings are not flapping, which means there is little thrust; but at a high enough speed he should be able to achieve "flapless" flight for a while as some birds do. Hovering, though, is an interesting topic; it's reserved for insects and hummingbirds, but some birds can also hover for a short time. There's a lot of hovering in RoB but considering it's hard to talk while flying, it's probably the only device to allow communication between the riders.

Body density is also kind of hard to estimate, which is why I used a Komodo monitor's weight and scaled it up; but I think it's hard for Toothless to weight less than around 600kg given his enormous size. The only dragon that I think definitely could achieve stable flight are the Typhoomerangs with their HUGE wings, and the least feasible one the Gronkle.

Of course, if we really wanted to figure this out and we had a LOT of $$$$$ lying around, then we could just 3D-print a life-size Toothless model and put it in a wind tunnel

[iridescent]

Oh, a funny example of HTTYD defying physics just popped into my head. I've been aware of this for a long time, and this is a good opportunity to share it.

Near the end of Gift of the Night Fury, Fishlegs spots Meatlug and rams into her, and the two roll at a speed that is very close to Fishlegs' speed before the collision. When you consider conservation of momentum, this is pretty funny.

Conservation of momentum states that when two objects 1 and 2 collide, m1s * v1s + m2s * v2s = m1f * v1f + m2f * v2f, where m1s is the mass of object 1 before the collision, v2f is the velocity of object 2 after the collision, etc. Let Fishlegs be object 1 and Meatlug be object 2, and assume that after Fishlegs rams into Meatlug, the two fly at a speed that is 3/4 of Fishlegs' original speed. Since Meatlug is stationary before the collision, v2s = 0. We have,

m1s * v1s + m2s * 0 = m1s * (3/4*v1s) + m2s * (3/4*v1s)

which reduces to

m1s = m2s * 3.

So with a parameter of 3/4, we get that Meatlug's weight is one third Fishlegs' weight. That's pretty hard to imagine.

Note that I didn't even consider angular momentum, which would have made the ratio of Meatlug's weight to Fishlegs' even smaller.

[torin13]

This doesn't have to do with physics, but more with chemistry. I was wondering exactly how Toothless made his plasma bolts, and I wanted the exact chemistry. I looked on the HtTYD Wiki, and found out that the bolt is made up of acetylene and oxygen. Since oxygen is easy enough, you only have to breath in, I focused on acetylene. After much Wikipedia and the likes, I got this:

Start off with water, calcium, and carbon. Mix calcium and carbon to form calcium carbide. Add water to form calcium hydroxide and acetylene (After some more research, I found calcium hydroxide can be used to purify water, help with digestion, improve sugar extraction, and can be used as an insect repellant). Obviously, acetylene is used for the bolt. It is also unstable, and will explode shortly after being fired, explaining why the shot exploded even when it didn't hit anything after the scene 'Test Drive'.

So while it doesn't exactly 'defy' anything, I thought I'd just inform you of that.

Physics 1:1 Dragons

[TheCube]

Ooh, hydrolysis. My chemistry knowledge is not that deep, but yeah, property-wise acetylene + oxygen should work fine.
A YouTube video showing hydrolysis of calcium carbide and acetylene mixed with oxygen exploding:



It's not as purty as Toothless's, but still, Exx--plosssions!


There is one problem, though, which would be the way to produce C₂H₂ without basically frying oneself.
Since production of calcium carbide requires an IMMENSE amount of heat (2000+ degrees celsius?), I think partial oxidation of methane, CH4 (or cracking of ethylene, C2H4) is a more plausible way to create acetylene just because it should require less heat.

CH₄ ⇌ CH₂ + H₂ ; CH₄ + CH₂ ⇌ C₂H₆ ; C₂H₆ ⇌ C₂H₄ + H₂ ; C₂H₄ ⇌ C₂H₂ + H₂ ...

(Notice the lack of oxygen in decomposition from CH4 into C2H2, this is when oxygen has been used up, and apparently known as "cracking")

[Serimon]

Jan 25, 2013 0:46:56 GMT -5 TheCube said:

I was watching the TV show on my phone, and the intro sequence with the sonic boom brought up some interesting issues: if Hiccup is not wearing any protective goggles, how fast is Toothless REALLY flying in order to prevent Hiccup from getting blinded and plummeting Toothless down onto the ground or sea? Or, going even further, can he manage to fly at that kind of speed without falling?

This intro sequence is a hyperbola, IMHO. It is not really happening.

[TheCube]

Jun 11, 2013 0:41:32 GMT -5 Serimon said:

Jan 25, 2013 0:46:56 GMT -5 TheCube said:

I was watching the TV show on my phone, and the intro sequence with the sonic boom brought up some interesting issues: if Hiccup is not wearing any protective goggles, how fast is Toothless REALLY flying in order to prevent Hiccup from getting blinded and plummeting Toothless down onto the ground or sea? Or, going even further, can he manage to fly at that kind of speed without falling?

This intro sequence is a hyperbola, IMHO. It is not really happening.

Oh God.

I'm gonna do this.

So the opening sequence is kind of like this?



*trollface*

But spelling errors aside, I am quite aware that this is a world where physics is fickle. You can fall through a pretty good distance and suffer no broken bones, and for crying out loud, Meatlug can fly.

[they fly]

All of the dragons in HTTYD can fly. Even a gronckle. They use inflation bladders filled with "lighter than air gasses" like hydrogen and methane. This allows them to fly without having huge wings, on the other hand, toothless is designed to dive bomb. He dosen't have an inflation bladder as it would slow his descent. So therefore he has wings big enought to allow him to fly. Most of the other dragons can breathe "normal fire" as they vent of some of the hydrogen inside ther inflation bladder and breath it out.

Now one thing I have wondered for a while is how do they light there fire. They don't eat catalysts like platinum as otherwise toothless wouldn't have been able to ignite his acetylene-oxygen.

Another thing I have wondered is is it possible to have ionized semi-solid acetylene-oxygen. According to many forums and some wikis its ionized enough to be plasma and it has to be semi-solid to form a sphere shape.

Thanks

[they fly]

All of the dragons in HTTYD can fly. Even a gronckle. They use inflation bladders filled with "lighter than air gasses" like hydrogen and methane. This allows them to fly without having huge wings, on the other hand, toothless is designed to dive bomb. He dosen't have an inflation bladder as it would slow his descent. So therefore he has wings big enought to allow him to fly. Most of the other dragons can breathe "normal fire" as they vent of some of the hydrogen inside ther inflation bladder and breath it out.

Now one thing I have wondered for a while is how do they light there fire. They don't eat catalysts like platinum as otherwise toothless wouldn't have been able to ignite his acetylene-oxygen.

Another thing I have wondered is is it possible to have ionized semi-solid acetylene-oxygen. According to many forums and some wikis its ionized enough to be plasma and it has to be semi-solid to form a sphere shape.

Thanks

[Pds314]

As for the inflation bladders, they aren't limitlessly floaty. It takes 1 cubic meter of Hydrogen to lift 1.1 kg to any height at all whatsoever. I don't know what a Gronckle's mass is, but I'd bet it's at least a few hundred kg, which means that those inflation bladders aren't even nearly good enough. A Gronckle would simply need to be much bigger than it is in order to lift its own body mass. The Gronckle would probably have to be lighter than a turkey or a small child in order to lift off on hydrogen and methane just makes it worse.

No, the Gronckle is completely unrealistic. Toothless could probably fly IRL, as long as his wings would lift him, and he could figure out how to haul his pudgy bulk up to 28 m/s or so, which drag-wise, should be easy, but figuring out how to get his legs to move that fast is problematic. Anyhow, assuming that Toothless has almost cheetah-like speed on the ground, take off would be quite doable, and his top speed should be around 60 m/s at sea level, or 47 sustained over long periods. Likewise, he should be able to reach about 20,000 meters, scarily high, and at that height, sustain 115 meters per second, barely above stall speed.

Here's the scary part: Hiccup's skin would bloat and his tears would boil at that altitude. It's roughly at the Armstrong limit, which means water boils at body temperature.

Here's the other scary part. Toothless going into a dive from that height would cause him to reach quite ridiculous speeds. His speed would peak at 7500 meters high, and 500 meters per second. Yes, that's about Mach 1.5. He'd probably be slowed to just below mach 1 by air drag slightly before reaching datum.

Curiously, this means that Toothless could probably kill another dragon just by flying NEAR them. During transonic flight, his 6 megawatt deceleration would be greatly amplified. Perhaps by a factor of 10 or more, into a lethal wall of sound. Being within a few meters of toothless would result in your nervous system being shut down by the shockwave, and you going from alive to deaf to dead in a matter of milliseconds. Likewise, if toothless does a somewhat dangerous maneuver and pulls up in the last couple seconds over your house, he might actually break your house down, and would EASILY shatter every window in it. This 12-mile dive of doom might explain why night furies are rarely ever caught. They fly so high that nothing and nobody can detect them, and then they dive so fast that by the time anyone can hear or see them, they've already scored a few kills and flown away faster than an arrow.

[h]

is toothless just as fast as other night furies? i am asking this question because of his tail fin

[Leah]

This thread is freakin' gorgeous! LOVE the scientific analysis of the dragons, especially theyfly and pds314. I concur with the second comment as if we go from an evolutionary standpoint, there is a time when reptiles and avians divide, as many probably know it's the Archaeopteryx! This means that it's perfectly conceivable for divergent evolution to progress in a way that is similar for both species assuming that they evolved in a similar environment with the result of being capable of flight. Natural selection would favor the members of the population that had less mass, meaning that things like bone density and muscle density would gradually decrease over time. Just look at Pelicans, they're big, but not dense. Though there's really no way of justifying a Gronkle being able to fly (except maybe bumblebees?), the rest of the dragons wingspans seem to be sufficient to provide enough lift for them to fly.

[Deryl]

I know this is kind of an off-topic question, but if Toothless and the Indoraptor got into a fight who do you guys think would win? I personally think that Toothless would win

[Violet]

Something to consider is Toothless's endurance. If he is too powerful, he might be destroyed by his own power. He can be injured by arrows, which means that he doesn't have super tough hide. So is it even possible for him move that fast or shoot plasma blasts?