(Film versions.)
I'm literally writing a 2,000 word essay about who would win between a multi-hundred-ton demon who shrugged off a wave of molten gold and a car-sized flying lizard with lots of gas.
I've put this post off for far too long. I'm going to do it—look into the meaning of the figures given in the character files for Smaug and Toothless. While I give a lot of numbers and stats there, the winner of a fight is of course not determined by pure numbers. We have to study what those numbers mean. Merely giving the KE of a bullet is not enough. Knowing the pressure it applies and the stress tolerance of the material it hits is important.
Also, don't contact me saying, "Toothless has friends who can help him." This fight is Toothless vs Smaug.
Table of Contents:
Speed:
Smaug's speed
Smaug reached 600 mph in BotFA, and that was in relatively level flight. We'll assume that's his top speed.
Toothless's speed
Toothless is often stated to be able to reach supersonic speeds. I decided to dig deeper to find where this claim came from.
"Toothless made a vapor cone!"
The first major claim is that we saw a vapor cone behind Toothless in the opening of Dragons: Rise of Berk, so Toothless must be faster than sound, right? However, Professor Mark Cramer of Virginia Polytechnic Institute (now Virginia Tech) states:
"Finally, it should be clear that Prandtl-Glauert condensation has nothing to do with 'breaking the sound barrier' and is not a Star Trek-like 'burst' through Mach one. An aircraft can generate a Prandtl-Glauert condensation cloud without ever exceeding the speed of sound."
Vapor cones can also form when something goes very fast (but not at the speed of sound) in very wet air.
The vapor cone doesn't mean anything anyway—it's from the opening of a video game which is only debatably canon, and Toothless never appears to go so fast in the films of show.
"Toothless outran lightning!"
Yes, but that was Skrill lightning. It plainly was not as fast as normal lightning.
Before you point out that the shot might be intended to be understood as slow-motion, watch it again. Toothless's plasma blast traveled at its normal speed (or maybe slightly slower than usual), so unless he somehow accelerated his shot, it's normal speed, or at very most 1/2, which would probably still give Toothless a speed under 100 mph.
Honestly, I'm sick and tired of people scaling characters' speed from lightning. Just because lightning is supersonic in our world does not mean that a fictional character who is elsewhere indicated not to be able to go supersonic is in fact supersonic just because they dodged lightning (which is usually shown as going quite slowly)! This should be apparent, right? I hope so?
For instance, this guy scaled HTTYD dragon speeds from the fact that out of 20, a Skrill riding lightning is 19. He then calculates the speed of dozens of dragon species from their given stats, and then prints the figures that indicate that the tiny Fireworm can attack with 2.9e8J (and then argues that the lightning is as fast as real lightning because it comes from clouds)! He does admit the problems with his method in the comments, but he still thinks that kinetic energy based on vague book stats which are based on surprisingly slow lightning is fine for dragons which run their prey down! The lightning takes a full second to reach the clouds, which are unrealistically low, unless the lightning widens a lot so it only looks like the Skrill travels about a few hundred feet.
"But this one book says Toothless is supersonic!"
(The book is Book of Dragons by Maggie Testa.)
First off, another reference book says Toothless can exceed 100 mph, and I'm sure they would have mentioned he can break the sound barrier if they believed he actually could.
Secondly, when the films contradict a reference book, the films are the one we should listen to. They never show Toothless going supersonic, even when it would be advantageous for him to do so.
"Fishlegs said Toothless can break the sound barrier."
In a special feature for HYYTD 2. In a dramatic fashion. Referring to his diving speed. Anyway, how would the Vikings know the speed of sound with any accuracy? The first real attempt in our world was by Newton.
I just came up with a rough approximation for the plausibility of Toothless breaking the sound barrier. Using the canon weight for the Night Fury, the drag coefficient of a bullet according to Wikipedia (remember, I'm trying to be as Toothless-biased as possible here), and a very generous area of 2 ft^3, I get a terminal velocity of 484.9237 m/s (1084.7434 mph) from this calculator. That's plenty fast enough. However, I'm giving Toothless everything I can, and note that to accelerate to this speed in 5 seconds would require an acceleration of over 9G even with a starting velocity of 50 mph—this would likely injure Hiccup, if the winds alone didn't rip his flesh off! Or, to get to that speed by accelerating at 1G, he'd need to dive for... almost 50 seconds! Which we never see him do. He never appears to climb high enough.
So, Toothless can most likely exceed 100 mph in level flight, but not by that much, and he might be able to go supersonic in a dive. It's clear he's outmatched here.
Agility:
Smaug's agility
Smaug does not appear to be very agile—he never performs any very difficult maneuvers mid-air.
Toothless's agility
Toothless's agility is quite impressive. A list of feats can be found here. Suffice it to say that he is the obvious and clear winner in this category.
Armor:
Smaug's armor
Those who cannot be bothered to do math often point out rightly that Smaug's armor was penetrated by well-placed shots from a ballista shooting iron or steel bolts. However, it's not his only toughness feat, as here we see him easily smashing through massive stone pillars with no sign of injury.
Let's calculate the stress tolerance (in this case either compressive strength or point shear, I think) of Smaug's scales, or the pressure required for an arrow to get through. The arrow had a mass of about 4.698 +/- 3.357 kg.
Maximum estimate
For this we will use m = 8.055 kg. Rhett Allain also estimated the velocity as 14 m/s. So the momentum is 112.77 kg*m/s.
Now the force exerted on the scale (momentum change divided by time to stop):
112.77 ÷ 100 microseconds (just a guess; you can probably figure out something more exact) = 1127700 Newtons, or over 1MN.
Now for the pressure. P = F/A is the formula. The tip of the arrow is very sharp, so let's give it an area of 1 square millimeter (0.000001 m^2).
1127700 ÷ 0.000001 = 1127700000000 pascals, or 1127.7 GPa!
Minimum estimate
m = 1.341 kg
18.774 kg*m/s is the momentum.
18.774 ÷ 100 microseconds (0.0001 seconds) = 187740N
Let's assume the arrow isn't as sharp as we did last time. Let's say it's got an area of 0.000005 m^2.
187740 ÷ 0.000005 = 37548000000 Pa (37.548 GPa), or less than the pressure exerted by a bullet.
Assumptions and possible inaccuracies
The calcs above assume that Smaug doesn't move or squish at all in response to the impact, which would decrease the force and therefore the pressure required for penetration. I just guessed for the time in which the arrow stops—it could very well be less, which would increase the force. The Black Arrow scene might be slow-motion to show its flight, which would increase the momentum dramatically (but Smaug does seem to be moving close to real speed, so I'll ignore this possiblity). Finally, the Black Arrow succeeded in damaging Smaug's armor, so the real value is a bit lower.
Therefore I think the real answer can be reasonably thought to be above my minimum value and below my maximum value.
As for heat tolerance, he flies through his own fire several times, no-sold blue-hot explosions, and shrugged off being submerged in molten gold, which has a temperature equal to some lava. Note that the gold touched his weak spot, so his bare skin has a very high temperature tolerance (molten gold sticks to objects and thus would transfer a very large amount of heat). Also, his jaw appeared to be open when he went under, which indicates a very high temperature tolerance even inside his mouth, and there isn't any gold in his mouth when he comes back out, so presumably he swallowed it (the other apparent possibility is that it was vaporized by his body heat, but that's absurd—simple thermo tells us he'd be turning the air to plasma and frying everyone nearby by opening his mouth even without the fire).
Toothless's armor
Toothless's scales were cut by a hit from a Razorwhip's tail right after he was hit with a blast of fire. Razorwhips can cut through rock. Toothless's scales were only lightly injured by the hit right after being blasted with bright blue fire, so we know that their resistance to cutting is greater than some rocks. However, it can't be much greater.
Calculation from crossbow bolts
Toothless tanked crossbow bolts as well. I will be quite generous and say that the bolts are traveling at typical arrow speed (though they don't appear to be) and that they weigh 4 ounces.
(90 m/s)(0.1133981 kg) = 10.205829 kg*m/s
10.205829 ÷ 0.0001 = 102058.29N, 102.05829kN
102058.29 ÷ 0.000001 = 102058290000Pa, 102.05829GPa
This is supported by the fact that a spine from a Whispering Death got through his armor. So I will take this figure as being the approximate strength limit (disregarding, out of wish for simplicity, any bending of the armor or recoil from Toothless, both of which would lower the force exerted and thus the strength of the armor).
Toothless was injured by a blast from a Whispering Death, which can shatter stone and based on color was about 1,200 degrees C (almost as hot as Smaug's fire). He was unharmed by being blasted with lava (though he got the lava off comparatively quickly), and also by a hit from a Razorwhip.
We also know that it burns at less than 1200C. This is because the Whispering Death's blast made his scales emit smoke after a less than one-second contact with the flame.
Firepower:
Smaug's fire
Smaug can engulf huge areas in flame with a temperature over 1200 degrees. His blasts can have a total yield of over 10 kilotons, and can wipe out wooden and even stone structures. He blasted through the main arch of Erebor as well. The total energy can exceed 40TJ, and the effective energy is almost certainly in the hundreds of gigajoules.
So if Smaug's fire is a cone measuring 1,000 feet by 200 feet (based on this shot), the total volume is 10,000,000 ft^3. That gives me 4 MJ/ft^3. If you need help visualizing that, he could fill more than ten mid-sized skyscrapers with fire that's hot enough to vaporize over half a kilogram of iron per cubic foot of fire (it would never have that effect in reality, but the comparison helps illustrate thermodynamic limits).
Toothless's fire
Toothless can vaporize large amounts of ice with simple fire, vaporized a large boulder with a plasma shot, and knocked over the Red Death, which likely weighs hundreds of tons, with a charged plasma blast. Note that the Red Death really appears to fall over instead of being purely knocked down, and that this likely represents the upper limit for Toothless's capabilities given that we never see him do anything like it again. So we can give a lower limit of 64GJ for uncharged blasts, and, being generous, probably an upper limit of 1TJ for the charged blasts (note that the charged blasts in the second film did not appear to be quite that powerful; this may be due to the fact that Toothless was diving when he hit the Red Death).
Also of note is that even a pretty good blast did not level a wooden tower.
Toothless's fire has a maximum temperature of 3100C (not far off from the surface of the Sun heatwise), based on the canon statements that it's Acetylene-based.
Rough approximations give me an energy density of 950 MJ/ft^3 (perhaps more) for Toothless's blasts. While this is significantly higher than the figure for Smaug, Smaug can envelope a much larger area in flame that, based on the HTTYD canon, can hurt Toothless.
Conclusion:
Smaug is larger, smarter, more durable, has more firepower (with a much higher if not infinite shot limit), and is probably faster. Need I say more? (Maybe I should mention he's way smarter, too.)
If you disagree, comment with your reasons or contact me. Please don't if your reasoning follows one of these ideas:
"Toothless is cuter, so he'd win!" (Interestingly, those same people probably don't think I could beat Azog or a stone giant in an arm wrestling match.)
"Dude, Toothless is the good guy. He'd win because of that." (No, good guys only win because they're given bad guys they can beat. Smaug is not one of those.)
"Can't Toothless just target Smaug's weak spot?" (Fair question. However, it's not ultimately relevant. A: Smaug's weak spot of bare skin had no problem with molten gold. Gold is a great thermal conductor and thus will transfer a lot of energy to the skin. While plasma is hotter, the gold will probably transfer energy more efficiently, and also was in contact for a lot longer. B: Toothless may not be intelligent enough to figure that out. Or even get a chance to.)
"Toothless is the Alpha, so he could control Smaug, you Tolkien-biased moron!" (Toothless has never shown any sort of ability to control any sort of being other than the dragons in his own universe. Also, Smaug showed both possible magical intuition and minor mind control powers in his conversation with Bilbo, so if any mind-controlling happened, it could well be Smaug doing the controlling.)
"Toothless will beat Smaug like he did the Red Death. A simple blast down the throat will do the trick." (A: Toothless will almost certainly never even get the chance to do this, because Smaug is a huge intelligent being who is fighting back and spewing fire. B: There is no evidence that it would even work on him. His fire, according to the VFX artists who made him, is ignited in his throat already, which matches with what we see on screen—a glow in his chest before he shoots. This means that he's already got fire in his throat and chest, and since he doesn't blow up, Toothless's trick won't do a thing of importance.)
"Dutch, you're smart, but I think you're biased." (Of course I am biased—I'm human, gosh darn it. However, will you please point out how exactly I'm biased toward Smaug? I've used very generous figures for Toothless in most cases, and my low-end estimate for Smaug's armor durability is as low as I can realistically make it. I didn't even cover intelligence, in which Smaug would dominate.)
"Toothless beat the Bewilderbeast, which is about seventy feet longer than Smaug." (True. Also, Smaug still outweighs it by quite a bit, as he sank in molten gold, which requires a density far greater than that of lead! The Bewilderbeast was able to walk across a beach, while Smaug crushed buildings and sometimes rocks. This is disregarding the facts that Smaug is more intelligent than the Bewilderbeast, has greater range with his breath weapon, and can fly.)
"Why'd you use movie Smaug? I don't like the movies." (Movies are inherently easier to analyze than books, and anyway book Smaug could actually be more powerful than the movie one. Also, your personal entertainment preferences have no bearing on this debate.)
"Wow, Dutch, you wasted a lot of time on this." (The fact that I spent time on it indicates that I don't think I wasted time. This is what I like to do, and hopefully this also helps some people learn.)
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