Physics from a Non-Brony: The Sonic Rainboom unraveled

[size=+2]The intent of this thread is not an attempt to convince you Rainbow Dash is subsonic; the purpose is to convince you that the entire "Sonic Rainboom" scene is far too inconsistent to consider applying real-world logic to in hopes of tote concrete values.[/size]

Hello there, Bronies. As the title suggests, I am not a Brony. Don't ask why I'm here, as I'm not quite sure why I felt the need to post this. The fact of the matter is: I am. While I enjoy some of the fan-created works on Youtube and such, I don't really think the show itself is anything special. I sincerely hope that doesn't cloud your judgment on what I'm about to share with you.

Although I can hardly call myself anything even close to an "expert" concerning any material MLP-related, I do have a tendency to take notice of things that most people don't notice, especially the parts relating to logic and the sciences. And I've noticed from the little bit of MLP that I do know of that, as expected from a children's cartoon setting, it's not very consistent. That is, it prioritizes the episodic story content over the over-arcing continuity. This isn't necessarily a bad thing, as one would prefer good plot to a consistent setting, but this makes it hard to make generalized conclusions of the setting. Especially in the fields of physics; obviously, the show has more than a passing resemblance to Loony Toons in terms of the physics.

For example: once, a good while ago, I was brought into a little debate, as a trusted source of information by someone I happened to know, over the matter of who was faster: Rainbow Dash or Sonic the Hedgehog? I'm a fan of neither of them, so I was considered a rather fair arbiter.

Now, I know from past experience that 'canon Sonic' (games only) has a casual run at over the speed of sound at sea level (Mach 1.0+; 340.3+ m/s; ~761+ mi/hr) and is capable of reaching over hypersonic speed (Mach 5.0+; 1.7+ km/s; 1.06+ mi/s), especially in recent games (the Sonic Adventure DX manual even states "he's the world's fastest, hypersonic hedgehog"). "Light Speed Attack" and "Light Speed Dash" are directly stated, in-game by at least two characters, to be literally "light-speed"; which would make his max speed as fast as light traveling through air at 1 STP (Mach ~880,764.5; ~299,704.65 km/s; ~186,227.8 mi/s). Furthermore, "Super Sonic" would be considered capable of "faster than light" movement thanks to having "Chaos Control" (limited time manipulation), and his normal movement speed is stated to be "speed of light" (and I still don't have reason to believe this is hyperbole); and from what I've gathered through evidence, he would have to be at least mid-to-high 'relativistic speed' anyways ('relativistic speed' is somewhere over 10% of light speed: mid-level would be 40-60%) in order to perform many of the feats from the games as Super Sonic. SEGA has also stated in the past during the 2D age that they literally couldn't code Sonic moving at supersonic speeds in real time because of (still WIP) hardware limitations, and because the human visual processing and reaction time would be unable to keep up, thus making it nearly impossible to navigate levels; therefore, Sonic is normally moving much faster than he appears to in the games, but is held back by inadequate hardware and slow human brains. There were numerous examples of confirmed high-speed supersonic feats for the Blue Rodent that I already had access to;

Spoiler: ...such as this example here from "Sonic Unleashed"

[youtube]JVcKhKCALCg[/youtube]

1. First checkpoint: 699 m/s (Mach 2.05)
2. Second checkpoint: 1939 m/s (Mach 5.70)
3. Third checkpoint: 674 m/s (Mach 1.98)
4. Fourth checkpoint: 820 m/s (Mach 2.41)
5. Fifth checkpoint: 1245 m/s (Mach 3.66)
6. Sixth checkpoint: 729 m/s (Mach 2.14)
7. Last checkpoint: 600 m/s (Mach 1.76)
8. Average Speed: 958 m/s (Mach 2.82)

...but at that time, I still didn't know anything about Rainbow Dash.

Many people arguing the on the Rainbow Dash side were saying things like "she's over Mach 5.0/Mach 10" or "she broke the light barrier, so she's light-speed/FTL". But none of it seemed to be very well based in solid proof, and most of it was riding on the evidence collected by that one "Physics Brony" on Youtube who calculated Dash's speed during her first "Sonic Rainboom" by measuring the shock cone vertex ('Mach angle') using the formula "sin(Θ) = c(relative velocity of sound)/v(velocity of object)", as seen in this video.

Now, personally, I would have preferred to use the formula "μ = sin⁻¹(1/[Mach number])", but that isn't the point here. No, the point is that he used the "Mach cone" Dash produced when accelerating. Now, normally I wouldn't have a problem with this sort of logic, but given the fact that this series isn't especially known for following the logical boundaries of physics (quite the opposite, it seems), his use of a "Mach cone" shown to figure Dash's speed seems to be of suspect reliability. In fact, I'm rather certain myself that the "Mach cone" Dash produces in this scene was only added because someone in the design process looked up images of supersonic flight, saw a vapor cone, thought it "looked cool" (AKA, Rule of Cool), and that no real thought was given to the actual physics of the phenomenon (as evidenced by the fact that it doesn't even follow the laws of aerodynamics in the scene). Also, since "velocity" is literally "distance traveled over time elapsed", measuring it by examining "distance traveled over time" will ALWAYS be the most reliable method, and will trump anything like a "Mach angle" calculation, every time. So, with that in mind, I set out to figure out the best way to calculate her velocity myself, gathering the evidence myself using the "Sonic Rainboom" scene, as seen in this video.

Unfortunately, there is a certain "content over consistency" problem that reared its ugly head multiple times. The visual perspective in that whole scene is rather inconsistent, so most of the scene couldn't be used to accurately gauge a reliable distances. For example, I considered the fact that the starting point (the coliseum-like area housing the audience) appeared to be located within a cloud layer that seemed to primarily have a similar structure to the cotton-like, low-to-middle moderate vertical altitude family D1 Cumulus-genus clouds, such as the sunny day Cumulus humilis (base height as low as 500 meters up to almost 2000 meters, and cloud-top height of 3000 meters, up towards 6000 meters when out at seas); possibly even the globular, middle-to-high altitude family B Altocumulus-genus clouds higher up in the sky, such as the tower-like Altocumulus castellanus (base height as low as 2000 meters up to almost 6000 meters, and cloud-top height as high as 9000 meters); however, since the depiction of the clouds is inconsistent (as expected, I've seen more than one clip of Rainbow Dash manipulating small cumulus-like clouds at an absurdly low altitude of a mere 10+ meters, among numerous other inconsistencies I won't list here), I decided not to make any distance conclusions involving the cloud heights, seeing as that information couldn't be trusted.

Likewise, the overall time lapse in the scene doesn't seem to be consistent; which is, as I'm sure you've all realized, rather common in fictional television and movie settings, used at certain parts of scenes to "stretch them out" in order to make it more dramatic, allow for narrative, or various other purposes. This means that I could only use consistent scene parts where there was no observable change to the perspective (such as "camera angle/position") in order to ensure that the conclusions I made would be as accurate as possible... at least for a generalization.

Something I knew for certain was Rarity's (and the three unnamed fliers) downward acceleration, and using that I could estimate her terminal velocity. Assuming the standard gravity of whatever planet Equestria happens to be on (as it turns out "Equestria" is a kingdom and not a planet, I will call it the "MLPlanet") is close to ~9.81 m/s² (~32.17 ft/s²) — and I still have no real reason to believe it isn't so — the terminal velocity of a human in a un-streamlined posture would be ~52-56 m/s (~116-125 mph), but in a "bullet-like" streamlined posture can reach up towards ~90 m/s (~201 mph); since the body structure of a pony is generally similar to a human's (torso, head, four limbs), these numbers should suffice for this analysis. And given that Rarity is flailing like a madwoman, I'd say she wouldn't be streamlined, so ~54 m/s (~120 mph) sounds right, so for the purpose of this example we'll assume that is Rarity's final velocity.

Now, if you stop the Youtube clip of the Sonic Rainboom I posted at almost exactly 1:26 (just before you can see Dash in the scene), we can clearly see the the four falling ponies about in the middle of the screen. Using the rules of perspective (as well as experience and common sense), I would have to say that they are ~100 meters (~109 yards) away from the viewers' perspective, judging by their relative size versus the size of the large and noticeable blue tree that appears to be just as far away from the viewer as the ponies. Thus, this would place Rarity and the other falling ponies at an altitude of ~50 meters (~54.7 yards) at that instant, nearly the height of Niagara Falls. In the next frame we see Dash come flying in from the top of the screen; I don't even need to do any calculations at all to tell you that if Rarity is ~50 meters off the ground when in the middle of the screen, Rainbow Dash would be a little bit more than ~100 meters off the ground when at the top of the screen. Over the span of this scene Dash makes it to the center of the screen, so she should be slightly more than ~50 meters off the ground, while Rarity and the others should be ~25 meters off the ground. So, a relative distance within the scene can been established.

Now, at 1:28-1:29 we see something similar to that scene, only from a perspective that is low to the ground (~1 meter) and at a Dutch angle. Thanks to the reference of the blue tree, we see that Rarity and the others are still ~25 meters off the ground (meaning the scene from Dash's perspective at 1:27 didn't actually happen in a scene-consistent time frame, as no observable distance was gained during it), and Dash is a little less than that distance from Rarity and the other ponies, meaning she is ~50 meters off the ground. In the time it takes Rarity and the other ponies to fall ~24 meters (~1 meter less than their altitude), Dash manages to cover almost ~50 meters.

Now, if Rarity and the others are falling at terminal velocity — which, if you remember, for this example we're assuming to be ~54 m/s (~120 mph), which is very reasonable — that calculates to the conclusion that Rainbow Dash (at least within the context of this single scene) is only traveling a little in excess of ~108 m/s (~242 mph), almost a third the speed of sound (just over Mach 0.317).

This is certainly a very stark contrast with the more... outspoken MLP fanboys' claims of Rainbow Dash clearly being "Mach 5/Mach 10" or even "Light-speed" and faster (I never considered that opinion to be even a remote possibility), isn't it? I'm sure many of you are thinking "no, you're wrong [Temporary Name], Rainbow Dash couldn't be this slow, it's impossible!" But I implore you to examine the evidence again and attempt to find a flaw in my logic; it wouldn't even matter if you were to discover something like that I botched the calculation of the actual distances involved, since it's still quite clear that Rainbow Dash is only flying twice as fast as ponies falling due to gravity in these particular parts of the scene. Now, the only other real possible way that I can think of to debunk my conclusion is to boldly make the claim that the laws of aerodynamics and/or gravitation of "MLPlanet" are somehow vastly different in an observable way, so that the terminal velocity of a falling pony would be closer to ~170 m/s (~380 mph), or whatever velocity they needed to support their particular position. However, this is quite a tall order to fill, since just claiming that the aerodynamics/gravitation are vastly different doesn't prove that they are in fact vastly different, and since there is no clear evidence to support such claims, it doesn't hold up and must be discarded for the simpler explanation of assuming the they are the same or at least similar to what we are used to.

Somewhat understandably, my original conclusion was met with considerable disbelief and baseless denials from fanboys, while others (rightfully, to be honest) criticized me because I didn't examine more than one source of Rainbow Dash's feats, and thus my conclusion was an inadequate generalization. So, I amended my original conclusion by saying that, judging by the name and nature of the "Sonic Rainboom", I seriously believed that the creators most likely intended for Rainbow Dash to be able to reach transonic speeds (Mach 0.8-1.2), and that I'd respectfully accept that assumed intention as being canon. However, I also warned that attempting to judge her velocity by such methods as "Mach angle" would be both dubious and futile due to the overall inconsistency of the show.

In conclusion: ...Sonic won quite handily. You my condolences, Rainbow Dash fans. It couldn't be avoided, he's just obviously the faster of the two blue speedsters given all the evidence. You're free to disregard what I've posted here and continue believing her to be the faster of the two. Just don't expect that to hold up in an actual match.

tl;dr — The intent of this thread is not an attempt to convince you Rainbow Dash is subsonic; the purpose is to convince you that the entire "Sonic Rainboom" scene is far too inconsistent to consider applying real-world logic to in hopes of tote concrete values. I am not a Brony. Measuring a "Mach Angle" to determine velocity isn't remotely reliable when the physics of aerodynamics aren't even considered by the creators of the show. By measuring Rainbow Dash's velocity using literal "distance over time", it was determined that she was vastly slower (~108 m/s, Mach 0.317) than the previously calculated velocity (~1633 m/s, Mach ~4.8), being only twice as fast as the falling Rarity. However, I conceded that the creators likely intended for her to be capable of reaching velocities close to the speed of sound, so I accepted that as the assumed canon. Also, Sonic is much faster than Rainbow Dash.

EDIT: For those wondering what the "rainboom" part was all about, and thinking it was "magic" or "breaking the light spectrum" or something silly like that... well, traveling at transonic-supersonic speed has a tendency to generate something called a vapor cone, which is the literally visual aspect of the "Mach cone" referenced in this message. Since it's made of water vapor, and a rainbow is produced by prismatic refraction of light within droplets of moisture in the air, it is possible for real vapor cones to produce rainbows, as seen here.
See? There is a simple, logical explanation for it after all!

 

I did concede that

There is also the fact that if we were to assume that Rainbow Dash were to be traveling Mach >1.0 (>340 m/s) and yet we can see her travel only twice as fast as Rarity, it would, as I mentioned previously, mean that you were assuming Rarity to be falling at Mach ~0.5 (170 m/s), which would be troublesome if you were attempting to logically prove Rainbow Dash's speed was Mach >1.0, since it would cause all sorts of problems, since a pony would not fall that fast due to gravity.

...Well, there was Joseph Kittinger, who holds the record for the highest, fastest, and longest skydive as a part of Project Excelsior, jumping from a height greater than 31 km (which is somewhere in the middle of the Stratosphere), which is comparable to the altitude weather balloons reach. He had a free-fall velocity of about 274 m/s (Mach 0.807, 614 mph). Of course, the atmospheric pressure up there would be a meager 4.788 Pascals, compared to the 318 Pascals at 3000 meters (mid-cloud levels), so it's no wonder he'd have almost negligible drag. I actually met him once, only a few years ago. Jumping from that kind of height, especially back then when they actually didn't even know what would happen to someone who jumped from that height (this was pre-spaceflight, so the aerospace physics were still infantile) would have been just as dangerous as facing any enemy soldier in battle. In fact, he almost died two times attempting the jump. Guy's a real hero, if you ask me.

However, the point of my work here was actually to point out that MLP is far too inconsistent to make generalized conclusions using physics.

...And yes, the Flash is much faster. He's effectively infinitely faster than light, with no set limit to how fast he can move, and can even gain a limited omnipresence. But, come on, it's DC comics! You should always expect absurd things from them and Marvel!

 

"MLPlanet" follows the physics of "episodic plot convenience". That is: they ask "does it somehow benefit or hinder the overall plot of the episode?" and if the answer is "not really" they say "then don't worry about it, stupid, and get back to work".

 

That's fine. I don't like Pinkie Pie anyways. She's like an annoying child who won't shut up.

INB4 Pinkie Pie fanboys gang up on me in the streets.

 

...Using the data calculated by the "Physics Brony" I mentioned before, who used a dubious method of calculating the velocity of the pegasus pony that I just logically debunked as being credible in this context. Read the "tl;dr" at the bottom of my original post.

They also failed to take Starscream's real speed into account: he's far faster than a real F-15 (because he's not a real F-15, he's a super-advanced futuristic synthetic lifeform that transforms into the shape of an F-15) according to actual in-series feats, above hypersonic speeds. He's also got the durability of an entire town-sized settlement, effectively, also according to in-series feats. I know that the wiki says "according to his technical specifications, he can reach speeds up to Mach 2.8". But that's from a databook, not from the actual series, and is thus considered secondary canon to the actual feats in the series.

Realistically speaking, he'd beat Rainbow Dash pretty readily, sad to say.

 

Thank you! I'm glad this was interesting to you! I means I'm not wasting my time sharing it!

...And here I was expecting a much more argumentative response from this group, like the responses I got from the original posting of this information months ago. Looks like I assumed too much, my apologies. Must of just been that group were rabid fanboys.

Cirrus-type clouds did not match the clouds in the Sonic Rainboom scene, which were iconic "puffy cotton" clouds: main cumulus-type clouds. Cirrocumulus look like pulled or shredded cotton in spotty patches, so they were never considered.

 

I wasn't aware Rainbow Dash could use magic.

Excuse me if I'm misinformed, because I'm not a fan of the show and am this relatively ignorant to it in comparison, but aren't the unicorns the ones that use magic while the pegasii can just fly and somehow manipulate weather?

And, I see we now have what seems to be a programming-enthusiast among us as well. This thread seems to be slowly drawing in people of diverse paths, isn't it?

Also, I'm thinking about finding a larger MLP-related forum to re-post this on. What do you all think? Any suggestions?

 

Considering that one needs something akin to either a brayton cycle or rocket propulsion to reach supersonic speeds in real life... you're probably right. Just flapping wings against the air won't cut it, due to Newton's third law... among other fluid dynamics laws and etc. that I won't take the time to bother posting, because screw that, it's too much work.

Also, this image I just found on "My Little Brony" is an interesting set of calculations that are similar but more complex than what I've done here. However, while some of it is similar to what I calculated, I have to disagree with it on two parts:

• "Rarity takes 46 seconds to fall to the ground, thus the altitude of Cloudsdale is 2530 meters": False. The time scale for the entire scene is obviously inconsistent and cannot be accurately calculated, and thus the time it takes her to fall is inconclusive. I'll elaborate on that more in the second reason.

• "Rainbow Dash's Mach angle is 21 degrees which means she's moving Mach 5.487 (1.867 km/s): Very false. On top of the fact that I've already made it clear that measuring her Mach cone is a foolish idea, if Dash was moving at Mach 5.487 she'd cover 2530 meters in ~1.35 seconds, and would put the calculated fall time of Rarity into question as the numbers would not match in both cases. This is obviously not how it happened.

Bronies, this is an example of how knowing some information but not actually comprehending it can be dangerous. The simplest working explanation is always better than one that is complicated and makes too many assumptions.