The Return of the Sonic Rainboom Unraveled: the Second Coming · 8:21pm Apr 5th, 2013

Recently, someone on this very website posted a thread about calculating pony feats. In it, he calculated that in order to make the 90 degree turn to avoid the ground at the end of the original Sonic Rainboom feat, Rainbow would have had to withstand an acceleration of almost 5.9k Gs, thus concluding that Rainbow Dash must have a durability at least comparable to modern steel alloys. Well, you may recall that last year I posted a certain blog describing my adventures exploring the Sonic Rainboom feat and detailing the follies of attempting to calculate values for a feat when it lacks consistency. So, because I had that available to me, I decided to post the link to it in the thread to expose the silliness of his calculation and to warn others of blindly accepting it as credible, since it is also an example of a inappropriate generalization fallacy.

I then pointed out that the feat he described was not only a durability feat, but also a strength feat (AKA, the torque required to oppose forward inertia while plummeting at mach 1.0+) and that in The Last Roundup, where Derpy spoke her first and last words (RIP, Derps), Rainbow Dash proved to be not in the slightest capable of slowing the fall of a wooden support beam whilst flying, a burden that I calculated could only have been ~600-700 kg (~1325-1545 lbs) at the most... this is provided that the building was actually made of wood and plaster, and not inexplicable building materials like lead, tungsten, depleted uranium, and unobtanium. This vast disparity between this obvious feat and his earlier Rainboom feat calculation exposes a huge contradiction, casting serious doubt upon the credibility of both calculations (mostly onto his, since it is the more complex and requires the most assumptions).

Long story short, OP then proceeded to take exception to this and got... uppity about it, and attempted to brush aside the issue of internal consistency by attacking with sophistic and fallacious arguments. In the end, I grew tired of his vitriolic attitude and just decided to walk away from the thread, washing my hands of him; I'd already made my point, and it was abundantly clear to me that he was unwilling to even bother himself with considering my argument.

———No, I am not planning on providing the link to the thread in question in this blog... but if you really must read it, just PM me a request and I'll send you the link. Really, it's just a mess though, and I'm glad I bowed out when I did, because it seems it has only gotten worse since then.

The reason I am writing about this now is that he pointed to a mistake I made in my original blog as being evidence that my logic was faulty, so I am going to attempt to correct that mistake now, just to 'humor' him.

...Actually, I'm doing this because I want to demonstrate to you all that the particular mistake I made is ultimately completely irrelevant, because it does not in any way change the conclusion of my argument, making his accusation an ignoratio elenchi.

Now, I am aware that this is not going to be accurate, and is based off of a lot of assumptions. But I'm doing the best with what little concrete data I actually have. If you aren't satisfied with this, I would like to see you attempt to do better.

———No really, I'm serious. I would honestly be legitimately interested in seeing what it is you could manage to come up with. If you think you can do better than this attempt, please do so.

The particular mistake I made is assuming that using the terminal velocity of a human would suffice for a Pony. However, this is actually incorrect; and I actually knew of that before hand, but I did not bother to attempt to calculate "accurate" values for Pony ballistics because that's obviously going to be impossible. But he was correct; the drag coefficient be different, and thus the terminal velocity would be too.

However, there is no true rule of thumb for finding coefficients of drag (Cd), certainly none that would be universally applicable to geometric shapes as extremely complex and variable as organisms like humans and Ponies. In all truth, if you wanted to know the Cd of a Pony, you would need to physically measure it using something like a wind tunnel. The Cd of a human in upright position (or in this case, face-down free-fall position) is commonly stated as ~1.0-1.3, while the Cd of a house cat (notable for the innate ability to survive falls from heights that would injure or kill other animals of comparable size) is supposedly ~1.2-1.5.

For the sake of simplicity—and because of a distinctive lack of access to Ponies, Equestria, wind tunnels, and sophisticated measurement devices with which I could properly perform the drag coefficient measurements myself—for this calculation I am just going to assume that, based off of the two examples above, the Cd of the average Pony should fall somewhere between ~1.1-1.4.

With this now in mind, the [generalized] terminal velocity of a Pony falling in either belly-down or back-down positions (also blithely assuming a mass of ~35 kg and cross-sectional area of ~0.35 m²) should be in the order of ~120-140 km/h (75-87 mph). By comparison, the terminal velocity of a human skydiver in a face-down free-fall position is ~190-210 km/h (118-130 mph), which is roughly 35-75% faster (~54% average). This is a significant difference from my previous analysis, where I did not bother to determine a possible terminal velocity for the average Pony, and just used the human values... since it doesn't make a single GODDAMNED difference in the end, proving that he either completely missed the point of the argument (unlikely, given I clearly stated the purpose, in huge bolded letters, at the top of the page) or that he just decided to purposefully ignore it (BINGO! We have a winner, folks!).

As this screenshot of this specific part of the Sonic Rainboom episode clearly shows us, in the time it took for Rarity to fall the distance of ~180 pixels, Rainbow Dash covered ~270 pixels.

270 ÷ 180 = 1.5

The only logical conclusion is that Rainbow Dash is literally only traveling half-again faster than Rarity in this scene, which according to our terminal velocity value above means her Rainboom velocity would be around ~180-210 km/h (75-87 mph), which is a laughably pathetic "supersonic" speed of Mach 0.15-0.17.

And even were I to substitute the OP's "fairly reasonable estimate" of ~125 kg (275 lbs) for a Pony, based off of the mass of a small Shetland pony (which—by the way—completely ignores the obvious observation of MLP Ponies possessing completely different anatomy compared to real equines, a factor I actually tried to account for in my own size and mass estimates), the terminal velocity becomes ~230-260 km/h (143-161 mph), and still means Rainbow Dash would only be flying at ~345-390 km/h (214-242 mph), a still feebly slow Mach 0.28-0.32.

EDIT: Actually, I believe I made a slight mistake in the pixel measuring, likely due to a mix-up while popping back and forth between windows to reference the source video. I believe I got confused and measured the blue line using different reference points at each end (using both the top and bottom ponies in the falling group) rather than using only one point, resulting in a line that was longer than it should be. Having estimated the extent of the error, I believe that Rainbow Dash is actually moving ~2.25 times faster than Rarity, which more closely matches my original figure. The first version (35 kg) becomes ~270-315 km/h (Mach 0.22-0.26). The second version (125 kg) becomes ~517.5-585 km/h (Mach 0.42-0.48).
—But, even with these new results, the conclusion still hasn't changed one bit.

Clearly, this scene is not reliable enough to use for feat calculation, as it is contradicted by its own internal inconsistency and incongruity with both earlier and later scenes. This feat is thus an outlier, and using it in calculations like the ones from the thread I described above will result in dubious to outright fallacious claims regarding the abilities of the characters involved. In other words, don't be that guy.

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Karna

Karna #1 · Apr 5th, 2013 · 3 · ·

Pony wank is always the most hilarious fanwank. I always get laughs off of people trying to use toon physics to calculate how "strong" animated characters are.

The thing is, MLP seems to be the only show where people take toon physics feats to legitimately claim things like, "[Pony's] could defeat a Warhammer 40k Space Marine in hand-to-hoof combat", and then try to defend such things. For pretty much every other show out there that involves toon physics, people seem to be able to understand that toon physics feats are about as consistent as Pinkie Pie.

Not so for the nutty FiM fans.

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The Return of the Sonic Rainboom Unraveled: the Second Coming · 8:21pm Apr 5th, 2013

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