Ah the Sonic Rainboom. A topic that has, dare I say, caused more than a couple tons of discussion in the fandom? After all, who doesn't want to fly at speeds of Mach 10 or higher? Seriously, that would be -- if you don't count the G-forces that go with that maneuver -- pretty flippin' awesome.
I've looked at the Mach 10 theory, and I have to say, I'm impressed with the math. It's not your everyday brony physicist who can deduce the speed of a flying magical pony by the angle of a mach cone. But here's something I'd like to pitch -- what if we've all been focusing on the wrong thing? We've all been looking at the animation -- the sonic boom, the mach cone, etc., when we really have no proof that the animation is 100% accurate.
Here's something that I think the fandom's been overlooking, and it's really quite simple. The distance Rainbow Dash flew to get to the ground is equivalent (give or take a few hundred feet) to the altitude of Cloudsdale. Now since we know Cloudsdale is a mobile cloud platform we can't get a solid number, but we certainly know that Dash didn't travel at Mach 10.
The formula I'm going to be using for this calculation is a very simple one -- the distance formula.
Distance (Cloudsdale's altitude) = Rate (RD's speed) x Time (How long it took her to reach the ground)
This formula (which is so simple and clear-cut that almost any 5th grader can understand it) states that the distance Rainbow flew (in this case, the altitude of Cloudsdale) would be equivalent to the speed of the traveler (her speed) multiplied by the time it took her to reach the ground.
From the moment Rainbow Dash took off after that iconic "Hold on, Rarity!", the time it took for her to reach the ground was 32.03 seconds (I timed her five times and took the average). Plugging in this number, we now have:
Cloudsdale's altitude = RD's speed x 32.03 seconds
But if we're to solve for speed, we're gonna need Cloudsdale's altitude. But just for bleeps and giggles, let's see how high up Cloudsdale would be if RD were travelling at Mach 10, shall we?
Cloudsdale's altitude =11253.30 feet/second x 32.03 seconds
Cloudsdale's altitude = 360443.199 feet (68.27 miles, or 109.86 km)
(I realize this calculation is not 100% accurate, since I used Mach 10 as a speed for the entirety of the flight (32.03 seconds), not just for the 11.67 seconds after the Rainboom occurred. However the conclusion reached would still be an enormously large number that would be just as unbelievable and easily serve the same purpose)
Any casual observation of Cloudsdale easily disproves this theory, I mean just look at it, it can't possibly be 68 miles above the ground! At that altitude, the ponies wouldn't be able to breathe due to the lack of oxygen. They'd also suffer from severe sunburn and skin cancer, since at that altitude the ozone layer doesn't block ultraviolet rays of the sun. And finally, if a pony that was somehow acclimatized to that climate were to travel from Cloudsdale to the ground, as we see in the episode, she would die due to an overdose of oxygen.
So, Mach 10 theory. Cool for one pony, not so hot for the rest of Cloudsdale, eh? So, what do we do now? Well we look for Cloudsdale's maximum altitude.
Consider this -- if Cloudsdale is a mobile weather platform, it must have some sort of altitude limit, right? I mean, how far up can you go until the ponies run out of air? What is the maximum tolerable altitude for Cloudsdale?
Well, sadly Wikipedia doesn't have an article for the "maximum tolerable altitude for flying magical ponies in a kid's cartoon", but I was able to find the maximum tolerable altitude for humans. According to the article, it states that human beings have survived for two years at an altitude of 5.95 km, or 19,250 feet. And although I know this isn't exactly accurate to the ponies, I can't do any better. I mean seriously, what do you want from me?
I could just plug in the numbers and say 'voila!', but while conducting this theory I did notice something. Since it's impossible to judge the distance traveled between the time that she took off and the moment when her Rainboom occurred,calculations from this point on will be for the average speed of her entire descending flight. Sorry, I'm just not about to go into a 6-day research-fest to find out the exact speed of a pastel-colored pegasus. I may love ya Dashie, but not that much. Sorry.
Now, with that little disclaimer out of the way, number-plug-in-time!
Cloudsdale'ssupposed maximum altitude (19,250 feet) = Rainbow Dash's speed x 32.03 seconds (again, solving for average speed)
19,250 feet/32.03 seconds = Rainbow Dash's speed
Rainbow Dash's speed = 600.9991 feet per second (409.7721 miles per hour, or mach0.534)
Again, this is her AVERAGE speed for her descending flight. During her acceleration period, which lasted almost twice as long as the period after the Rainboom, she was still gaining speed, so she could have broken the sound barrier. I firmly believe that at the moment of the Sonic Rainboom, she breached mach 1, and due to her natural tendency to leave rainbows in her wake (check the intro yo), the rainbows mixed with the sonic boom, creating what is known as a Sonic Rainboom.
Now before you go all butthurt rage on me, listen up. Rainbow Dash may have only breached Mach 1 during her first run, but something that I found interesting was the fact that she never stopped accelerating. How do we know? Well, surprisingly, her return speed to Cloudsdale is incredibly faster than her descending speed.
That's right. During her return to Cloudsdale, she clocks in at a mind-blowing 5.45 seconds, less than a fifth of her descent speed! Plugging this new information into our distance formula, we get this.
19,250 feet = Rainbow Dash's speed x 5.45 seconds
Rainbow Dash's speed = 3,532.11 feet per second (2408.26 miles per hour, or mach 3.14)
Mind you, that's her average return speed. As a rough estimate, she could have easily breached Mach 4, and possibly higher if she had time to build up speed.
Although we cannot conclusively quantify Rainbow Dash's top speed, we know based on the distance formula that her first Sonic Rainboom was indeed a breach of the sound barrier. We can also deduce that, based on her quick acceleration from mach 1 to mach 3.14, it is plausible to theorize that her top speed is above this, perhaps even mach 10.
So this question arises: if Rainbow Dash could fly at much higher speeds than mach 1, why did she take so long descending when she knew Rarity's life was in the balance?
Here's my theory -- Rainbow Dash knows that she's impossibly fast compared to the average pegasus. With this power, she could have easily raced down and caught Rarity before she was even near the ground. But she also knows that, at high speeds, she might not have as much control as she would normally flying. Taking this into account, she slowly descends towards Rarity, moving at just the right speed to catch her and the Wonderbolts, and still have enough time to level out. Once she had them, there was no reason to prolong the flight, so she made the return trip back as quick as possible, but only once she was sure they were safe.
Rainbow Dash is like Superman in this sense. She knows she's fast, but if she had abandoned all pretense and raced down to save Rarity at top speed, she might not have had enough control to level out, and they would both die. Although I very much dislike some of Rainbow's character flaws, I think we all can greatly appreciate this aspect of self-control. When her friends' lives are at stake, she doesn't rush recklessly into the situation without a plan. Granted, the plan may not always be good, but it's better to have at least a semi-cautious savior than a bumbling idiot.
And in my opinion, anypony who has enough self-control to consciously subdue her full potential in order to ensure the well-being of her friend is more than worthy of the Element of Loyalty.
...Welp, now I'm tired, so I'mma head off to bed. G'night everypony, and stay frosty!
Edited by Meson Bolt