RainbowDash has a Top speed of 123.83 MPS, or 7,610 MPH

[Meson Bolt 2,648]

I am not sure we can calculate like that. Rainbow Dash didn't fly at a static velocity. Her speed varied a lot, from low speed to supersonic, and its value depends on too many variables. but we can estimate the height of Cloudsdale by Rarity's falling. If we use finite element methods, we may be able to find the drag of rarity at one particular speed. Thus, we can get Rarity's coefficient of drag and use equation D=C*ρv^2*A/2 to estimate her drag as a function of velocity.

With  another two equations a*dx=v*dv ,  a=(G-D)/m(Rarity) , we are able to obtain the distance she fell before reaching an equilibrium point where drag is equals to her weight. 

The total distance Rarity travels is x=x(before equilibrium) + v(equilibrium)*t(after equilibrium)

The distance between Cloudsdale and ground is equals to x-x(R's initial position relative to stadium) -x(R's final position relative to ground)

As rarity's equilibrium speed should be much lower than the speed of sound, and I estimate that this velocity should actually lower than 120m/s (I assure you the actual equilibrium speed should be mush lower than that), the altitude of Cloudsdale should be no more than h= c*t=120m/s * 50s=6000m (less than 20000 feet)

if rainbow dash did travel at mach 10, she only had less than 2 seconds before she hit the ground.

 

While this theory may hold weight, I stated several times that I was solving for Rainbow Dash's AVERAGE descending speed, since we cannot exactly calculate how far she traveled between the point of her taking off (0 seconds) and the point of her Rainboom's occurrence (20.63 seconds). Therefore, when we solve for her average speed and get a value of mach 0.534 (for her average descending speed) that by looking at the times (her accelerating period was almost twice as long as the period after she performed the Rainboom), it is safe to assume that she breached Mach 1.

 

I'm actually restating stuff I already said. If you didn't read the whole theory through, I suggest you do. Seriously, I didn't think I'd have to underline every time I said "average".

Edited December 7, 2015 by Meson Bolt

[Humphrey 49]

While this theory may hold weight, I stated several times that I was solving for Rainbow Dash's AVERAGE descending speed, since we cannot exactly calculate how far she traveled between the point of her taking off (0 seconds) and the point of her Rainboom's occurrence (20.63 seconds). Therefore, when we solve for her average speed and get a value of mach 0.534 (for her average descending speed) that by looking at the times (her accelerating period was almost twice as long as the period after she performed the Rainboom), it is safe to assume that she breached Mach 1.

 

I'm actually restating stuff I already said. If you didn't read the whole theory through, I suggest you do. Seriously, I didn't think I'd have to underline every time I said "average".

Sorry, I didn't realized you were calculating RD's average velocity based on Cloudsdale's altitude...

But I still don't think its a good idea to use human bio-limit as a reference. My methods can provide a more reliable solution for Cloudsdale altitude and I think we can combine our methods together to obtain a better answer.

[Meson Bolt 2,648]

Sorry, I didn't realized you were calculating RD's average velocity based on Cloudsdale's altitude...

But I still don't think its a good idea to use human bio-limit as a reference. My methods can provide a more reliable solution for Cloudsdale altitude and I think we can combine our methods together to obtain a better answer.

 

Well just consider this -- during Equestria Girls (which IS canon, by the way), Twilight (as a pony) traversed dimensions to become humans. Despite this magical portal going unexplained, it is not unbelievable to state that ponies (in Equestria) and humans (in the Equestria Girls universe) have similar bodily functions.

 

(In addition, humans actually have a higher altitude tolerance than real-life horses, so it would stand to reason that Cloudsdale would be lower. However since we can't quantify it, we use the human value and move on)

 

Despite this, I am using Cloudsdale's theoretical maximum possible altitude. And while I highly doubt that Cloudsdale was as high up as it could possibly be, we have no other static number to compare against. My theory properly reflects the maximum possible speed Rainbow Dash could have achieved given the circumstances.

 

Also, just a heads-up, your theory requires us to assume that Equestria has the same gravity and air density as Earth, something that I tried to avoid. Admittedly I am using a similar assumption -- that Equestria's atmosphere is similar to that of Earth's, though notice I said similar, not equal to.

Edited December 7, 2015 by Meson Bolt

[Holiday Agnaktor 1,436]

Also, just a heads-up, your theory requires us to assume that Equestria has the same gravity and air density as Earth, something that I tried to avoid. Admittedly I am using a similar assumption -- that Equestria's atmosphere is similar to that of Earth's, though notice I said similar, not equal to.

Yeah, that seems to be a thing. When Rarity fell, she seemed to be falling at a constant speed, which is normal, but that speed was rather low... So perhaps the air is denser, or the gravity is lower, or a mix of both? It does explain how pegusi can maneuver without beating their wings like...something that flaps really fast. (I'm bad at those comparisons... )

[Meson Bolt 2,648]

Yeah, that seems to be a thing. When Rarity fell, she seemed to be falling at a constant speed, which is normal, but that speed was rather low... So perhaps the air is denser, or the gravity is lower, or a mix of both? It does explain how pegusi can maneuver without beating their wings like...something that flaps really fast. (I'm bad at those comparisons... )

 

I think it's generally agreed upon that Pegasi magic allows them to fly, even though their wing-to-body ratio is smaller than would normally allow for flight. That's why when Tirek took the pegasi magic, they all fell to the ground.

[Holiday Agnaktor 1,436]

I think it's generally agreed upon that Pegasi magic allows them to fly, even though their wing-to-body ratio is smaller than would normally allow for flight. That's why when Tirek took the pegasi magic, they all fell to the ground.

Aaah. I forgot about that. Thanks!

Still, Rarity falling to her doom rather slowly still counts.

...When I think about it, she would have probably survived a collision with that speed...

[Humphrey 49]

Well just consider this -- during Equestria Girls (which IS canon, by the way), Twilight (as a pony) traversed dimensions to become humans. Despite this magical portal going unexplained, it is not unbelievable to state that ponies (in Equestria) and humans (in the Equestria Girls universe) have similar bodily functions.

 

Also, just a heads-up, your theory requires us to assume that Equestria has the same gravity and air density as Earth, something that I tried to avoid.

Well, we have to assume something, if the gravity and the gaseous states of air are too much different from earth, the ponies may not evolve like this, their physiology may be nothing similar to any of the creatures on earth. At least we can assume Equestria is in a M-class planet. But if we assume the pony physiology is similar to human, the error could be so great for different species have their unique suitable habitat. Bos grunniens can live in the plateaus  from 3000m to 6100m. Some bird can even cruise at the altitude of 9000m, though restricted by their food source, they can not live that high. There are still many creatures can not endure the low gauge pressure and temperature, including most human. My mom went to  field research in Tibet plateau few years ago, she suffered acute mountain sickness in a village only with a altitude of 3500m, and has to retreat with other colleagues suffering similar symptoms. As all mammals on earth have same cellular structure, chemical composition, origin and similar skeleton, their physiology are way different with each other., so do ponies the humanoid life forms in EQG (even if the mirror can not change the body functions too much).  There are to much uncertainty  if we use human standard to measure ponies. 

[Meson Bolt 2,648]

Well, we have to assume something, if the gravity and the gaseous states of air are too much different from earth, the ponies may not evolve like this, their physiology may be nothing similar to any of the creatures on earth. At least we can assume Equestria is in a M-class planet. But if we assume the pony physiology is similar to human, the error could be so great for different species have their unique suitable habitat. Bos grunniens can live in the plateaus  from 3000m to 6100m. Some bird can even cruise at the altitude of 9000m, though restricted by their food source, they can not live that high. There are still many creatures can not endure the low gauge pressure and temperature, including most human. My mom went to  field research in Tibet plateau few years ago, she suffered acute mountain sickness in a village only with a altitude of 3500m, and has to retreat with other colleagues suffering similar symptoms. As all mammals on earth have same cellular structure, chemical composition, origin and similar skeleton, their physiology are way different with each other., so do ponies the humanoid life forms in EQG (even if the mirror can not change the body functions too much).  There are to much uncertainty  if we use human standard to measure ponies. 

 

To this I reply, do you have a better altitude?

[Humphrey 49]

To this I reply, do you have a better altitude?

Not yet, I am setting up CFD, it may take a while to get a answer with a higher resolution.

[Unlikeable Pony 2,698]

>breaks sound barrier

>Wing power is still just 16.8

[Humphrey 49]

To this I reply, do you have a better altitude?

Limited by my meshing skill and my laptop performance, I have to assume Rarity's body is a cylinder with a length of 1.5 m(5/3 times pony's height), and diameter of 0.5 m. The coefficient of drag of such geometry is about 0.18+_0.02. Assume her weight is 110+_20 kg, the equilibrium velocity should be 120+_20 m/s

Before the equilibrium, Rarity has fallen more than 5160 m, If there was no ground, she should have fallen for 51.6 s. Actually, the time duration is only 49+_1 s, the distance she traveled is only about 4800m. Rarity's initial position from the ground is only 3 times of the height of the stadium, comparing to the error in the calculation, it is negligible. Her final position can also be regarded as 0 meter from the ground. 

∴The altitude of Cloudsdale is around 4800 meter.  

[Meson Bolt 2,648]

 

Limited by my meshing skill and my laptop performance, I have to assume Rarity's body is a cylinder with a length of 1.5 m(5/3 times pony's height), and diameter of 0.5 m. The coefficient of drag of such geometry is about 0.18+_0.02. Assume her weight is 110+_20 kg, the equilibrium velocity should be 120+_20 m/s

Before the equilibrium, Rarity has fallen more than 5160 m, If there was no ground, she should have fallen for 51.6 s. Actually, the time duration is only 49+_1 s, the distance she traveled is only about 4800m. Rarity's initial position from the ground is only 3 times of the height of the stadium, comparing to the error in the calculation, it is negligible. Her final position can also be regarded as 0 meter from the ground. 

∴The altitude of Cloudsdale is around 4800 meter.  

 

Using 15,748.03 feet (4,800 meters) as the altitude of Cloudsdale, this puts Rainbow Dash's average descent speed at mach 0.44, and her average return speed at mach 2.56 -- considerably slower than previously calculated, however still undeniably faster than the speed of sound.

 

At this point I'd like to push forward a table of data that I hope you can complete. I haven't taken physics yet and as such am not familiar with problems discerning acceleration, but maybe you (or someone out there) is.

 

Distance         Rate                            Time

0 meter           mach 0                        0

Unknown         perhaps mach 1?        20.36 seconds (Rainboom)

4800 meters   Unknown                      32.03 seconds

 

Keep in mind Rainbow's average descent speed (mach 0.44).

[Fractured 2,684]

There's this... there's also the multitudes of times that Rainbow has contended with lightning as well however, from dodging it from the source in the last round-up (Notice that she reacts to the bolt first, then drops to evade it):

 

To dodging it point blank from multiple sides:

http://www.dailymotion.com/video/x17kazq_my-little-pony-friendship-is-magic-season-4-episode-1-and-2-princess-twilight-sparkle-hd_shortfilms

10:15-  ~10:40
To, in the comics, being able to maneuver up and around lightning before the bolt can extend a few meters:

To being able to weave a net around a storm cloud under similar circumstances.

 

 

Considering that natural lightning's average propagation speed 149,000 m/s, Rainbow Dash needs to be moving at least faster than mach 440 that for these feats to be possible.

[Meson Bolt 2,648]

Considering that natural lightning's average propagation speed 149,000 m/s, Rainbow Dash needs to be moving at least faster than mach 440 that for these feats to be possible.

 

That's the problem -- natural lightning. This is Equestria, where clouds can be walked on, rainbows can have their color literally sucked out by a vacuum cleaner, snowflakes are hand-made (I'm not saying hoof-made... er... dammit!), and where lightning travels much slower than normal static electricity. All of these are weather-related, and as pegasi control the weather magically, it's not too much of a stretch to imply that these natural occurrences are magic-based as well, and therefore break the laws of normal physics.

 

I know it seems like a cop-out, saying that magic is the answer, but in reality the lightning shown both in the episodes and in the comics doesn't behave like the lightning in our world.

 

Not to mention that moving at a speed of mach 440 in any atmosphere would disintegrate Dash.

Edited December 8, 2015 by Meson Bolt

[Humphrey 49]

 

 

 

 

Using 15,748.03 feet (4,800 meters) as the altitude of Cloudsdale, this puts Rainbow Dash's average descent speed at mach 0.44, and her average return speed at mach 2.56 -- considerably slower than previously calculated, however still undeniably faster than the speed of sound.

 

At this point I'd like to push forward a table of data that I hope you can complete. I haven't taken physics yet and as such am not familiar with problems discerning acceleration, but maybe you (or someone out there) is.

 

Distance         Rate                            Time

0 meter           mach 0                        0

Unknown         perhaps mach 1?        20.36 seconds (Rainboom)

4800 meters   Unknown                      32.03 seconds

 

Keep in mind Rainbow's average descent speed (mach 0.44).

 

I'm sorry, but I'm afraid it is beyond my capability. Even assume Rainbow flies with a static power, I still need to calculate the drag as a function of velocity which I can not use a single equation to approximate. The transonic flow is too difficult to me. 

[Fractured 2,684]

That's the problem -- natural lightning. This is Equestria, where clouds can be walked on, rainbows can have their color literally sucked out by a vacuum cleaner, snowflakes are hand-made (I'm not saying hoof-made... er... dammit!), and where lightning travels much slower than normal static electricity. All of these are weather-related, and as pegasi control the weather magically, it's not too much of a stretch to imply that these natural occurrences are magic-based as well, and therefore break the laws of normal physics.

 

I know it seems like a cop-out, saying that magic is the answer, but in reality the lightning shown both in the episodes and in the comics doesn't behave like the lightning in our world.

I think what you're referring to is the difference between magical occurrence and magical interaction. The difference is that the first is purely constructed of magic, whereas the second just changes how things normally work based on the former. Thus, rainbows are rainbows, until they interact on whatever magic is in the vaccuum cleaner. Frogs are frogs, until hit with a transmorgification spell, and natural lightning is natural lightning, unless interacted directly on by magic. Considering that the only stormcloud that fits that criteria above is the one that Derpy touched, (The second being from the Everfree, a place reputable for its wild and magicless nature, and the last two being a storm cloud that the gremlins just happened to live in), it doesn't make sense to immediately put the cause on magic. Unless we're assuming that everything in Equestria is magic based, whether its interacted on or not. (including previously mentioned untamed Everfree, natural animals, etc.). But then, we would need to throw physics out entirely; we'd be unable to solve anything.

 

Not to mention that moving at a speed of mach 440 in any atmosphere would disintegrate Dash.

Different universe, different biology. The same biology that would allow earth ponies to pound boulders into dust or carry around entire train cars by fours without issue, and the same biology that would allow Twilight Sparkle to magically heft several tons worth of rocks and rubble to magically fix a bridge without being crushed by the weight. Its simply how ponies work. (If you want an obvious example, look at Ash from pokemon; obviously human, by their standards, but perfectly capable of surviving being bathed in 3000+ degree flames from a Charizard. It's just a world mechanic for the "humans" there.)

[Starkiller 2]

My Bad, 123.83 is her Miles Per Minute! 2.063 is her Miles per Second!

 

From the show you can see a Mach cone forming around Rainbowdash before she does a sonic rainboom.

 

During the first stage (where it is round) she has broken the speed of sound and has created a Sonic Boom with ease. She is now going at speeds above 761 MPH, or the speed of sound.

 

Her speed increases at the cone's angle becomes lower and lower until it is an actual cone at Stage two.

Here her speed is Mach 5 and above.

 

Then the Sonic RainBoom happens in which Her speed nearly doubles to Mach ten, The sonic RainBoom is so powerful it shatters the visible light spectrum. Upon reaching Mach 10 she is going 10x the speed of sound which is 7160 MPH or 2.063 Miles per Second.

 

WHY IS SHE NOT IN THE WONDERBOLTS ALREADY!?!?!

I only did some of these calculations and the rest of the info i got off the internet such as the speed increase rate as her mach cone becomes an actual cone.

 

TL;DR: after her sonic Rainboom RainbowDash is going at Mach 10, 7,610 MPH, or 123.83 Miles Per Second this range of speed is called "High HyperSonic". RainbowDash is going at High Hyper sonic Speeds she REALLY need to be on the Wonderbolts.

 

Discuss away at how mindblown you are!

Well just to put this into perspective, as a current individual trying to get his bachelors of science in engineering the escape velocity required for any object to escape earths gravity is 25,000 mph or mach 25. At this speed one would need to be traveling 7 Miles per second to escape earths gravity. Rainbow dash can fly at mach 10 at around 7,610 MPH. At this speed one would need to be traveling at least 2.063 Miles per second. That means that Rainbow dash can reach 29% of  the escape velocity required for any object to escape the gravity of the earth. Even at this speed Rainbow dash is still faster than the worlds fastest manned aircraft the X-15 at Mach 6.72. Besides space shuttles however Rainbow dash is slightly slower than the fastest aircraft ever flown the NASA X-43 space plane at Mach 9.6. Even so at this speed Rainbow dash is traveling extraordinarily fast  without any silicate plating or Nickel Titanium Plated skin. In addition at this very high speed, Rainbow dash can maintain this speed even though the air that is flowing around her body at this speed is traveling so fast that the airflow is Chemically reacting and causing free flowing atomic oxygen to corrode material traveling at this speed.  Also the fact that she can travel at this speed without being hurt stuns me. This is mainly because at mach 10 a phenomenon known as aerodynamic heating begins become a factor in flight control. Aerodynamic heating is the heating of an object produced by its very high speed passage through air where by its kinetic energy is converted into thermal energy by skin friction on the surface of the object. The rate depends on the viscosity and speed of the air flowing around the object. So in theory going this fast unprotected would ultimately kill you because the thermal energy that you would experience due to friction would be so intense that you would actually start to cook slowly. Its sad that she inst faster than NASA's X-43 but hey maybe she will break that record within a few years.

[Meson Bolt 2,648]

 the escape velocity required for any object to escape earths gravity is 25,000 mph or mach 25.

 

Um... no, actually. Mach 1 isn't 1000 mph, it's more around 761 mph. Therefore, mach 25 is 19182 mph, not 25000 mph. If Rainbow Dash could indeed travel at a speed of mach 10 (which I actually highly doubt), that means she travels at 7673 mph, or 30.44% of Earth's escape velocity.

 

Secondly, comparing Rainbow Dash's speed to NASA's aircraft's speed is completely unreasonable, since Rainbow Dash was travelling down for both rainbooms, with gravity's aid, and NASA's aircraft fly upwards, against gravity.

 

In fact, since the Royal Princesses "raise and lower" the Equestrian sun and moon (and since the moon is never shown to be up in the daytime), we're almost certain that the planet MLP takes place on isn't Earth (since our moon is sometimes visible at day). This means that the planet has different air density, different gravity, etc.

 

So, in conclusion...

 

as a current individual trying to get his bachelors of science in engineering

 

...Good luck with that.

[Starkiller 2]

It should be made known that all of these calculations and comparisons are based on the planet earth and that the gravitational force may be different than that of earth but the principles involving the escape velocity as well as all the hazards it poses are still present. But i still appreciate your input though

Edited October 26, 2016 by Starkiller

[cider float 2,538]

Wonderbolts seem to be about team coordination and having different skills. It's not clear that Rainbow Dash can fully control herself while flying at top speed and when she is coordinating with the team she can't be flying at top speed.

[Starkiller 2]

Its like they say as you go faster the harder you become to control.

[EmeraldStar04 250]

She wasn't in the Wonderbolts on day 1 because she was too fast and she made the other Wonderbolts look bad. Spitfire needed time to train the new ponies and replace the old ponies.

[Humphrey 49]

I just did more researches and find out a common mistake and this mistake makes most people believes that rainbow dash travels really fast while actully her speed is not that impressive. The Mach cone is transparent not neccessarily invisible though, The white cloud we can see is called the Vapor cone, which is actually not the same as the mach cone. It is possible that they are in the same shape, yet they can be quite different. The vapor cone is basically the shape inside the surface where air is cooled down and the the water vapor forms clouds. According to some CFD simulation done with FLUENT 17.2, Rainbow dash might only fly at the speed of the sound or slightly higher.

[Meson Bolt 2,648]

I just did more researches and find out a common mistake and this mistake makes most people believes that rainbow dash travels really fast while actully her speed is not that impressive. The Mach cone is transparent not neccessarily invisible though, The white cloud we can see is called the Vapor cone, which is actually not the same as the mach cone. It is possible that they are in the same shape, yet they can be quite different. The vapor cone is basically the shape inside the surface where air is cooled down and the the water vapor forms clouds. According to some CFD simulation done with FLUENT 17.2, Rainbow dash might only fly at the speed of the sound or slightly higher.

 

Again, I reiterate this point:

 

The mach cone animation does not accurately reflect Rainbow Dash's speed (since travelling at mach 10 would make Cloudsdale more than 60 miles above the surface, and any casual observation proves that wrong).

 

And again I reiterate this point:

 

Regardless of how fast RD traveled downwards, she traveled nearly 5.88 times as fast upwards. We know this because she traveled the same distance (Cloudsdale stadium to ground, ground to Cloudsdale stadium), but her downward trek took her 32.03 seconds, and her upward one 5.45 seconds.

 

Crazy, I know. Go re-watch the episode if you doubt me.

Edited December 19, 2016 by Meson Bolt

[Humphrey 49]

Regardless of how fast RD traveled downwards, she traveled nearly 5.88 times as fast upwards. We know this because she traveled the same distance (Cloudsdale stadium to ground, ground to Cloudsdale stadium), but her downward trek took her 32.03 seconds, and her upward one 5.45 seconds.

 

I don't think those scenes are continues, since when Rainbowdash flying around the stadium, she travels only (12+1/2)*pi/2=19.6 inches on my screen while her length is 7/16 inches in 0.9s. Assuming when flying, a pony's length is 250/210 times pony standing height

She only flied 26 pony heights in one sec, unless ponies aresuper huge, her speed at that time is lower than standard speed of sound.

 

 

She only flied 26 pony heights in one sec, unless ponies aresuper huge, her speed at that time is lower than standard speed of sound.

 

Rainbow dash does not slow down when she travels around the stadium and it is illogical for her to do so. Thus I believe she actually travels at similar or same speed when she is flying up. Even if we assume pony's height is 1.2m, her speed is only 31.2 m/s, considering the temperature might be low (-20 C, 253K) , Even the air in equestria is pure SCl4(sulfer tetrachloride, sound travels only around 115m/s in it), her speed is still less than  Mach 1.