Saw this weeks ago on Reddit. Still quite mind-bogglingly awesome nonetheless.
but what about the allmighty princess luna!? D:
My Brain......is full of fuck...
I read all of that, and understood it. I'm frightened, my education seems to be teaching me things.Also who needs Physics? Apparently not Rainbow Dash.
I suppose that in addition to allowing them to fly and manipulate clouds, Pegasus magic creates a naturally occuring inertial dampening field around the pegasus. It is this field that allows them to pull these otherwise suicidal maneuvers without their internal organs turning into so much paste.
@SandmanThat or their bodies are hard as hell.
A little interesting perspective: if Dash could sustain this sort of acceleration for ~.7 seconds, she could achieve (Earth's) escape velocity.
I've thought about this before and I am pretty sure this is wrong. You need to calculate centripetal acceleration, not the change in velocity in the y direction. If she came to a complete stop, this would be correct, but she just changed direction.
@Aluzird If their bodies were "hard as hell" then they wouldn't be able to bend the ways they do. A dampening field allows for such movement. Also, a "hard as hell" body would only apply to the skeletal structure, not the soft, squishy organs like the brain, eyes, etc...
All that math made me go derp-eyed.
Dash is tapping the speed force. Not to the lengths her red costumed brothers can but, enough to do stuff like this.This is good news because Dash seems like the type to not care and go too fast and be reabsorbed into it.
@TecknoJockRadius is 5m. I got about 2357 G's.
Oh geez, in that case I wonder how many G's filly Dash hit when she did the sonic rainboom at an immediate 90 degree angle? O.o
@TecknoJockThis thing keeps eating my comments..ANYWAYS, the radius is 5m, dunno what you were doing there. I got about 2357 G's.
There is actually a much easier and more accurate way to calculate how many Gs Dash had to deal with. First, her velocity as she enters the turn is equal to her velocity as she exits the turn. From this we can assume that the magnitude of her velocity through the turn is constant, and therefore that she is not experiencing any tangential acceleration. Her normal acceleration is given by v²/r. We assume that v = 340 m/s and r = 5m, as in the example above. 340²/5 = 23120m/s². Converting into Gs we get 23120/9.81 = 2356.8 Gs of normal acceleration. This is assuming a perfect quarter-circle turn. If you have the turn varying in radius, then you will see higher Gs in some spots and lower Gs in others. The margin for error here is rather high though, due to the rather lose estimates given. A more proper number (assuming the 5m figure is accurate to only one decimal place) would be 2000 Gs, due to significant figures rules. Of course, this is from a rusty memory of Dynamics, and is probably not perfectly accurate.
@Anonymous You are right. That's what I got, but this thing keeps destroying my comments..
Ah man, I was going to use the sonic rainboom in a physics class presentation on physics impossibilities in shows/movies, I'll have to find another scene from MLP
@Post-Above-This Do it! You can calculate the G's and show how it would crush any normal being into a creamy paste.
How do we know that it's a 5 meter turn? Did someone measure the turn radius?
@The-Post-Above-This-Because-It-Won't-Let-Me-ReplyGuesstimated from perspective and the trees, I believe.
@Thomas Cool But now it may be seen as plagerism in the off chance that the teacher or a student is a closet brony
In comparison, a turn at the maximum Gs a human can withstand (9) and at the same velocity would have a radius of about 1310m, or 1.31 km. That's 0.81 miles, for those who don't do metric. I remember reading somewhere that the maximum that a unmanned plane could handle before being ripped apart was 27Gs... Which would need a 436m (0.27 mile) radius to survive that turn.So Rainbow Dash (and all the ponies holding on to her) are either tougher than anything the universe should be able to make... Or the laws of physics are entirely different in Equestria. Most likely the second.
I've said it before and I'll say it again. There's no way a pegasus could fly with wings that small in an atmosphere as thin as Earth's. There is clearly a much thicker atmosphere, and therefore a slower speed of sound. For reference, Peregrine Falcons frequently dive and catch prey at speeds of up to 89 meters per second with no ill effects.
I'm getting 2356.778797 m/s^2 using centripetal acceleration, however that doesn't take into account the fact that at some point she begins fighting gravity while turning adding to the total centripetal acceleration needed. Ponies help me study for AP Physics C exam, hooray!
Also for reference, since somepony was mentioning aircraft, the Hercules X-265/271 accelerated at 100g, reaching mach 10 in 5 seconds. (much better than 27 g)
Ugh, that made my brain hurt a little. Still awesome, though :)
@AnonymousIn straight-line acceleration, not turning flight. No aircraft could survive a turn at that many Gs and keep it's structure intact.
I'm glad that had a TL;DR
Damn...At 100Gs, death is almost certain. Dash pulled almost twenty times that amount in this instance. Thing is, this was only a 90 degree turn within a five meter radius. A screenshot of the one she did in Cutie Mark Chronicles shows a 110 degree turn in a pinpoint turn. That's zero meter diameter. To calculate that, one would have to divide by that zero, which isn't possible.TL;DR: Rainbow Dash theoretically pulled an infinite number of Gs as a filly.
@Anonymous And there's actually a way to figure out just how thick the atmosphere on Equestria is... Too bad I don't know how.
Friendship goes in (SAVE RARITY!) and magic comes out. Never a miscommunication.
@GentThat would be (340^2/0)/9.8. In other words, it's impossible to calculate.
Cool. Now somebody do the math explaining how Dash caught the Wonderbolts & Rarity at the speed of sound without turning them into pony paste.
The explosion you see is actually the effect of Rainbow Dash tearing a hole in the space time continuum, where she makes a gentle 2g turn through a 7 dimensional wormhole, then re-appears an instant later going in a different vector.
@VenbrouWell, a turn radius of one centimeter would have been impossible to notice on the show, so if we take that as an assumption for the turn radius...1,180,000 Gs.Ok, Rainbow Dash is invincible. Also, this conversation has made me realize that I would have done MUCH better in dynamics if everything was done in terms of ponies.
Nothing like applying real life Physics to cartoons....
As a fellow physicist, I contend this info graphic. In the initial setup, it is assumed that RD turns a radius of 5 meters HOWEVER, it is over 90 degrees (vertical to horizontal). The initial graphic is wrong. If the arclength (R*theta) of her turn was 5m, then the radius of her turn was actually ~0.06m. However, if the radius was indeed 5m, then her turning actually took 450m.If her arclength was in fact 450m (as the initial graphic implies) then she actually pulled ~17.7 gs (still quite a lot), not the bone-smashingly impossible 1670 gs.As we can clearly see, < 20 gs is far more reasonable and therefore correct.
Honestly, this math isn't anything more difficult than introductory physics plus a force diagram. Trivial really.
Must take into account the resistance and viscosity of air.
@AnonymousThat would just be wind resistance. It would just be the cross-sectional area of Rainbow Dash (with wings outstretched if I remember correctly) times something (I forget). More importantly is the friction on the hair and feathers of an animal at those speeds. It might not be unlike receiving a noogie with a power sander.
9:13 PM, Arc length has nothing to do with centripetal acceleration! Average centripetal acceleration = (v_tangential)^2 / average radius of turn (340 m/s)^2 / 5 m * 1 g/9.81 m/s^2 = 2356 g, rounding to 2000 for significant figures.
Shouldn't there be some way of figuring out the relative weight/thickness of wingbones that a pony would have in comparison to a bird's body frame? In other words, if the atmosphere is thicker, then the winged pony body frame (which probably would have a somewhat lighter hollow bone structure similar to a bird) would not have to compromise as much as it would in our atmosphere to fly?
@AnonymousIt seems, sir, that you are indeed correct. And rounding it 2000 is more accurate as Mach speed is actually around 315 m/s not 340.
By all accounts, Rainbow Dash should have torn her hair out, liquefied her organs, and pulverized her bones.
So physics guys, how about you explain how she can BOUNCE OFF the sound barrier and get thrown the complete opposite direction.
Yay, an aerodynamics question!If we remember the episode, we can see a bow shock form around Dash; she's already flying past Mach 1 if a bow shock is forming. Bow shocks only occur if the turning angle of the flow exceeds the flow's maximum turning angle for the given Mach number. Notice that as she continues to attempt to make the rainboom, the bow shock becomes an oblique shock and attaches to Dash, signifying that she's focusing on streamlining her body to reduce the drag. An oblique shock produces a lot less drag than a bow shock, but if Dash doesn't stay focused, the oblique shock will detach, becoming a bow shock again, greatly increasing the drag, and thus the forces acting against her. Notice also that when she stopped in midair during the first rainboom attempt, she flared her wings slightly right before she flew off. This would rip the wings off any lesser creature or machine, but not Dash. In this case, instead of her wings being torn away, she simply gets sent into a very fast, very high G pullup that sends her into the opposite direction.
Also, forgot to mention, the maximum turning angle of an oblique shock increases with Mach number. Dash is either streamlining her body to reduce the turning angle of the flow, or increasing her speed, or both.
I love this fandom. :D
Hah, you bronies are silly.@AnonymousYeah, I was going to say an acceleration related to radial velocity approach would be simpler than breaking down the event into components, gravity's pretty much negligible at this point anyway.I'd be curious to see the original work, I'd like to see where the 5m comes from.@AnonymousWhile the point you make is true, your calculations appear to be off.L=5=(90/180)*pi*rhttp://en.wikipedia.org/wiki/Arc_%28geometry%29#Arc_Lengthr=3.18mI think this answer makes more sense just from a sanity check, the trace along a quarter of a circle shouldn't be two orders of magnitude different than the radius.~< 20 gs is far more reasonable and therefore correct>>Flying at super sonic speeds and making a turn on a dime does not really sound like 20gs would be the expected solution.I think of all the dynamics to look at, the number of g's pulled seems most trivial. She shouldn't be able to breathe at those speeds. She'd need machine-level precision on her wings to ensure she neither flies off in an arcing path nor crashes into the ground (jets that travel at these speeds have intricate control systems that fly the plane, it's not as simple as taking joystick input and adjusting the wings a proportionate amount). I'd have to check the math, but I'm not even certain this could be accomplished since Dash's wings have a specific area and air can only provide so much lift, meaning there's a lower bound on the radius she could turn where her wings could provide the necessary upward force to help her turn. Of course, that calculation would assume her wings were fully extended, when in fact they were crumpled at or near her side when she surpasses the speed of sound.@Anonymous~how about you explain how she can BOUNCE OFF the sound barrier>>Another good cartoon absurdity@Anonymous~Must take into account the resistance and viscosity of air. >>With a jet this would be perfectly counteracted (assuming a constant velocity) by the thrust provided by the engines since they act in opposite directions, so the net acceleration would be zero. Presumably Dash has some sort of similar thrust since she maintains her speed and even gains altitude without falling back below the speed of sound.~Engineering brony
2356 g is the correct figure, based on the 5m radius and constant 340m/s. Seeing these calcs makes Twilight Sparkle cry... You don't really need to account for gravity. Dash would just need to adjust her thrust such that the resultant vector is the centripetal force required, but pulling a turn like this it's pretty much negligible.
How do we even know that Equestria has the same gravitational force as Earth does? Hey, maybe it's a way bigger planet, since, y'know, its star ORBITS IT. Or maybe it's way smaller. Point is, we don't have all the data and most likely never will.
Now, thats some heavy free time right there.
Not really. Nothing quite like studying for aerodynamics final like applying it to ponies.
oh man i can't read it!!!!!!!
Ahh, I see, they used V^2=2ad. That is an awesomeexample of using what you learned in school practically :DOn a seperate note, I'd like to clarify how amazing that kind of G resistance is. Once you convert those G's back into an acceleration (16355.2 m/s/s) and then use the average weight of an adult pony (and let's call Rainbow Dash one strapping and fit pony and put her weight at 200kg, or 440 lbs (ponies are surprisingly weighty)). Now using 200 kg times 16355.2 m/s/s, through Newton's Second law, Force=Mass x Acceleration, you find that Rainbow Dash sustained a force of 3,271,040N, or a whopping 734,315.1 pounds of force! That's roughly equivalent to the weight of 2 Boeing 747's. And considering Rainbow Dash weighs 440 lbs, that means she sustained a force roughly 1669 times her own weight. This puts her strength on par with that of Mr. Incredible, and in the general ballpark of Superman. Now THAT is what I call a pony.
I'm comin' up with 32.33... repeating of course... percentage of survival.
@Abdul Lol, I commend you for that reference.
In the words of Applejack, don't you use yer fancy mathematics to muddy the issue!
Well now, it looks like Rainbow Dash needs to be going up against Superman and Goku.I'd assume she's comprised of the same hard to destroy matter that those two are made of. Anyone have a physics sheet of calculating just what the heck superman is?
if this is the only thing school teaches me, then i'll consider that a success.
Assuming the calculations used are correct, I plugged in the updated speed from the MLP Physics Presentation (http://www.youtube.com/watch?v=muVfidujxRg) and come up with our little filly pulling a 38,552g turn. Miss Dash is constructed entirely of unobtainium.
I beg to differ too. In this kind of problem,the use of the polar coordinate system is way easier than the cartesian coordinate system.2357 G is the correct answer
Blast from 2012! YES RAINBOW DASH IS NEXT PRINCESS, SHE IS BEST PONY.
currently using this to disprove some troll on youtube.. oh fandom, you so awesome!
@AnonymousSO what is her max speed in MPH or mach???
I think, that Rainbow dash should have for her pet boeing 373 instead of turtle...
sorry, a boeing 737 :x