I don't pretend to understand this stuff. My major is in computer science, not this physics magic. I don't even understand half of the math in the original diagram for Dash's Rainboom. I did only get a C in Calculus II, though. Either way, another physicist has taken another look at the magic math and given an alternate take on the scene.
Click to make bigger, of course.
27 comments:
Thank you for reminding me I have a Calculus test on monday...
ReplyDeleteAt least I have programming today to cheer me up...
Computer science, eh?
ReplyDeleteWhy why haven't you coded that Story Archive Seth's been asking for? :P
That's great and all, but it didn't have much of a conclusion (then again an econ major knows nothing of the physics). Wasn't the point of the other ones to prove that Rainbow would have been ripped in half, and therefore there is pegasus magic keeping her safe?
ReplyDeleteover 2k g's?
ReplyDeleteWow...
"Next time... we better test these ideas with real-world physics"
ReplyDeleteI was really wondering why the first "sonic rainboom physics" page didn't use a = v^2/r. They used some overly complicated way with projectile motion and got an answer that wasn't exact. Props to the brony who did this.
ReplyDeleteill stick with the "its magic i aint gotta explain shit" theory
ReplyDeleteUm... You guys do realize it's a kids show right? :P
ReplyDeleteSome russian brony beat this guy FEW MOTH AGO:
ReplyDeletehttp://i.imgur.com/tS6Lj.png
http://i.imgur.com/tS6Lj.png
I posted in on Ponychan in "Sonic Rainboom" thread.
Ceeral, can you attach this one as well under the break?
At my college Computer Science majors have to take Physics I and II.
ReplyDelete/eyes Cereal quizzically
More Physics 101 stuff? Come on guys, I know you can do better than this.
ReplyDeleteI remember several of us doing this exact same calculation in the previous Rainboom Physics post.
ReplyDeleteDoes this mean that http://img88.imageshack.us/img88/3/7349t.jpg is wrong, then?
ReplyDeleteSo wait, when was it decided that the radius of her arc was 5m? Or that she's moving at a constant speed of 340 m/s? How did anyone get those numbers?
ReplyDeleteI look at this and all I see is an acceleration measured in m/s and I cry!
ReplyDeleteso some fun visualizations - assuming rainbow dash has a the minimum healthy weight of a Shetland pony (150kg)....
She could carry TEN C-130j(Hercules) aircraft!
If she hit the ground instead of saving the other ponies ... its equivalent to an earthquake!
I don't know where the 5 meter thing came from but it's quite ludicrous. And I imagine this G figure is very sensitive to that particular variable.
ReplyDeleteThe 5 metre radius and 340 m/s speed are kept from the previous rainbow physics diagram that was floating around a while back. The whole point of this is to show that using centripetal acceleration is the better way to analyze it - using projectile motion equations makes no sense. Also, I'm going to write off the acceleration in m/s as a typo... hahaha...
ReplyDeleteThe assumed radius of the turn does in fact have a correlation with the calculated g forces. From the equation, you can see that it has a 1/r relationship. The speed she's going at plays a larger factor though (v^2 relationship).
the values are accurate enough... we are talking about a cartoon pony, after all. and the conclusion?
ReplyDeleterainbow dash : 1
physical laws: 0
My English Major and I will just settle for suspending disbelief.
ReplyDelete@Anonymous
ReplyDeleteExactly this! The biggest misconception that is yet to be cleared lies in that 5 meters. With this variable we can manipulate the final force affecting Dash as we please.
When the distance decreases, the acceleration needed to make the turn increases. Acceleration in m/s^2 (or g's) goes towards infinity when the distance in meters approaches 0.
If we "assume from the height of the trees" that r is equal to, say 0,05 meters, her acceleration probably ends in bazillions of meters per square second. And if she can pull this off for a split second needed to make the turn, she probably can pull it off for one second. And if she can accelerate with that value for one second, then I dare ask - where is the Equestrian Intergalactic Exploration Programme? Cause they clearly have the technology already...
Oh wait, I guess it's Celestia who keeps it secret:D
Getting better but we need to do some serious experimentation to determine how the stresses of such extreme g-forces would affect somepony.
ReplyDeleteTo put things in some perspective: the "canonical" view claims that Rainbow accelerated at around 23120 m/s^2. What does it mean? Well, for starters - it means that she can at will accelerate at that rate. One second of acceleration at 23120m/s^ and - assuming standing start - she is moving at velocity of 23120 m/s = 23 km/s = 82800 km/h. After one second of acceleration. Now, this is fast, right?
ReplyDeleteThe escape velocity for Earth is only 11,2 km/s. Now if we assume that planet Equestria has a mass roughly comparable to Earth, Rainbow Dash needs to flap her wings for 0,5 seconds to gain enough speed to get into space...
Wait... It's not right! Luna has wings too! Granted, she may not be as fit as Dash, but Moon's escape velocity is way lower - only 2,4 km/s. I bet she could do this without breaking a sweat. This whole "banished to the Moon for a thousand years" thing seems fishy... There must be some conspiracy at work here...
Is there a page 2? It just kinda ends, doesn't seem to finish.
ReplyDeleteim not sure this is right. this is basing the assumption that she is going only at the speed of sound (340 m/s). in the video she was going sevral times that
ReplyDelete@Anonymous
ReplyDeleteErm, sort of. I think the equations they were using were for the case of constant acceleration in a particular direction. However, in the first diagram they used, it shows that RD was travelling in a circular path. In which case, you would expect the person to use the relatively simple equation for centripetal acceleration used in this news story's feature image.
Anyway, for those that are wondering why all these different equations and numbers are popping up, keep in mind that these are all approximations. Physicists do this all of the time. If you would like to use 4 m instead of 5 m in the calculations, that is fine. 340 m/s was chosen for the speed because that is roughly the speed of sound in air. (You need to be travelling at roughly the speed of sound to create sonic booms, so people assumed RD would have to do the same to create rain booms.)
The final thing to note is that although the fellow in the image made all of the physics he talked about seem very complicated, it isn't. And I'm not saying that because I'm receiving my BSc in astrophysics next Tuesday. I'll sum up his argument bellow as simply as I can.
Say you are on a bus and that bus turns left. Sitting on this bus, you will feel as if something is pulling or pushing you away from the corner the bus is turning around. This is called the centrifugal force. To calculate roughly how big this force is, you can assume that the bus is travelling in a quarter circle around this corner, at some fixed distance away from this corner. You then take the speed the bus is travelling around this corner, maybe something like 20 miles per hour, multiply that number by itself, divide that number by the distance to the corner, maybe 20 yards, then multiply that number by your mass. That will give you a number representing the size of the centrifugal force acting on your body. To get that number in terms of g's, divide that number by your mass again as well as the rate at which a falling object's speed changes, 9.81 metres per second squared, and you will end up with the number of g's your body experiences as you turn the corner on the bus.
Now, if that bus was replaced with a race car going much faster around a similar corner, you are going to feel a greater centrifugal force, and therefore more g's. The same can be said for a corner oriented vertically, for example, a fighter jet, or pony, diving straight down then quickly turning upward and travelling parallel to the ground. Both an increase in speed and decrease in the radius of the circular turn will increase the size of the centrifugal forces acting on the thing turning. Although in a bus, you would typically never experience a centrifugal force when turning a corner greater than a fraction of a g, in a fighter jet, experiencing 5 or so g's is not uncommon. RD seems to be experiencing a force of roughly two thousand g's, which is crazy huge.
Anyway, hopefully that description isn't more confusing than helpful. Although deriving the equation the fellow above used does take a little bit of math, using and understanding the equation usually isn't too difficult although you normally would never see unless you had taken an introductory physics course of some kind in high school or university.
Comp Sci represent!
ReplyDelete@Pinkie Guy
ReplyDeleteYeah, the mistake was one of the diagrams which showed a circular path instead of a parabolic one. http://i.imgur.com/GMDGn.jpg
HOWEVER, because the motion used in that one assumes constant linear acceleration, I like to look at it this way: what causes RBD's acceleration is her making a single, incredibly fast and powerful flap of her wings (taking ~0.0294 seconds).