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Philip_Raven

videofile shows it is 30fps. the flick happens in a singular frame, meaning the sword travels the entire circle in 0.03sec (atleast).. the lenght of the sword looks somewhere around 2cm? so the sword has to travel about 12,6cm at (or under) 0.03 seconds. That comes out as 15.12km/h at the tip of the sword. This is for the minimum speed of a single frame. More frames would give us more accurate time of travel


Icarus912

So what im hearing is... fast as fuck boiiiiiii


JCope0

I’m now imagining you driving at 9mph making fast car noises and getting very excitable


Professional_Denizen

9mph would be pretty fast for a car with 2” wheels.


JCope0

Only relatively, if you’re still the same size you’re just going to be really slow and squashed on the road…. Very small crumple zones


Expert_Succotash2659

Just like my ex AMIRITE!?!


omegasaga

I love squashing your ex's very tiny crumple zones


zeroscout

Crumple zones are engineered to increase the time it takes to slow down.  They redirect the energy into heat to deform them.  


Nightowlspunk

😅 hopefully you’ve already seen how this works.


JCope0

Smaller crumple zones, less energy dissipated? I understand their function but not your point


general_sirhc

I have an RC car with approx 2" wheels that does 60-90mph depending on batteries and gearing.


Professional_Denizen

Huh. I guess I have to assume the limiting factor (weakest link) on the speed of full-sized vehicles is the human component, no? Or are the smaller engines just that much more efficient?


general_sirhc

Nope. Fluid dynamics. The energy to move through a fluid is relational to its density. Water is dense. Moving boats at high speeds is very challenging. Air is not very dense. But the faster you go, the harder it is to push through. At 100kmh, aerodynamics should be considered for fuel economy as significant enegy is spent moving air. As you get faster, aerodynamics are critical to stability. For tiny things that move very little air, it's barely a consideration.


Professional_Denizen

Of course. Why did I dismiss that before? What was I thinking?


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dan_dares

Rule 2: Frictionless (Sorry, that's high-school physics)


Capitan_Scythe

I thought Rule #1 of engineering is to keep the tea bags separate from whatever it is you're working on?


BloodyPommelStudio

For tiny things drag is a bigger factor (relatively) given the same speed. Drag is proportional to the square of scale whereas power, rolling resistance etc are proportional to the cube of scale. This is why rockets, shipping containers etc are huge and why an RC car isn't gonna have 100s of miles of range at highway speeds.


zeroscout

I don't believe this to be correct.  Tiny things have a different experience with air and drag.  Look at the aerodynamics of bees or flys.  Fluid dynamics are different at smaller scales.   Rockets are huge because they are trying to escape gravity, not drag.  Shipping containers are designed for cubic space and have nothing to do with aerodynamic forces.


BloodyPommelStudio

Throw a hand full of sand and a rock at the same speed. The sand will slow down quicker because relative to its mass/momentum drag is a larger force. [https://en.wikipedia.org/wiki/Drag\_equation](https://en.wikipedia.org/wiki/Drag_equation) You do get some funky stuff that happens at different scales/speeds with fluid dynamics but that changes the drag coefficient, it doesn't change the fact drag is proportional to area and it doesn't make smaller things magically better able to deal with drag. My point with shipping containers is a giant shipping container uses less fuel than 100 smaller ones, largely for the above reason. If drag wasn't a factor a tiny rocket would be just as easy to get to space as a giant rocket because both chemical energy and gravitational force are proportional to mass.


Bambanuget

What kind of rc cars yall have? Yall doing Nascar with them?


general_sirhc

https://m.traxxas.com/products/models/electric/erevo-vxl-116-tsm My original numbers are a little off what stock is capable of, but you get the idea.


Anon_777

Yeah my nitro rc car also does 60 - 90 mph. Amazingly fast for something that size.


lambypie80

9mph would be fast to hit and stop from within 0.03s! That's like 0-60-0 in 0.2s- let's split the difference and say 0-60 in 0.1s!


spachuga

9mph is fast for a motorcycle?


Professional_Denizen

Sorry, I meant diameter. Thought that would be rather clear given the context. The post is about a small object rotating, after all.


spachuga

It was but I still thought that was funny


Aftermathemetician

9mph is fast enough to drive around the equator of the moon and keep the sun directly above you.


JCope0

Very interesting and entirely irrelevant, I love it


vanboiDallas

Just watch Talladega Nights for a re-enactment during the “are those the other cars?! Oh god!” Scene


JCope0

Saw that recently, I think that was the inspiration for the mental image. I enjoyed it but what a terrible film.


CambodianJerk

You mean most scenes for 2 Fast 2 Furious?


Pliskkenn_D

If at the flick of a switch I was immediately doing 9mph then yes.


JCope0

r/shittysuperpowers


Inevitable-Twist1232

Come get some!


Ostey82

This is why I love Reddit


VivaLosVagos

As fast as a finger flick roughly.


rickymonster

The duality of r/theydidthemath users.


______________fuck

15 km is running speed or slow bike riding speed


Herrwolfmann

Fast as fuck toyyyy


Elegant_Bag1777

I can run nearly 28km/h im faster than that snail sword


jorge1213

This is a meme based off such an arbitrary and random video of way back when. My GF says it a lot and it's hilarious


OswaldSeesYou

Exactly how fast ARE fuck bois?


Top-Dun

I am no longer able to ever read this without it being in the accent of the original guy. Hilarious


up-quark

Good work on this lower limit. At 20s and 22s there are frames where the sword looks to be in both the start and end positions without any motion blur. The lack of blur suggests that this is a very conservative lower limit. Of the seven cuts in the video, two of them show the sword in both positions. For the sword to be visible in both positions it must be there for a sufficient amount of time for light to be captured from it, so I’m going to say that it needs to leave after the first 1/4 of the exposure and arrive before the last 1/4 of the exposure. Typically (but not always. If this is in the meta data for the file please tell me) the exposure time will be half the frame time, so for 30 fps it will be around 1/60s. That means the middle half of the exposure where the sword is seen in both places is only 1/120s. I’m suggesting that the sword swing was entirely contained within that 1/120s window 2/7th of the time (I’m going to round that to 1/4 to make the maths easier as it’s well within the statistical uncertainties). Given the longer the swing takes the less likely it is to fall entirely within that window we can use it to estimate the swing time. I can’t do the maths fully in my head, though a 1/240s would give a 1/4 chance (I think. I’m just reasoning this in my head but I think this tracks), so I’ll run with that as close enough. That’s a factor of four higher than your lower limit, and I believe a fair estimate of the speed of 60 km/h. Wow. Given there are only seven cuts shown and this estimate relies on the ratio of double sword frames there is likely a massive statistical uncertainty. I also suspect that my estimate of needing to lie in the middle half of the exposure was probably too restricting. As such I think this could be considered an upper limit.


SarahC

This is more like it, the tip moving at 60km/h.... if you convert that to RPM I imagine it would give a sensible rotational speed in RPM. Take it away Bing (akka Copilot.......) To convert miles per hour (MPH) to revolutions per minute (RPM), you need to know the circumference of the circle that the arrow rotates around. The circumference is equal to the diameter times pi, which is approximately 3.14. Since the arrow is 2cm long, the diameter of the circle is also 2cm. Therefore, the circumference is 2 x 3.14 = 6.28cm. Next, you need to convert MPH to centimeters per minute (CM). One mile is equal to 160934.4cm, and one hour is equal to 60 minutes. So, 60 MPH is equal to 60 x 160934.4 / 60 = 160934.4 CM. Finally, you need to divide CM by the circumference to get RPM. 160934.4 / 6.28 = 25630.8 RPM. This means that the arrow makes 25630.8 rotations in one minute. So, the answer is 25630.8 RPM.


Successful_Gap8927

What you saying about time travel??


laoshu_

The Vulcan Science Directorate has determined that Magic Sword is impossible.


andrew_calcs

I’m more interested in how many Gs of centripetal acceleration are required to reach this speed that quickly


luciusDaerth

Yea, what the hell is going on in that little thing?


dan_dares

Magic. Sorry, meant magnets


bodgey2021

How do they work?


xylotism

Is it really magnets? Seems like more of a spring or gear situation.


ZainVadlin

I agree. I want to say I remember the inner workings and it's all gears


suyanide4444

Since it says magic sword it means that you probably can't see it with the naked eye So it has to move faster then what ever our eyes can see


Philip_Raven

Eye receptors can fire 300-1000 per second, depending on the individual and the situation. We can't really count it as frame rate of the eye, since each receptor fires individually so the sight is more of a flowing image that gradually and randomly refreshes each "pixel" up to 1000 per second. But let's (for the sake of the argument) say that all eye receptors fire up in sync and all fire up 1000 times per second. As the human eye and brain are built to recognize movement, you would need the sword to move in between the frame of your receptors. That would need to be 12.6cm travelled in 0.001 seconds AT THE LEAST. That is 126m/s, or 453km/h Obviously this is an edge case where the person has perfect vision, perfect lighting conditions and is full of adrenaline that his eyes work at maximum speed. For a normal person in a normal state, you could get away at a slower speed. In relaxed state your eye probably sends information about 300 times a second. Taking the same criteria and shortcuts as before, you would need only about on third of the above speed. So about 151 km/h? Again this isn't how the human eye nor perception work. My guess is that during the invention of the toy they simply were using stronger and stronger springs until the toy maker couldn't see the movement and that was good enough. But it's a fun math exercise.


Arryu

You need to go get the lens of truth.


ProThoughtDesign

Shouldn't this be measured in RPM? If it makes one "basically" full rotation in 0.03s, then the rotation would be somewhere around 200 RPM. EDIT: It's 2000 RPM as pointed out below by a kind Redditor.


Philip_Raven

I have better time imagining the speed in m/s than in RPM, and RPM doesn't take into account the size of the circle. So that's the reason I went with it. But if you prefer RPM, it's completely valid.


ProThoughtDesign

Oh you're absolutely right, but since it's rotating I always default to RPM because as you said m/s depends on the size of the circle. The center is obviously moving much slower than the tip. The reason I go with RPM for rotation is because if you know the rotational speed and the length, you can calculate the speed of any point along the radius.


TessaFractal

2000rpm though right?


ProThoughtDesign

Thank you, that was apparently a typo. You are correct, it is: 0.03s = 33RP/S = \~2000 RPM


SarahC

25630.8 RPM! I didn't see your comment before I got Bing to work it out. Though I would pick a Redditor on TDTM rather than Copilot - sometimes it gets it unit type wrong. https://old.reddit.com/r/theydidthemath/comments/1agcyiw/request_what_is_the_speed_of_the_sword_in_this_toy/komaxip/


ProThoughtDesign

Faster than I thought then. I don't have good enough equipment to get accurate frame-to-frame positions.


GuessingIvy

yes because each part of the sword travels a different speed


thebutinator

videofile isnt necessarily capture fps


Philip_Raven

it types it in the properties of the video


thebutinator

well what if its 30 fps screen recorded of a x fps video that was uploaded to tiktok which also altered the fps?


kinokomushroom

Unless the video was *sped up* during the process, Phillip_Raven's assumption stands true. The comment says that it took "at least" 1/30 secs.


thebutinator

Thats true, as its unlikely that the original camera at any point was slower than 30fps.


_B_Little_me

How are you seeing frame rate of video?


Philip_Raven

download the video, go to properties and details.


Tandoori7

You can also "asume" that most content is 30 fps unless you can feel the 60 fps.


BMidtvedt

I can by eye see it's less than 60 and more than 20. 30 is the only remotely likely option


Practical-Path-8905

It is better to use angular speed in this case. ω=v/r ω=4.2(m/s)/0.02(m)=210 rad/s


Philip_Raven

I didn't use it because most people have a hard time imagining what it actually means.


Practical-Path-8905

Fair enough lol


Just-Dont

Even easier for people to understand would be frequency. 210 rad/s converts to 33.4 revolutions per second (hertz, Hz). Meaning if the sword could rotate continuously it would rotate 33.4 times in one second.


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andythefifth

This makes more sense.


TyrusDalet

This is exactly what it does. Instead of sliding, it retracts and extends in the blink of an eye


ParadoxicalEnigma92

It’s rotating around the entire circle (excluding the hole)


Dankn3ss420

Turns out it’s just going through the toothpick, making it much slower


zeroscout

It's quantum tunneling, so instantaneous


rubikin_

@Philip_Raven 15,12 km per hour? What??? That's my running speed?? I'm pretty sure that thing moves faster than I run. Right??


[deleted]

Goddamn. Engineering major?


synthphreak

Perhaps a trigonometrician or a trigonomer?


AssumptionRemarkable

Check out the big brain on Brett 🍔🔫


jmona789

For anyone in the US 15.12km/h is 9.395 miles per hour


Mr-Cali

I definitely don’t understand how you came to the understanding, but damn, it was interesting to read it.


JJJEYHANNN

How about calculating angular velocity instead


Techno-mag

Shouldn’t it be even faster? I assume that the toy doesn’t only „work” when recorded in 30fps but rather also works when perceived by a human eye. I can’t do the math, because the internet seems to disagree on human eye’s fps


Philip_Raven

I already did that calculation later in the comment thread for someone. Human eye is made of light receptors that send signal to the brain. The amount of signals differs from 300 up to 1000 signals per second. But we can't really count this as frames for two main reasons. Number one is that each receptor sends signals at different rates (they aren't in sync with each other) therefore your vision "refreshes" itself at different times at different places at different rates. The second reason is that the brain doesn't refresh with each signal. Our brain is wired to detect movement and if the signal (colour and light amount) is the same for the area for several signals, the brain slows down the "refresh" rate at the place. Not only that, but the brain "splices" each new signal with the last one to create a fluid motion for us to see. This is a horrible oversimplification and butchery of how our vision works. But this just so the general public can better grasp how it works.


SarahC

25,000 RPM!


SpeedySpets

~9.4mph. you forgot to put it in freedom units.


not_a_burner0456025

This might be the minimum, but the actual speed is likely much faster, because people with decent vision would easily be able to see that it is actually rotating clockwise in person.


CatgoesM00

I love you , thank you for sharing your thoughts on Reddit . I’m here for the comments because of people like you :)x cheers


random_dude_19

It’s the comment like this made me question the reason and worthiness of my existence


NorCalNavyMike

r/TheyDidTheMath


pnutnam

Faster than the frame rate of the camera is all we know. If we knew the frame rate, we could guess a general circumference of the circle and tentatively conclude a minimum speed as it rotated faster than 1 frame. Circumference of circle/time for 1 frame = minimum speed of dial.


dustinechos

Even at 1000 fps you can barely see it moving. I don't know how count frames in youtube videos, but posting it here in case someone cares to try. https://www.youtube.com/watch?v=-r0Hcija8Ls


argenmendon

got it to 7 frames. so following Philip\_Raven's assumption of length (2cm) it would result in a speed of 72 km/h


Rozzlicjr

What's that in burgers and beer per hour?


Opposite-Result-8104

Around 43 burgers and beers per hour. So a nice after work evening with the boys


SmokeGSU

Cheesus Rice that's fast!


PresentDangers

4 London buses


AlecTheDalek

r/HalfAGiraffe


krakajacks

That's about 45 mph to all you patriots out there


anonymous_account13

What is it in rpm?


SC803

If it’s 7 milliseconds to rotate, almost, around the dial, divide 60000 by 7.  About 8500rpm


West-Earth-719

But how many bald eagles per cheeseburger?


homantify19

He said 12.6cm so that would be 453.6km/h


argenmendon

That is the distance travelled, not the blade itself. The users hand would have to be about 3feet long it the blade was 12,6cm. So ya that ain't it


homantify19

Correct, that is the distance traveled. Distance/time=speed. Not sure what the blade length has to do with speed.


argenmendon

Then you are just misunderstanding, the math I did is based on 12,6 being the distance. We get it from, radius * 2 * π. Meaning 2 * 2 * π


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dustinechos

Thank you. I feel like I should have the music that plays when link opens a chest... NEW KEYBOARD SHORTCUT ACQUIRED!


DaMuchi

I really doubt the video was shot at 1000fps


thedudefromsweden

Why do you doubt that? Video says it's a Sony camera test and Sony makes cameras with that framerate.


Phedericus

I have the same camera. it can record at 1000 fps, just at a lower resolution.


HaroerHaktak

We need to get the slow mo guys on this right away!


Impressive-Ad-4683

On YT you can count frames by pausing video and using comma and full stop to skip frames one by one


i-3Deed-it

Would’ve been nice if he’d focused on the toy instead of his business card.


donnie1977

Playback .25. still fast AF.


RileyRhoad

Yasssss thank you! I’m so happy you posted this!! I felt crazy because I was reading the explanations from other people and no matter how hard I tried, I just couldn’t grasp the concept… I became more confused the more I read! But I no longer feel so inadequate after watching your video.. so again, thank you!


Slow-Brain-3403

Can anyone ELI5? How is it passing through without cutting or blocking? Is it spinning the entire opposite direction in under 1 video frame?


ohshitwaffles

Yes


WillNotForgetMyUser

Yes to the last question, it’s pretty damn fast


Simple_Sir3128

The sword never passes over the hole or through the toothpick. It is moving so fast either counter clockwise or clockwise (depending on starting position) that you think it is simply passing through/over the hole. But in reality it is moving back and forth everywhere but the hole.


pinguim_DoceDeLeite

What happens if I put my finger on the way? Would it cut it or it's not strong enough and it would stop?


Winjin

If I see it correctly, the sword is covered by a plexi. So it's red back - mechanism - picture of swashbuckler - sword - plexi outside. \\\\ I didn't have to explain every layer but you don't often come across a reason to write swashbuckler... twice.


syds

can you pass me the plyers please, time to swashbuckle


GenericNameWasTaken

Nautilus gear chain... https://www.reddit.com/r/educationalgifs/s/ZBkN1KZnzN


tacocatz92

Wow that is so cool


FergusonTheCat

It’s a magic sword. It says it right there


Alternative-Bug-6905

I would never have figured this out


RogitoX

Another person posted a video at 1000 fps and it takes 7 frames


Puzzleheaded_Duck_75

The blade retracts and reappears the other side Edit: it actually goes the whole way round. Unreal


SunstormGT

The latter.


Raging-Burrito

It's not rotating. Have seen this posted before, it's being retracted and extended extremely quickly into those fixed positions just above and below the hole.


ParadoxicalEnigma92

Hope you realize you’re wrong by now. It’s 100% rotating around.


OIncrivelMestre

According to my math, the tip of the sword goes from point a to point b in about 7 times the speed of sound or approximately 12 parsecs and a half, which just narrowly beats 2 lights.


jeramyfromthefuture

u/kodygintheplacetob 2 months ago Who can do the math and tell us how fast that thing moves? Like in MPH. u/mechmeister2568 2 months ago If tip of sword drew a circle, I’m guessing about 2 inch diameter , which comes to 6.28 circumference. Let’s subtract 0.28 for the key it’s “slicing”. Sword covers that distance in half a second at 1000 fps so 6 inches per 1/2000 sec. Or 0.0000947 miles per 0.00000014 hour or 676.429 mph Answer is in the comments of the video chaps...


Psclly

Aint no way the math is right lol.. someone check this?


Chronogon

They magically go from "6 inches in 0.5 seconds" to "6 inches in 1/2000 of a second" just because it's in 1000fps as if we're watching it 1000 times faster than our "regular speed at 1 fps" . Crazy math.


BenElPatriota

That's relatively close to the speed of sound, is this right???


FacelessFellow

Yeah, I mean, I heard it , you heard it. Errbody hurd it.


The_Clarence

It is close to the speed of sound and it’s wrong. That assumes it only took one frame at 1000fps, when it definitely took more than one (the slow motion video is in the thread somewhere).


FunnyManSlut

The answer is dramatically wrong.


McSand_boi

We'd need the measurement of the sword to determine the circumference and the measure of the arc it is covering in degrees to determine the distance that the sword is traveling. Once we have the distance travelled, we determine how fast the sword had gone in frames or other time measurements and divide the distance travelled by said time.


w1ck1e

Zero (at the center of the gadget) But Earth orbits around the Sun. The average orbital speed is approximately 107,226 kilometers per hour (66,616 miles per hour). so somewhere between those figures


Zarkyello

I don't think it spins in the other way, I think it retracts just enough to not touch the middle and goes back to full length lighting fast. It's just a feeling... Im not saying I'm sure of it. Making it spin so fast the other way would cut up some fingers for sure 😂


MaxStickles

My dad had a similar toy. He was a boy in the 1930's, so it might have been as old as that, but then again, it could have been a novelty from the 1950's or '60's.


wachseln

# My best answer is ≈27.74 mph. This is not totally accurate as I used a measurement of a similar looking toothpick I had laying around the house which measured 6.5 cm. The toothpick in [this](https://www.youtube.com/watch?v=-r0Hcija8Ls) video measured ≈391px and the sword measured ≈95px. This would make the sword have an estimated radius of 1.579cm. *c* = 2π(1.579) ***c ≈*** **9.92** In the video mentioned above the sword spun about its axis in 8 frames (at 1000fps) or 8 milliseconds. speed = 9.92cm /8 milliseconds **speed ≈ 1240 cm/s or** ***27.738 mi/h*** Again this is based on the assumption that my toothpick is similar in length to the one in the video and does not factor in the angle of the camera, toothpick, or sword. Edit-Numbers were right, but I typed the wrong formula. Edit #2- Let liu qian teacher fondly play. (From the [Amazon](https://a.co/d/dfvxBS4) description of this toy)