Under the ruler faster than the ruler

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TMAH : You have a remarkably calming voice. 

thatguywiththeegg : You're a witch.

The Robot : Why'd you have to spoil the answer with the title?

ACG : Guys its the angle of the ruler, He`s gently applying pressure to one side.

NightwingASMR : Very interesting! Funny how physics work.

Gamakun : He is pushing down while moving to the right creating the opposite direction you expect it to move.

Matthew Maciej : I didn't hear the animals say anything,my sound must be broken.

AlephNeil : For anyone who is both (i) confused and (ii) knows high school algebra, let's break this down like a textbook exercise: 1. Suppose the inner radius of the lower wheel, at the point where the big wheel touches it, is r, and the outer radius of the lower wheel, where it touches the ground, is R. Show that, unless the wheels are slipping, (the speed of the cart relative to the ruler) = (r/R) * (the speed of the cart relative to the table) 2. Define F(x, y) to be the rightward speed of the cart if the ruler is moving right at speed x and the table is moving right at speed y, and the wheels are not slipping. Using the previous exericse, show that for all v, F(rv, Rv) = 0.   (Remark: We can interpret v as the angular velocity of the small wheels.) 3. Given the result of the previous exercise, explain why it must be true that F(rv + k, Rv + k) = k for all v and k. (Hint: Imagine that the entire room and everything in it are moving right at constant speed k.) 4. Suppose that the ruler is moving right at speed 1 and the table is not moving. Solve the simultaneous equations rv + k = 1; Rv + k = 0 for v and k. Deduce that the cart must be moving right at speed R / (R - r), which is > 1 (therefore 'faster than the ruler').

Horhay Fernandez : My brain just exploded

kittenesque : every so often I come across this video, and, having forgotten the results from the last viewing, get it wrong. it's still interesting, and gave myself and my roommate an interesting conversation because I still remember how it works

Amplitude Maximum : well that was a creepy demonstration

Robert Warren Gilmore : Coolaun! Where did you go? I would love to see more videos.

jasminamuffin : thank u tichy this vid is 10/10

Francis : This is all about friction. The friction between the little wheels and the paper is higher than between the big wheel and the ruler. If the friction between the big wheel and the ruler were higher than the little wheels and the paper, the cart would move to the opposite direction of the ruler.

Ag3ntW1nd3x : kush

Blopartyhut : This is sorcery. Burn this man and his demonic contraptions at once I say!

enndubful : Draw the free body diagram people. It's obvious it will move in the direction of the ruler. Then you look at the gear ratio and see how much faster it goes.

Bo Huggabee : the ruler is straight so it creates an illusion, and you forget to imagine the ruler as a gear turning. if you take the two points between which the wheel travels then curve that line, it become part of a gear and it's easier to imagine whats happening. . having two gears with one in between will result in the outer gears spinning the same direction. the trick to making it speed up is the different radius of the bobbins. clever trick.

T Blake : lol anti clockwise

WoodenPotatoes : Yeah lol he totaly has the voice for it doesnt he :D

prosthesis_ : Explanation?

sflogicninja : Ah cool. i see the error of my ways. I did this myself and see what the overall concept is. That's what skeptical thinking is... the ability to say hey, *shrug*, my bad. I've been watching all of these perpetual motion and 'wind-powered-machines-moving-faster-than-wind', and I put this is the same category. I'll be more careful in the future. Thanks for keeping me in check. -D

sflogicninja : Actually, you're right. I need to try this myself. I wasn't very mechanically minded as a child. -D

sflogicninja : He tilts the ruler. This causes the force to be sent reverse the direction of the ruler. Shenanigans. Magic tricks. I don't trust soothing voices.

sflogicninja : daz, what I'm saying is that he's using downward force on the left side of the ruler to create the proper motion of the large wheel. Does this make sense? I'm just saying that the narrator seems to be implying that the motion of the ruler to the right is causing the anti-clockwise movement, which is incorrect. I might make a video to show what I mean.

Bryson : I found this video when YouTube was barely starting to get popular and before ASMR was popularized. I remember I fell asleep to this video but lost it and never found it for at least 10 years. I can not believe I found this video again my mind is blown

Frabjous : You sir, are so captivating, and yet you could snap your finger and I would fall asleep. Your voice is perfect.

warvad : I got it wrong, like George.

AcanLord : clever contraption. has this principle been used in any technology?

Colin Levy : Really enjoyed this.

Benjamin Chodroff : So, what happens to the cart if the ruler is moved at the speed of light?

Thomas Åhlén : This video rules!

AlexPleaseHelpDotCom : So counter intuitive! But sweet! Nice demo.

TD : Soon this will be on Brain Games @ nat geo. ~_~"

UDT116 : Lateralus.

Kacrna Khut : big wheel keep on turning...proud mary keep on burning. rollin

coolaun : nadahere, mathematical analysis shows that the size of the blue wheel plays no part in the relation between speed of cart and speed of ruler. This is easily confirmed in an empirical test. If the radius of the ends of the cotton reels is b, the radius of the part of the cotton reels where the blue wheel touches them is a, Vr is the speed of the ruler and Vc that of the cart, then: Vc = Vr(b/(b-a)) The cart goes faster when the two values are close.

coolaun : Watch the video carefully to work out how the cart was made. Here's what I used: - 2 cotton reels (v. important: the radius at the centre is considerably less than that at the edges). - A simple frame with two axles on which the reels can turn freely. - A wheel with a flat profile tire that will sit neatly on the cotton reels. The hardest part was finding suitable cotton reels. You may have to improvise: you could build rollers similar to the cotton reels with parts of a construction kit.

coolaun : The energy for DWTFTTW is coming from the relative movement of *air* and *ground*. This energy is always available, no matter at what speed the vehicle is running, as long as the vehicle has contact with both air and ground. It is correct that the vehicle "sees" an apparent headwind when running faster than the wind: you may think of the vehicle "screwing itself through the air", just as the mechanical cart pulls itself along the ruler.

coolaun : That sounds as if everything is working correctly. I've never seen LittleBigPlanet. Can you make things with propellers, like aircraft? Can you make wind blow? If so, it might be possible to do a machine that goes downwind faster than the wind...

coolaun : It not a proof, but it demonstrates the same working principle: that the relative lateral movement between two media can be harnessed to create a faster movement in exactly the same direction. In the case of this machine the two media are ruler + table top. The blue wheel engages with the ruler and the cotton reels with the table top. In the case of the DDWFTTW cart, the two media are air and ground. The propeller engages with the air and the wheels with the ground.

coolaun : There's nothing to debate here: Counterclockwise = USA English Anticlockwise = British English

coolaun : You need to look at the machine as a whole: the cart is a gearing system *between* two surfaces that move relative to one another. If the centre of the blue wheel was fixed relative to the table top, it would indeed turn the other way. The gearing causes the centre of the blue wheel to advance to the right faster than the highest point of the wheel, which is touching the ruler.

coolaun : Correct. In exactly the same way, the down wind cart goes faster than the wind because of the ratio between the pitch of the propeller and the circumference of the wheels touching the ground.

coolaun : propwner, do you imagine that there is only one language in the world? Counterclockwise = American English Anticlockwise = British English

coolaun : protztom, I have talked with several pilots who understand exactly how this works. The propeller will not simply stop because it is geared to the wheels. It is creating thrust, not functioning as a turbine. Mark Drela (professor of aerodynamics at MIT and world-renowned pioneer of human-powered flight) has analysed DDWFTTW. If you go to the Boatdesign net forums and look at the thread with the title "The Wind Powered Sail-less Boat" you can find his analysis.

coolaun : ESRogs: the gearing is such that the top point of the top wheel is moving slower than the cart. If the gear ratios were reversed so that the top point of the top wheel moved faster than the cart, the cart would still move in the direction of the ruler, but slower than the ruler. If I could turn the whole cart upside down (would be fun, but my cart isn't stable in that position), the cart would run in the opposite direction to the ruler, slower than the ruler.

coolaun : to schwer13: If you're going downwind _slower_ than the wind, you feel the wind on your back. If you're going downwind _faster_ than the wind, you feel the wind on your face: it's the proof that you're going faster than the wind.

coolaun : You're right about the axle. But the important point is not that the bottom wheels are smaller than the top one: the size of the top wheel doesn't matter. It's possible to make a cart where the rotational speed of the top wheel is more than that of the bottom wheels (I'll do it if I find the time!). What's important is that the *edge* of the top wheel is moving slower than the *edges* of the bottom wheels, since it is in contact with the smaller centre parts of the cotton reels.

coolaun : When it's working correctly, there is no slippage between ruler and wheel. You could do the same thing with cogwheels and a rack and pinion gearing, to make sure there's no slippage. Since my cart is very light and all wheels turn easily, there's not much loss of energy due to unwanted friction, which means I don't have to apply much pressure with the ruler.