Under the ruler faster than the ruler

Another model demonstrating the principle of the cart that moves down wind faster than the wind. Inspired by some ideas posted on the discussion at forums.randi.org, I made a simple cart that is propelled underneath a moving surface, faster than that surface. The large wheel, turning against the direction of movement of the ruler, is very similar to the propeller of the wind-powered cart, turning against the wind.
The next episode is here: • Under the ruler 2: the...
PS. Several people have asked where Louise comes from. She was made in Sri Lanka for Barefoot: barefootceylon.com/toys/#
If you want to read more about downwind faster than the wind:
peswiki.com/index.php/Director...
dwfttw.blogspot.com/2008/12/co...
en.wikipedia.org/wiki/Sailing_...

[@Omenxiiii]

I found this video when KZbin 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

[@definitelynotadragon]

THIS

[@hj8607]

watching this video drives you to use mind blowing drugs ? understandable .

[@willsweeny8903]

this is exactly my story too...

[@josha2828]

Same

[@pi314159265358978]

I came here from the latest Veritasium video. For me this is a much more intuitive way of thinking about the behavior of the cart. Thank you for this nice demonstration.

[@charonme]

how did you find this? It took me several days of googling to finally find this gem after seeing the Veritasium video

[@pi314159265358978]

@@charonme I started with the "spool riddle" that I remembered existed, but the spool seemed a bit too simple. I searched "cart faster than wire" and this was the 3rd result on YT.

[@charonme]

@@pi314159265358978 nice!

[@bryanjackson8917]

Intuitive, but wrong. The only reason the cart moves faster than the ruler here is because it is being forced to move contrary to how gears work if allowed to move freely.

[@pi314159265358978]

@@bryanjackson8917 Why would you say wrong? That's the feature not a bug. The cart in Veritasium's video has a rotor that is also "being forced to move contrary to how" the wind would normally turn the wind turbine. This is a direct analogue to it. It just uses a different medium - i.e. a solid ruler instead of an air.

[@EchoBuildsThings]

Here from Veratasium! Such a soothing video :) This will totally blow up once the algorithm catches his video and sweeps it away

[@tomharding]

You have a remarkably calming voice.

[@Skull_Gun]

Get this guy an audiobook contract at once!

[@Jedlmind]

Many of us would appreciate a video of you explaining this phenomenon in detail. Great demonstration!

[@WoodenPotatoes]

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

[@seanattikus]

It works because the ruler is moving the whole cart, not just the top wheel. The ruler moves to the right, pushing the cart to the right; the little wheels move clockwise, the big wheel moves anticlockwise, which pulls it along the ruler faster than the ruler because of simple gearing. To understand the unexpected direction, you have to stop thinking of the ruler as another wheel in a system of gears. Instead, think of it as an object that is pushing the whole cart via the top wheel

[@NithinJune]

terry is the real hero of this story

[@coolaun]

Well, that's what George thought...

[@NithinJune]

very nice Anyone else from the veritasium video?

[@TheSLK66]

Omg! I watched this many many years ago and now veritasium revived it!!

[@wecksell]

Yes, this video should be linked.

[@Everfalling]

As soon as I saw the Veritasium video I immediately thought of this video. I donno when I first discovered these but it’s been years

[@Masterfortinero97]

Wow, this is the same device that Vertasium used recently!! And to justify the downwind car!! It seems the same debate already took place 12 years earlier :O

[@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.

[@Aheitchoo]

The real way to explain "Faster than the wind directly downwind"

[@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]

The wind is not affecting all the vehicle to the same amount. It is mainly affecting the propeller: the rest of the downwind cart offers very little resistance to the wind. Since the propeller is turning (being geared to the wheels), is is interacting with the air even when the cart is moving at wind speed. When the cart has reached wind speed, the propeller is producing forward thrust that accelerates the cart to above wind speed. The cart reaches equilibrium at a speed above that of the wind.

[@coolaun]

Have a look at "Under the ruler 3: tilting the ruler" to see what happens when the ruler is actually tilted.

[@Walkabout19]

The pacing of your narration is masterful.

[@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.

[@puppeteers420]

weird, yet extremely cool, im defiantly adding this one to my favorites. thanks man

[@dcorman]

This is fun, until one realizes that the ruler is not, in fact, moving in the same direction relative to the apparatus as it is to the observer. Once you realize that, the illusion is broken.

[@Rick_Cavallaro]

A brilliant demonstration. Very well done.

[@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]

The ruler pushes one way, the paper pushes the other way. The way this cart is geared causes it to move faster than the ruler. With other gearing, you could make a cart that goes slower than the ruler, or in the opposite direction.

[@treatb09]

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.

[@mahmoodkharsa6454]

+Bo Huggabee where did you get the one in between from ?

[@treatb09]

Mahmood Kharsa what?

[@mahmoodkharsa6454]

+Bo Huggabee "having two gears with one in between" what is the one in between

[@treatb09]

Mahmood Kharsa i still don't see your point. take two gears, an put one in between see what happens...

[@mahmoodkharsa6454]

if you are referring to the ruler and the two small wheels to be the outer gears then the outer gears are supposed to rotate in the same directions... but they are not .. look closely .. the small wheels are rotating the opposite direction ... listen all i could say about this, that it's a friction game .. the ruler are pushing all the cart in the same way .. it isn't supposed to do so .. but because of a trick in his movement it does .. btw i hope my english is fine because i have an ielts exam soon hhhhhh.

[@trekgeek1430]

Here's a great way to visualize it. Imagine your computer screen is rotated 90 degrees. Now it appears the table is a wall. The ruler is another wall. The cart is stuck between the two walls and under the force of gravity, falls downward. When you visualize it as such, this is the only function that makes sense. In this configuration, the behavior is intuitive.

[@coolaun]

Civbert1, that's a good clear explanation of the analogy. Apparently more is needed, though, to convince the skeptics. I think some of them won't believe it until they are passengers in a DDWFTTW cart feeling the wind on their faces. And even then there will be some who pretend that they're being tricked...

[@bgizcool]

This guy has an amazing voice. Please keep making more videos!!

[@Karkenou]

Your voice is so soothing! You would make an excellent educator!

[@karlsan6397]

I wonder is we could use this to prove that you can build a car that powered by the push of the wind and goes faster than it. 🧐

[@IDoNotLikeHandlesOnYT]

Veritasium's second video on that (a couple of weeks ago) uses exactly this demo for exactly that.

[@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.

[@RobertWarrenGilmore]

Coolaun! Where did you go? I would love to see more videos.

[@peterawesomeness1]

He ran out of cotton reels.

[@ramanmono]

George is so attentive, but just like me gots it wrong and this blows my mind.

[@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').

[@treatb09]

AlephNeil there are two types of people. i can see this and understand it. there are those who have to explain this with numbers and math or it doesn't make sense. the one who can do both, owns this reality…..

[@zestyping]

Very nice breakdown! Each step follows logically and leads to the answer.

[@coolaun]

To make such a machine, look around and see what you can use! I first found the two cotton reels, where the radius at the middle is about half that of the ends. Then I looked for bits of construction kit to make a very simple chassis, and added the third wheel. It's important that there's enough friction between paper, wheels and ruler so that the wheels don't slip: a wooden ruler and cotton reels are better than plastic ones and the rubber tire on the blue wheel has a good grip on the ruler.

[@jasminamuffin]

thank u tichy this vid is 10/10

[@toastednoodle1996]

The animals giving different answers is super cute

[@coolaun]

Of course a slight downward force is necessary to ensure that there is no slippage between wheel and ruler, but that's not what determines the direction of movement. The direction of movement of the cart is determined by the direction of movement of the ruler. The people who compared the ruler to a straightened-out gearwheel have understood this correctly: the ruler engages with the blue wheel just like the rack of a rack and pinion gear system.

[@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.

[@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.

[@ColinLevy]

Really enjoyed this.

[@chewinggum2001]

I LOVE this man's voice

[@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.

[@HerbalJah]

Can you make more videos. Your voice is so soothing... lol i get like a pressure in my forehead/center of head when i listen to your voice explain things that feels so good... others seem to agree! (Its almost feels like an opiate, your voice that is!)

[@David-bc3nj]

Best video on KZbin

[@corriscant]

Magic... i know how it work now, but it still looks magic )

[@kylezehmahn]

I literally come back to fall asleep to this video all the time. I don't think I'm alone.

[@thefreemonk6938]

Here from Veritasium. Thanks to him that I came to know about this good video.

[@JimNifter13]

Cool! Did not expect the last one...

[@coolaun]

Absolutely right. It's fascinating that such a simple mechanism can produce such a surprising result. It's really no more than a gearing mechanism to convert a movement into a faster movement, just like a bicycle or an egg whisk, but somehow the way it moves doesn't correspond to what instinct or "common sense" leads us to imagine.

[@diezel157]

i think the use of teddy bears in a video is actually pretty funny,but a very fascinating video,also available on iTunes

[@planetofthescums]

@nitaell To clarify, you asked what the point in all this was, and it is to show certain people that they do not know everything. I don't need to be harassed for answering your question.

[@ajpal]

Say the small wheels couldn't spin. Moving the ruler to the right would just drag the contraption to the right at the same speed because of the friction between the ruler and rubber wheel. But the wheels CAN spin, so it gets dragged to the right at the same speed, which spins the small wheels clockwise, which spins the big wheel counter-clockwise moving it even further to the right.

[@RouletteRog]

This is a cool video. I'll be bookmarking it to show to some of my physics major friends.

[@teslapower220]

@coolaun Exactly. If b=a, the no slip condition will not work unless the ruler is not moved at all.

[@coolaun]

arctic, you're right that the important thing is the relation between the rims and the shafts. However you wouldn't get the same result by running the ruler over the shafts: the essential function of the large wheel is to reverse the direction of rotation (its size is irrelevant). You'd get the same motion without this wheel by running the ruler _under_ the shafts (like in "along the paper faster than the paper"). Running it over the shafts will make the cart advance slower than the ruler.

[@pkuky]

they gave us this in physics camp (without showing the end) and asked what was going to happen. only one person managed to explain why.

[@kylezehmahn]

I watched this twice. The second time I just listened to his voice. This guy should be a voice actor.

[@blacksilkblacksilk]

Where have you been when I had my gear classes back in engineering school ? Great vid. TH & * * * * * Take care and have a nice day silk ;-))

[@coolaun]

Since a few people think I'm tilting the ruler to push the cart to the right or to the left, I made a short clip to show that it's not the angle of the ruler that determines the direction of travel. See "Under the ruler 3: tilting the ruler".

[@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.

[@Frabjous1]

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

[@besgeo]

what i meant to imply was that the angle of the ruler was probably an indication of you pushing down on the machine to increase the friction of the wheel moving against one another, though i havent quite thought about the gear ratios yet haha

[@coolaun]

Phantom61994: If you read through the comments, there are many that should help you to understand. Here's another way to demonstrate the same principle (it also makes a nice brainteaser for a physics class): if you have a bicycle, put one of the pedals at its lowest point and tie a string to it. Now, with somebody else holding the bicycle steady, pull *backwards* on the string. Which way do the pedals start to turn? Which way does the bicycle move?

[@yuvraj7214]

Let the comments begin!!!

[@coolaun]

Thanks: your analysis is correct. You could also make a cart that goes in the opposite direction by turning this one upside down. This particular cart isn't stable upside down: maybe I'll make one that is :)

[@coolaun]

When we look at the big wheel rotating, it seems we automatically take the cart as reference: our eyes move with the cart. You can see the same effect if you watch someone riding a bicycle. Look at a pedal in the bottom part of its circuit, as it passes the lowest point: it seems to be going backwards. It is indeed going backwards relative to the bicycle, but it's going forwards relative to the ground.

[@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.

[@DoriSmori]

The awesome moment when Terry is the same little monkey toy i still have since i was 5 :') made my day. WAY TO GO TERRY

[@MoRic76]

I got directed here from the podcast - you've blown my mind. I tried to build this in the Playstation3 video game "LittleBigPlanet" last night (a game where you can create and play with your own (and other peoples) Physics based machines and levels). It was driving me nuts to try and replicate this, but I think I have it figured out... the key to this is the shape of the Cotton Spools... the shafts will spin slower than the wheels (reduction gear?), causing it to move forward. Try again 2nite.

[@Sarevok12778]

The ruler acts as a "gear" as well. Ruler goes right, wheel goes left, spools go right. Since the spools are smaller, they must turn faster than the ruler moves. It's a simple problem really, what is throwing people off is the fact that the ruler is straight rather than a wheel like a normal gear problem.

[@assman1337]

it all has to do with the spools on the bottom. the part of the spool touching the ground has a larger radius (assume 2x) than the part touching the big wheel. this means the wheel only rotates at half the speed of the spools. so when you move the big wheel instead, the spools move twice as fast.

[@shreepoornasrao]

Thanks Veritasium

[@teslapower220]

@coolaun When you use Vc=Vr*b/(b-a) you're assuming that Vr is non-zero, AND the no slip conditions that you used to derive this hold. Then, you get infinite speed. Both are not possible simultaneously however. If you calculated everything in the frame of the cart, you'd get V1=V2*b/a where V1 and V2 are the speed of the cart relative to ground and ruler respectively. If b=a, V1=V2 , which is Vc = Vc - Vr or Vr =0. Thus the ruler cannot move if the no-slip constraint has to survive.

[@thecrusadingdebator]

I think that the energy he needs to exert down on the ruler to generate friction between the ruler and the cart makes it impossible for the big wheel to spin either way. But when he moves the ruler, that friction causes the cotton reels to roll, and once the cotton reels roll one way, the other wheel rolls the opposite way, at the same speed, but due to their size differential, the big wheel turns the little wheels much faster then with just the ruler pushing. Explained.

[@spammmy]

This is the most important footage of all time

[@onehundredpercentice]

Look at his other video, "Under the Ruler 3: Tilting the Ruler." He shows in the video that tilting the ruler does not determine which way the cart will move.

[@SuperToastytoast]

My theory is that he may have put pressure on the ruler, canceling the big wheels spin and as he moves to the right, the prussure and movement will make the bottom wheels move in that direction, turning then big wheel the opposite, so it's as if it is an illusion

[@coolaun]

Yes, that's right. That means that If the speed of the ruler is V, the speed of the cart is (c2/(c2-c1))V.

[@nadahere]

I made a general statement regarding ratios of gears/wheels their velocities, power transfer and non/functionality. I should have clarified that if the center wheel was small the ruler might not be able to transfer enough force to make the device work. Ergo, even the center wheel contributes to making this device move faster than the ruler.

[@herecomemacOnTT]

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

[@aleksandr_berdnikov]

A rule of thumb approach that simplifies such puzzles a lot is rephrasing the question from something like "which way car will move if the top of the wheel is pulled forward?" into something like "during which way movement of the car the top of the wheel would move forward?", it makes it quite more straightforward in my opinion.

[@zakkhartwig]

This could have some interesting applications!

[@ericstarmer]

Would I be correct in thinking that if you "bent" your ruler into a circle around the device, then rotated it, it's equivalent to a planetary gearbox, with the associated gearing effects? If so, this helps me understand DDWFTTW as a means of "gearing up" the vehicle speed relative to the windspeed. It would then be equivalent to holding the central sun gear (ground) fixed, and rotating the ring gear (wind), with the result that the planetary gears (vehicle) travel faster than the ring gear.

[@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.

[@audiofile8311]

the absolute OG

[@coolaun]

@StargateMunky I've already done that. Have a look at "under the ruler 3: tilting the ruler".

[@wa0000]

Confusion arises from the expectation that the direction of the big wheel's rotation is dependent upon the direction of the ruler's motion. That would be true if the big wheel's position were fixed in space by an axel on brackets, bolted to the paper -- but not if the big wheel is free to move, as it is. The ruler pushes the big wheel, spinning the little wheels, which turn faster because they're smaller, which moves the cart against the paper, and against the ruler (in the same direction).

[@Skelymage]

hm... I never thought that would happen. I have to admit, i have never seen anything like this before. I just can't put my finger on it. I have to try this out. its so interesting. Subscribed.

[@coolaun]

It's not a question of a difference in friction. There is enough friction both between ruler and big wheel and between small wheels and table so that in both cases there is no slippage. It would work just as well with rack and pinion gearing. The speed and direction of movement is dictated by gear ratios. In fact the big wheel could be any size: the important relation is that between the radii of the cotton reels at their edges and at their centres.

[@PasDeMD]

Make sure the thickness of the bottom wheels is very small. (look at the shape of a spool of thread, the ends are very thin and wider than the inside)

[@aRi9977]

Perhaps, if you implemented that system into a dynamo, with the outside physical force as the ruler and the the coil or magnet as the cart you could harness far more kinetic energy and thus produce a higher voltage?

[@JinGwee]

who else came here from veritasium's video

[@WizDaPenguin]

Me

[@Hankxc]

To Lightening Rose, how can wind do work on a device moving faster that the wind? One answer is that the parcel of air on the inclined surface of the prop moves BACKWARDS relative to the cart, reducing its speed to less than that of the wind.Thus the wind can push on it this parcel of air and add power.Power added = (force in a given direction)X(Velocity in the same direction).The wind does work on this air pushed back by the prop to compress it. the compressed air, in turn, does work on the car

[@Luclecool123]

Veritasium team here !

[@ramanmono]

Yayyy

[@EpiX7]

what the actual that broke my brain please make a video explaining the physics behind this

[@hareecionelson5875]

I found this video through veritassium. If you want an explanation, watch veritassium's videos on going faster than the wind, it was controversial when it came out at a year ago

[@coolaun]

The paper is indeed pushing the cart forwards, just as the ground pushes a car forwards. When the wheels of a car push backwards against the ground, the ground pushes forwards against the car. if it didn't, the car wouldn't move forwards.

[@hermannpaschulke1583]

I'm here because of veritasium's video :D

[@tanakatarou7615]

It's funny reading all the comments posted by people who can't accept the physics behind it and trying to disprove the theory. In my opinion this is an excellent video, explaining in a way which is certainly not boring but actually very interesting. And you, coolaun are the perfect person for making these types of videos. Please make more! Also, to everyone that is saying "it's counterclockwise": that is American English. Anticlockwise is British English. Counterclockwise sounds weird to me.

[@Stormgebieder]

Got here thanks to Veritsasium's "A Physics Prof Bet Me $10,000 I'm Wrong" video. Too bad I discovered this channel so late.