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Bicycle Riding on Square Wheels
Roland Piquepaille writes "Before starting our long working week, let's relax with this story of a bicycle with square wheels. No, it's not a joke. And it even rides smoothly. But there is a trick: the road must have a specific shape. The Math Trek section of Science News Online tells us more about this strange bicycle -- actually a tricycle with two front wheels and one back wheel. Read this overview for some excerpts and a picture of the tricycle, or the original article for an additional animation."
I'll bet it stays smooth on turns. :P
I'll get right on that change-the-shape-of-all-of-the-roads project right away ...
Wasn't this the technology The Daleks used to climb stairs?
The reason the trike has smooth motion is simple - the centre of mass (where the axle is attached) doesn't move vertically. It's exactly the same reason as for a hoop rolling on a plane surface except the hoop is more obvious.
When you turn, the square shape doesn't fit so well, so the c.o.m oscillates vertically, and you get a more bumpy ride - the larger the angle you turn through, the worse the fit, and the bumpier the ride. Wheels (round ones) don't have this turning problem so much; my vote goes to the round wheels
I remember doing a 'Granada power game' (schoolkid teams are set problems to do, and compete to produce the best solution). For the challenge in the year we took part, we had to construct (entirely from cardboard) a device that would travel forward under its own power for 5m, turn through 45 degrees, forward 1m, turn back through 45 degrees and throw a ball-bearing into a target, accuracy being rewarded. There were 2 walls at given positions that you had to get over as well, at 2.5m and 5.5m from the start. We just cut slots in our wheels - there were some really outlandish solutions to getting over the walls though
Simon
Physicists get Hadrons!
they did re-invent the wheel, not a good invention though...
See picture here
:)
Ya yew betcha! I wonder if that basket on the bike is to hold the hot dish? Only in Minnesota would we spend the time determining if square wheels would work... Perhaps from the potholes on 494?
I reside in Minnesota so I am permitted to make these important scientific observations
Perfect for Michigan roads.
I rode one of these at COSI (in columbus, ohio) maybe 10 or 15 years ago. Pretty cool idea, but I always thought that turning at intersections would be kinda hard....
Why does teh blog theme look almost exactly like Groklaw????? Should Pam stop observing IP lawsuits and get involved?
Great!
Now all we need is to lay some curved roads all over the place, make loads of these bikes, and we can all ride bicycles with square-shaped wheels!
I'm calling my Senator right now!
I hear there's rumors on the Slashdots
The successor to the overly hyped Segway?
Wheels? Who needs wheels when rhombuses work perfectly fine!
Nothing disturbs me more than blind loyalism towards some unrealistic and over-idealistic notion of one's nationality.
Being a bit of a bike nut I notice this bike would have some issues with turning and fixing flats. Notice that massive saddle (probably gel.) The closest i could find to a real world application of this would be cog trains which have existed in europe for probably a hundred years (notably in the Alps.)
Isn't this kinda light-weight for slashdot? I mean, where's the tech angle?
Maybe I could wire up my Zaurus as a trip computer.
A feeling of having made the same mistake before: Deja Foobar
The question at the bottom that states they don't have a wheel the same shape as the surface, I tend to disagree, wouldn't a common circular wheel, while going over a steep hill both be circular shapes? What about tank tracks? They are both flat? A flat wheel and a flat surface = the same!
Mod +5 Drunk
It's the next Segway!
literally
An Indian-American Hindu committed to non-violent thought/speech/action alarmed by the global explosion of radical Islam
Will be be seeing pentagonal wheels or maybe even octogonal wheels? Or better yet n-gonal wheels where n is an incredibly large number?
EVERYDAY IS CATURDAY
This is basically the same principle as the odd-shaped pieces in your old Spirograph set....
We'll have your anger management class booked for later in the week. Please enjoy the complimentary tranquilizers.
It's good to use your head, but not as a battering ram.
This story is almost as interesting as the latest case-mod story or the latest news about the state of the Linux x-box port.
I wonder what shape my wheels have to be to ride smoothly over the screwed up roads that my town refuses to fix?
Today in the news: Inventors discover new way to make road construction ( and repair ) even more expensive....
He's working on a water powered car I hear... just requires a really big hill.
No word if the car will support square wheels or not.
...but does it run Linux?
Orginally posted in '98 only updated in 2004. Isn't that a little bit old news? But you get used to that on slashdot :-). It's a cool concept but most people could find that out, you don't need to finish univerity for that I hope.
"for just about every shape of wheel there's an appropriate road to produce a smooth ride, and vice versa.
surely Mr Wagon(!), you have never driven on Indian roads!
I had a life before I got karma
...obviously you'll need a square drill.
Economics
"The following theory assumes there are no external factors"
External Factor = People
Sociology
"The following theory is based on a majority sample"
Majority = 50 in a sample of 99.
Slashdot
"The following company/technology categorisation is correct given the sample data"
Sample data = Slashdot
And now we have
"The following design is correct for a given definition of road"
Reminds me of the old maths joke
"1+2=4 for sufficiently large values of 2 and small values of 4"
An Eye for an Eye will make the whole world blind - Gandhi
A catenary is the curve describing a rope or chain hanging loosely between two supports. At first glance, it looks like a parabola. In fact, it corresponds to the graph of a function called the hyperbolic cosine.
Yeah, I always get those confused...
[frink]Oy, with the wheels and the squares and the riding and the graphing, ng'hey, glaven.[/frink]
I want to drag this out as long as possible. Bring me my protractor.
And I was always told that was the wrong approach to use.
"It's the height of ridiculousness to say for those 9 lines you get hundreds of millions."
Seems to me this is a good analog to proprietary file formats. Instead of having people pay tolls, maybe the government should build roads with inverted caternary bumps and sell the square wheels!
Where's the squirt gun that shoots grape jelly?
Where does the school board find them and why do they keep sending them to ME?
How many roads do you have in where you live that has perfect bumps in it?
Also, steering with this would be impossible. Basically, this goes in a straight line only.
And, this is good food for thought. Perhaps this priciple can be applied to other things.
I just realized that any geek cred I thought I had was just an illusion. I don't ever want to hear jokes about Emacs again. Understand?
Dewey, what part of this looks like authorities should be involved?
"So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel."
That backwards tricycle sounds like the Buckminster Fuler's Dymaxian Car. That beast was designed for minimum air resistance. Also having the two wheels in front provides better stability when cornering during hard braking. Still, tricycles do have some roll-over stability problems because the CG is closer to the sides of the wheelbase.
Two wrongs don't make a right, but three lefts do.
Why those people , who drive like crazy on the roads, drive like so....it's the road stupid, not the driver.
for the last time people, I am "frodo from middle eaRTH", not "middle eaST".
I've seen the South Park kids travel to French Canada. They have square wheels on their bicycles as well as their cars. I really don't see what the big excitement is all about.
They should have used triangular wheels. One less bump.
Think about it. What happens to a n-gonal shape as n approaches infinity? Starts looking like that round shaped wheel I have on my car already!
I mean, how many people clicked that link and thought "how to make a square wheel work?" and then thought "Well, make the road humpy do that the corners of the wheel match the depressions"
This is not news. This is anti-news.
While a mathematical solution is technically perfect, I can think of an easy way to determine the requisite road shape: use a square wooden block, cut a hole in teh center so you can roll it, then do so over a reasonably soft surface. You can even observe how the shape of the catenaries elongates as the rotational speed stays constant but the horizontal velocity increases. Would be fun for downhill rides. :)
Every college physics class has one day where they talk about this,where the road is lumpy in a specific way, and then the bicycle with square wheels can drive. You know what else has a smooth ride? the space shuttle crawler. If you weigh enough, you just crush anything that would otherwise be a bump. I'll be happy when I see a vehicle besides a tank whose method of ground contact changes shape to accommodate for the road (i.e. tank tread on a bicycle). That would be sweet!
http://www.fulcrumgallery.com
stuff |
I rememeber back in 4th grade my school took a field trip to the boston science museum and they had one of these. Im in college now. Thanks for keeping up with the time slashdot.
I was wondering when someone was going to get around to improving the wheel. The current version is so impractical, inefficient, and has such a limited range of applications it has been screaming for a face-lift. Someone get this guy a $250 million research grant ASAP!!!
Random possible application of this otherwise pretty useless idea: maybe it's easier to ride than a bike with actual round wheels, for [insert obscure technical reason here]. Maybe they could have gyms or something where toddlers or really young kids could get the hang of how to ride a bike. Or at worst they could be used in an amusement park or something. Ride a bike with square wheels! Fun! Or whatever.
Jokubonis Square Wheel (from crank.net)
this has been there for years. I two classes with Wagon, one 5 years ago, one 6 years ago, and he brough the square-wheeled bicycle up in both, repeatedly in the calculus class.
having taken a spin on it once a few years back (I think the original bike was two wheels in back, one in front; didn't work so well that way), I wasn't particularly impressed. it's a neat concept/fact and to see it in action was interesting for all of about 15 seconds, even as a math major, which I was.
Now if only the train to Chicago didn't run 1/3 as fast as the train to New York and leave 2 hours earlier.
Stan Wagon, a mathematician at Macalester College in St. Paul, Minn., has a bicycle with square wheels. It's a weird contraption, but he can ride it perfectly smoothly. His secret is the shape of the road over which the wheels roll.
...
Is it me or do others find it amusing that a chap researching vehicles with square wheels has a surname "Wagon" ?
nick
Electronic Music Made Using Linux http://soundcloud.com/polyp
Dear Esteemed Committee: I would like a million dollar grant. As a good geneticist I am going to see if I can cross a cat with a canary. I will call it "cantenary"! (Since you refused my grant for the monkey with four asses research) Part bird and part cat--that is something useful. Regards, Dr. Mephisto...
Harpo Tunnel Syndrome--my wrist feels funny.
A Wagon with square wheels.
-Patrick
"They never stop thinking about new ways to harm our country and our people, and neither do we."
It actually has 1 front wheel and two rear wheels.
My beliefs do not require that you agree with them.
The best ones conform the invention's design to fit the environment, not the other way round.
They say the first thing to go is your penis. Well, it's either that or your brain. I forget which...
hey-the brakes will be killer though.. It is the only thing I c that is better than the original invention [ round wheels ;) ]
This coin has 7 sides so you wouldn't expect it to roll smoothly.
However, they are cleverly made so that the diameter is equal right the way around the coin. Therefore, since the center of mass doesn't move, the coin will roll smoothly in slot machines etc. Try it!
I'm not sure whether the 50p is the same or not. I don't have one in my wallet to test as I used it to buy a packet of wine gums...
MMmmmm wine gums...
Imagine coming up with pneumatic tires for such a thing. I suppose they'd need to be tubulars, as a clincher simply wouldn't work out. Then there's the non-uniform pressure, which means some parts of the tire wear out faster.
The real engineering isn't these catenaries, but try making an actual usable vehicle from them.
I'm sure Wankle started out something like this.
A feeling of having made the same mistake before: Deja Foobar
wow, looks like the furrows in a field, if you had a large rectangular solid, you could move across a field without disurbing the furrows.. hmm, wonder if there is something useful in that idea.
meh
I believe it's still sitting in the basement-level lobby of the Olin/Rice building at Macalester. You can just walk up and give it a ride.
In practice, it doesn't work perfectly: the wheels slip a bit on the upslope. But if you get a bit of speed, it rolls along nicely! Quite fun.
Also neat is the Reuleaux Triangle that is not round but even so has a constant width as it rotates. If it is used as a roller between two planks, it will roll smoothly and the distance between the planks will remain constant. This java applet demonstrates it.
Standard gear and rack interaction is well understood. Racks are usually straight-sided, while gear teeth are involute curves. Two gears which will mesh with the same straight-sided rack will mesh properly with each other. This fact reduces the size of simple gear inventories from O(N^2) to O(N).
"Mesh properly" has a specific meaning. There has to be contact on both sides of each gear tooth when the axes of the meshing gears are a constant distance apart. Getting this right improves gear life by orders of magnitude.
There's a nice little section in the back of every Boston Gear catalog which explains all this. Available online, too.
Nonstandard rack shapes are rare, but not unheard of. The drive system on the IBM RS-1 electrohydraulic gantry robot used a curved-sided rack.
Says Who?
the square bicycle could only ride straight line... predetermine road track... well... does that sound like a train to you? have the inverted thigie lay-out in straight - but it can be curve to left and right a bit, put the bicycle or a bicycle with an engine with it, get it to drag some coach at the back, and it is a new train design. :-)
--
baganjermal[at]gawab[dot]com
So, I guess a speed bump on that type of road would simply be a flat surface. :-)
Where I live (here for anglophones), the roads are bad enough in the spring that we could probably all ride on square wheels. There is even talk of having an International Pothole Festival here right before Jazz Fest!
way
too
much
time
on
his
hands.
Ok, I'm risk asking this, but by definition, a "wheel" cannot be "square...."
wheel
n.
1. A solid disk or a rigid circular ring connected by spokes to a hub, designed to turn around an axle passed through the center.
And, without pasting it too, a disk must be circular....
So, whatever those things are on that bicycle frame, they are not wheels
"All great things are simple & expressed in a single word: freedom, justice, honor, duty, mercy, hope." --Churchill
For roads filled with speed humps!
Free Firefox news reader.
On any other kind of road I think I'm going to be needing a cup for this thing. And I don't mean the drinking kind, either.
The bike in the article is a trike (i.e. three wheels). Riding one of this would be no different than riding a normal trike. There would be no advantage - it may actually be counterproductive to teach someone ride on a two-wheeler with square wheels. That's much harder than normal wheels.
Do mathematicians have to justify the purpose of their paper/research in the papers they publish? If so, I would be interested in reading it for this project because he would have to be a damn good English professor as well to pull that one over the eyes of the committee. :-)
EvilCON - Made Famous by
This has been around for a long time. Square wheel, round road. I remember an exhibit at a nearby museum (no not the san francisco one), when I was a little kid. That guy had gotten the idea from someone many years before. It probably goes back more than a century, but I'm too lazy too look it up.
::sigh::
Now a wheel the same shape as the road, that would be cool.
Square wheel. Round road.
Upstairs Dog, Downstairs People.
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians.
Umm, since our existing roads follow the curve of the earth, I'd say this challenge has been met already. It should be re-worded to add that the shape needs to be of equivalent size.
while sco {
wget -O
}
20 or 30 years ago (i searched the web, sorry, couldn't find) honda (an engineer there, for an internal contest) built a bicycle with square wheels that rode smoothly on a flat surface. It worked with a cam on the swingarm, so the axle could move up and down while rolling, and the bike frame (and rider) stayed level. I'm sure the center of mass also moved.
I am intrigued. What the hell are 'wine gums?'
Comparing it to Windows will be a moot point, since El Dorado is going to have a 40% larger code base than XP.
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians.
/T
ehh... how about a cog-wheel against a rack?
IMAGE
Warning: This sig contains a small bug. ==> *
I sure hope Stan Wagon comes to New York and tells me which frigging wheels I should be using, I can never get a smooth ride in the Big Apple's "roads"
ok, as we all see, you CAN try to reinvent the wheel.
But one question should be allowed: Are there any advantages of using a square wheel on a strangely shaped floor?
Something like "lower friction" or "less energy consumption" compared to a standard wheel (the circular one, you know...)
So what is the most energy efficient surface-wheel combination to get ahead? Are there differences, is a square just as efficient as a wheel?
For next gen mega SUVs.... "When GM starts using square wheels we will able to corner the market...." Said a GM spokesperson.
Why the Mac Weekly had it (well in photo form at least) in Feb.
YES! Finally a way to take the speedbumps as fast as I want!
The coin doesn't have seven sides, it's flat like a normal coin, just "septagonal" in shape. When you said seven sides, i was thinking of a more three-dimensional coin. Would be a pain to keep in your pocket, I'd imagine...
This concept was on exhibit from about 1994-1997 at Omniplex Science Museum in Oklahoma City, OK (http://www.omniplex.org). They still have the exhibit, but it's not currently on display. It was called the "Irregular Tricycle".
Be very, very careful what you put into that head, because you will never, ever get it out. -Thomas Cardinal Wolsey
My town's roads have so many potholes, the square wheels might just be the solution I have been searching for...
"First you get the Linux, then you get the power, THEN you get the women"
From the article:
:-)
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians
Well, how about a road that goes straight around the globe. Ride it with normal tires and you get the same shape for road and wheel: a circle.
Ok, next please
If 4 wheels needs small hills to run on.... lets add a side so we have 5 sides. 5 sides will need smaller hills saving material in the rebiuld the road project.
And if 5 saves materal lets keep adding sides... 6, 8, 20, 100, 1000. Imagine how small the hills will be... we don't need to redo the roads as much.
Infact if we keep adding sides... we'll get.... a circular wheel... with no need to change the roads.
Well. That was easy.
Does the rate of forward motion vary or stay constant, assuming the wheels turn at a constant rate? It would be interesting to ride a bicycle whose wheels turned at a different rate depending upon which side was touching the ground; even more interesting if it had a fixed gear and your legs had to match the varying angular speed of the wheels.
---
Find out more about the impending downfall o
In order... to pay to your $699 license charge, the male it is the chicken teabaggers which smokes.
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians.
Seems to me you could ride a bike with circular wheels on the inside (or outside) of a circular track (2001 space odyssey-style). The wheels and road would have the same shape then, right?
Read my keyboard review.
What you're talking about is, in essence, a suspension system. Which is used to overcome a rough ride. What you're all trying to say is "The smoothness of a ride is determined by how much axle movement is passed along to the rider". Or something like that.
'Standards' in computing only impress those who are impressed by things like 'standards'.
Stan Wagon, a mathematician at Macalester College in St. Paul, Minn., has a bicycle with square wheels.
So it's a Wagon wheel?
actually a tricycle with two front wheels and one back wheel
I see one front wheel and two back wheels.
Hmmm, with the number of speedbumps there are today I'm not sure what would be the smoother ride on the road.
I remember a few years back there was an exhibit on precicely this at the Boston Museum of Science. They had a four-wheeled car though, rather than three. One could sit in it and pedal it back and forth along a short piece of track they had constructed. I was extremely surprised at how well it worked and how smooth it was. It would have been impossible to tell that it wasn't a wheel on flat pavement without looking at it. A nifty trick indeed.
"I may disagree with what you have to say, but I shall defend, to the death, your right to say it" - Voltaire
Here is the conclusion of the article.
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians.
Well, if you consider earth circular (albeit spherical), bicycle wheel and earth already have same shape....just different scale!
What if the wheel were not radially semetrical? Imagine it being flat on one side and then having a curve on the other side, sort of like a half of a pizza (although probably with catenary curves). If the road was then made of flat surfaces alternating with curved surfaces, could the wheel be aligned such that the curved surface of the wheel rides on the flat surface of the road, and vice-versa?
The physicists and mathematicians can decide whether that would really work. It's just the first thing that came to mind....
This is the kind of shit "research" that makes scientists look bad! This should not have been taken any further than the guy showing his grandson a "neat invention", and he should certainly not make it! What a waste of time.
Alrighty. Square wheels that ride smooth (on a particular surface). Round ones will ride smoother and be able to turn if they are large enough. And just for arguments sake, let's say some jackass wants to build a bike path for the "elite who can afford square tires". What happens when debris gets on the path, or the path starts to wear down, or ..., or...
It must be nice to waste time and money on impractical b.s. such as this.
So when should we be expecting the square wheeled Sewgay?
"actually a tricycle with two front wheels and one back wheel."
Really.
When I look at the accompanying photograph, I see one front wheel and two back wheels. Although, I suppose the back wheels could be the front if he's riding backwards....
--Insert catchy
Reminds me of a short story, by JG Ballard, called "The Subliminal Man" (I think), set in the future. Where the roads are layed down with a specific pattern of ridges and bumps. Your tyres would need to 'match' these, otherwise the vibrations would become unbearable. The only catch is that they replaced the road surface regularly, requiring you to replace your tyres, before your car shook to pieces.
My UID is prime!
sounds plausible to me.
try { do() || do_not(); } catch (JediException err) { yoda(err); }
-- All views expressed in this post are mine and do not
-- reflect those of my employer or their clients
should also work on such an inverted catenary surface. Seems just a matter of getting the wheel's cusped angles to match that at the trough in the catenary. Should work for n-gons, n > 2.
To-do List: Receive telemarketing call during a tornado warning. Check.
I think it's already the case :
The average car tire, is round.
And, according to current scientific beliefs, the world on which these cars drive isn't flat, but is round too.
...unless you still believe that our world is Disc shaped, and is sailing thru space on the top of a giant turtle called Great A'Tuin.
"Sufficiently advanced satire is indistinguishable from reality." - [Tips: 1DrYakQDKCQ6y52z6QbnkxHXAocMZJE61o ]
Unless he's riding this thing backwards I'd say it clearly has two rear "wheels" and one front.
This brings to mind a cool exhibit in the Chicago Museum of Science and Industry. In one of the stairwells (not the one with the slices of human body, nor the one with the Focault Pendulum!) there are these really cool mechanical demonstrators you power with a hand-crank.
One has square gears - the two gears mesh so that the apex of one hits the center side of the other and vice-versa as they go. The center of mass (axis of rotation) never moves. They also have elliptical gears that do the same thing.
There are other fascinating things there that transfer motion; screws, rods, axles, etc. Even a replica of Hero's Aleopile (sp?) steam engine, but the thing I remember most is those incongruous square gears!
-- You are in a maze of little, twisty passages, all different... --
I don't know how, I just know that no Tech article on slashdot is complete without someone ignorantly declaring said technology's promising future in enhancing cellphone functionality.
It's just a little too obvious.
But, what would be a cool adaptation of this, would be to have an active suspension that with those same squares wheels, you would be able to ride on a level surface. (Hint: the wheeles would need to move up and down in the same pattern as that shaped "road")
From the article:
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians.
I don't get this part. A wheel is a small closed shape, you go once around it and you're back where you started from. On the other hand, a road has to GO somewhere along the ground - if it was a closed shape suspended in the air then you would fall off when you come around to the bottom side of it - so of COURSE they can't be the same shape - one has to have open topology and one has to have closed topology.
The only way to get around this, really, is to use the whole earth. Pave a road all the way around the earth in a circle - it will require some bridges for the water, and it will require some risers to make the road circular when the earth is eliptical - but hey, we're talking theory not practice - so let's pretend we have the money to pull this off.
Now, you have a circular road. Drive on it with a normal circular wheel.
That's pretty much the only way to do it.
Don't label something "offtopic" unless you know the topic well enough to tell what's on topic.
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians.
I thought the earth was round...
Seriously. Take a big cylinder and paint a yellow line on its circunference. Then run a bicycle with cylinder-shaped wheels. Is that the intriguing challenge?
My website
looking at the link from the over view, the picture shows a normal tricycle with the 2 drive wheels in the rear...
That being two back wheels and ONE front wheel, why was it stressed that the bike had two front ones?
How about reinventing WINDOWS with circle windows.
Opera Watch - An Opera browser blog.
I think a screw-like shape might work here.
You see? You see? Your stupid minds! Stupid! Stupid!
>You can even observe how the shape of the catenaries
>elongates as the rotational speed stays constant but the
>horizontal velocity increases.
Not quite.
The revolving wheel will ALWAYS travel the exact same distance per revolution.
For a circle, this travel distance is exactly the circumference of the shape. A square or other regular shape will travel a slightly different distance, but something around the circumference of a circle transcribed on the shortest diameter of the shape.
So speed will not elongage the catenaries.
Look at it another way - by this logic, moving very slowly would result in very small catenaries. Taken to extremes, that would become a comb-like surface, with the original wheel shape - not exactly possible.
--Brandon / Split Infinity Music
but I had a sudden nasty vision of some maths-hater with mod points attacking my post. warning: spoiler follows
When you expand it as a series you will see it contains only even powers. That should be obvious anyway from inspection, as the curve is symmetrical about the Y-axis {series with only odd powers exhibit first-order spin symmetry about the origin}. For x < 1, x**2 is smaller than x, x**3 is smaller still and x**4 is practically non-existent; so only the constant and squared terms are significant. Hence, the catenary approximates to a parabola for small x.
Je fume. Tu fumes. Nous fûmes!
An appropriate name for a square "wheel" would be squeel?
Eeghh, cmon Mods. +4 Interesting? At least it wasn't informative. Look at the coin, where is the center of mass? In the center! What happens when the coin rolls? The center moves up and down. What happens to the center of mass? It MOVES! What the equal diameter allows you to do is roll something flat over a coin and not have -that- move vertically, but the CM of the coin will move.
From theme parks: vary the road with the wheel and have a "bike" path. This path is specially designed for wheel shape and diameter. Off the track, the bike is useless.
of course, it does make unplanned turns rather difficult... Hey is documented now, so its a feature!
Slashdot's rate-of-post filter: Preventing you from posting too many great ideas at once.
Yet Another Waste Of Brain Power.
I like things that are sweet and not things that are lame. --
This is completely worthless. I think i saw something like this at a CoSi science center when I was like 10, and I thought it was dumb then. What the hell is the point? What are they trying to prove here? That not only wheels can make things move? No shit, jackass. Now go play with some Tinker Toys.
n/t
Actually, this isn't entirely true. i don't know if the diameter is equal all the way round the coin, but i do know that the centre of mass is not at the same height as the coin rolls. You can check this either by comparing the rolling of a 20p (or 50p) coin vs. say, a 1p or 2p coin, or if you want to get technical about it, draw the outline of the coin, find the centre of mass, etc. The centre of mass oscillates vertically as the coin rolls.
The 20p coin rolls much more bumpily than a round coin, and stops rolling a lot quicker than a round coin.
Was an interesting theory though.
So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel. That's an intriguing challenge for mathematicians.
Um, how about circles on circles, like how all the roads are now? Assuming the Earth isn't flat or anything.
Speak truth to power.
This was done years ago on the Tonight Show by Leno's science guy.
Hmmm... Suppose I propose a flat teflon road, and flat teflon wheels. Taking it a step farther, I might suggest an air cushion vehicle if you want a more *efficient* ride... Mod me up for interesting, or down for stupid. Or both.
Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's
... WHY?
Be one heck of a way to keep "Undesirables" off your road.
Scott Carr
...to improve his "ride," Stan Wagon will be adding a "spoiler" (shaped like a rectangle) and a cylindrical exhaust "muffler" to make the vehicle more appealing to "the bitches."
If moderation could change anything, it would be illegal.
Researchers in Garden Grove, Calif. are attempting to design a proper chair for people whose knees are backwards.
This sig no verb.
Actually, I think the intriguing challenge would be to prove that the road should have the opposite shape as the wheel. That's why flat roads (lines) and curved wheels (circles) work so well today.
Have fun: Join D.N.A. (National Dyslexics Association)
n-gonal wheels
Hmm... Sega and Namco racing games from the early 90s. Daytona USA anyone?
When I think of all the times my sterling comments have been ignored...
Let's see if I can explain this correctly without the aid of pictures.
... though fairly simple.
I was a die hard Mr Wizard fan. One show he did a feature on non-round wheels. He cut four rounded triangles out of 1" thick wood and stuck dowells through their centers as accels. Then he laid another board on top and pushed it the direction of the wheels proving that he could get a 'smooth ride' with non-circular wheels.
Because the changing supporting diameters were all equa-length the board moved evenly. The points were opposite the sides and the approaches to the points were eliptical in their curve, maintaining the consistant diameter.
Of course, the accels were going around in circles, not just rotating, as well and thus were useful only in keeping the paired wheels aligned.
Cool stuff
No sig for you. YOU GET NO SIG!
I remember seeing something years ago on TV (Mr. Wizard, probably. Is there anything he *didn't* know?) He demonstrated a sort of squashed-triangle wheel. I don't know what the geometric shape is called, but essentially, it's a triangle, but the sides are somewhat curved out instead of straight.
At any rate, he demonstrated a toy vehicle with these wheels. When he pushed it along the flat table, the bed of the vehicle stayed perfectly level and didn't rise up and down because the diameter of the wheel at any given point was constant. The difference being that it didn't require any special "road" for it to work properly. It also didn't require any of the wheels to be in synch with each other or the road.
If someone has seen this or knows what I'm talking about, please reply, since this clearly shouldn't make sense. I just remember it worked perfectly.
"Tell me doctor, with all of your defenses, are there any provisions for an attack by killer bees?"
Quick, patent it, then convince a couple of major cities to make their roads
this shape. You'll do a booming business in wheels, then!
Cut that out, or I will ship you to Norilsk in a box.
Please
Take the shape in one direction and you get an infinite number of facets; a smooth circle in practice. Here's a challenge: Go the other direction and reduce the number of sides. A triangle is easy; the hills on the road are a bit steeper and the curve is more pointed (quickly decreasing radius). Go one more side removed and you have...a two-sided wheel and.. triangular hills that are equal on a side to the "radius" of the "wheel". Now, that I'd like to see in action!
I've seen this guys work before. He does some incredible snow sculptures. Much better then the stuff I've seen at Michgan Tech. ;) It's all planned out in Mathmatica, then sculpted from a huge block of snow.
Check out the first few links from his webpage.
http://www.stanwagon.com/wagon.html
I can't wait to put my pyramid-shaped bicycle seat on this.
IYRTA you can see that this machine cleary has 1 front wheel and 2 back wheels. I thought this was a technical audience... ?!
All seven of them!
One man's worthless horse excrement is another man's primo fertilizer.
Not all research yields immediately practical results. And frequently you can't tell before hand. Most of the world probably said "Well, duh" when Newton pointed out that apples fell down.
And sometimes researchers just do things for their humor value. Lighten up dude before you blow out an anuerism.
But if we use a fractal patterned tread, we'll need an infinite amount of road surface!
I vote for the smartwheels with zillions of radar-guided extending foot-spokes, a'la Hiro's motorcycle or Y.T's skateboard in Snow Crash.
I'd say being able to skateboard smoothly down stairs would probably give you the upper hand in the simpler conditions of municipal roadway battles.
"We have to go forth and crush every world view that doesn't believe in tolerance and free speech." - David Brin
Simply don't get it why triangle wheels wont work! It's just a matter of fixing the surface to keep constant the sum of the distance between the center of the triangle and the edge (given by an equation eq1), and the height of the surfface. Beeing the surface defined by eq2 = max.height - eq1 Can anyone explain why not..?
Wow...this guy really had me in mind when he decided to build this tricycle. Yes, doubters, there is definately a market for this bike. I will now be able to traverse my overzealously speed-conscience neighborhood without feeling one speed bump!
In the spirit of abstract higher math, consider a special case of wheel, one with a rotational speed of zero. In this case, the road and "wheel" may be planes, (e.g. "skis" or military tank treads).
Breathing would be a bitch.
road the same shape as the wheel. Simple a full pipe being the road and some gifted skate boarder.
This bicycle is the perfect metaphor for Microsoft. It has changed the wheels from round to square and requires a special suface to be ridden on. The wheels represent a standard that has been embraced and extended. The road represents a "proprietary" system.
If I wasn't at work I would be rolling on the floor laughing.
Really, I'm not trying to be clever with my signature.
Check out the picture of him on a climbing expedition on Mt. Logan with THREE BABES!!!!
"So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel." How about a unicycle riding around the inside of a circle. I saw something like this once at a circus. Some guy was suspend in a giant rotating hamster-wheel 50 feet or so in the air, riding a unicycle around inside. The road and the wheel where the same shape, so there!
About a year ago, it occurred to me that this technique of making square wheels work could form the basis of a good analogy as to why Microsoft was such an entrenched monopoly. It goes something like this:
Once upon a time, Microsoft made a square wheel. To make the square wheel work, they got people to build roads of inverted catenary curves so that the wheels would roll smoothly. Now, most people had never seen a wheel before, much less how to evaluate wheel quality and design. So when they started buying their first wheeled transports, they bought the one that most easily came to hand which, thanks to Microsoft's backroom dealmaking, usually had Microsoft's square wheels on it. This led to the building of more wheels, which led to the building of more inverted catenary roads.
Of course, people who were experts in the sciences of wheels and roadbuilding knew for a fact that square wheels were a perfectly stupid idea -- that it had been long established that circular wheels work much better, are far more flexible, and make roadbuilding much easier. Furthermore, they were safer. A square wheel hitting a hole or debris would make the car leap into the air violently, causing damage to the car and occupants. A round wheel rolling over a road imperfection would perhaps thump, but would usually recover immediately without incident.
Unfortunately, circular wheels didn't work too well on the inverted catenary roads being built everywhere, and no one was building flat roads because, well, where was the demand for them? Everyone's cars had square wheels.
The result was millions of cars with square wheels, running on thousands of miles of roads that require constant, precision maintenance. Flat roads are starting to appear here and there, but even though everyone who's changed over to the round wheel loves it, they still reluctantly keep a square-wheeled car around, so they can go places flat roads don't go yet.
Schwab
(Slashdot: Where we can work Microsoft-bashing into any topic.)
Editor, A1-AAA AmeriCaptions
Comment removed based on user account deletion
and MSAsphalt
A Microsoft spokesman said that it had struck a groundbreaking deal with the US government to to repave the entire nation's freeways. "We believe that this new technology will protect road users from the dangers of open source road surfaces."
You guys obviously don't come from Scandinavia. Happy easter vacation!
Oh, why am I spending my non-working time here again?
"I tend to think of OS X as Linux with QA and Taste", James Gosling, creator of Java
Think about it again...
The diameter is the same, all the way around.
So, how can the centre of mass move up and down?
It's the same point as the bicycle... The centre of mass of the bicycle doesn't move up or down either.
When the coin reaches a bump, the opposite side is shorter (because the diameter is the same). Therefore the centre of mass does not move.
Picture here
and they do say it allows it to roll smoothly, but not quite how. Anyone want to find a more informative site?
OK, so the parent post was kind of silly, but it gives me a chance to mention Imre Lakatos, my favorite mathematical philosopher. (Yes, I have a favorite favorite mathematical philosopher. Don't you?)
He wrote a marvelous little book called Proofs and Refutations -- here's a very brief bit of summary and context -- which present a very interesting very of the process of mathematical discovery: instead of accumulating an ever-increasing series of perfect truths, he argues, mathematicians are constantly shifting their perceptions of what is true, because they're constantly shifting the very definitions of the things they're writing the proofs about. (This happened in a major way with calculus during the 19th century, for example, when limits, derivatives and integrals were redefined more formally, giving birth to the field of analysis.)
The book is a lot of fun, and actually not such a hard read. It takes place in an imaginary classroom, where the students and the professor, having just proved a simple little theorem about polyhedra, start coming up with counterexamples by "stretching" their notion of what a polyhedron is. (Should a cylinder be a polyhedron? Why not? What about a box with a box-shaped hole on the inside? etc.)
Through their arguments, they end up sharpening the definition of "polyhedron", eventually replacing their naive notion with something clearer and more formalized through a process of proofs and refutations.
So, Stan Wagon challenges our definition of "wheel" with an apparent counterexample: Does the bike have no wheels? Or are wheels not round? We might propose sharpening the definition of "wheel" to account for the new counterexample:
A wheel is a solid object designed to rotate about an axle, with its perimeter in constant contact with some other surface.
(Make a ridiculous post, get a ridiculous reply!)
a Far Side comic in here somewhere.
If you could reason with religious people, there would be no religious people
This exhibit has been at the Exploratorium science museum in San Francisco forever. Iirc there are recipes for square-wheeled carts in the Exploratorium Cookbook, a guide to building science exhibits and projects. See also, "An Amusing Property of the Catenary" "...the catenary, this marvelous graceful thing, this joy of physics, this perfect balance between rebellion and obedience, is God's own signature on earth. I think it pleases Him to see them raised.'' Quoted from Mark Helprin - Winter's Tale. (Copyright (C) 1983 Mark Helprin).
yeah, but if we used a fractally patterned tread, the wheels would lock into the road and then you'd have a hard time going anywhere, regardless of the fact that you have an infinite road surface to drive on. :-)
It was a near future America where consumerism had run amok. People worked 60 hour weeks and bought new things all the time, even when the old things were still perfectly good. Planned obsolescence gone berserk. The roads all had bumps in them that matched car tires. People had to buy new tires every month when the govt. changed the bump paterns on the roads.
Eventually the Government just put up huge mind-control billboards everywhere. Story ends with the protagonist absent-mindedly sticking his newly purchased carton of cigarettes into the glove compartment with the other five cartons. He didn't smoke, and he didn't even realize he was buying them...
Luckily nothing like that could happen in real lif.
- None can love freedom heartily, but good men; the rest love not freedom, but license. -- John Milton
Simple. Make the road out of lots of tiny spheres (1inch dm), multi or single layered. Then make the wheel a 10ft diameter monster truck wheel. If you really want to be anal, the road can be made out of cheese-wheel shaped bits of material, stacked in rows. Voila, a smooth comfortable ride. No one ever said a thing about scale anywhere in there...
The "diameter" you are measuring doesn't pass through the center of mass. If it did it would be a circle - as 5 seconds of thinking would show you.
. html .
It's completely different from the bicycle since the bicycle uses straight sides on the wheel and a curved surface - the exact opposite of the coin.
It's the seven side version of a reuleaux triangle, the center of mass oscillates as it rolls. Mark the center of mass and roll one if you can't prove it to yourself with less than 5 seconds of thought.
And it does not have constant "diameter" is has constant "width" - the two terms mean different things (and are the same for a circle and only a circle).
See http://mathworld.wolfram.com/CurveofConstantWidth
Besides making strange bicycles and writing books on and in Mathematica, Stan Wagon makes tremendous mathematical snow figures. Check out his web page at (you guessed it):
stanwagon.com
PS. As a Macalester student, I get to ride it daily. Its license plate reads "Catenary."
Interesting, but what about turning? :-)
Fish bulb, bulk flush.
Nah, your taunt is off the mark. The square wheels really fit better with the Linux subculture: "Look! I made Linux run on my toaster, and put it inside a modified TRS-80 case with neon lights! And my bicycle has square wheels! Uh...What's this 'why' of which you speak?"
Microsoft would just sell lots of these, and then find a way to make it impossible to ride anything else on 95% of all roads. Square wheels are way too creative.
The had a science guy riding a bike like this on "Hey hey its Saturday", and Australian prime time variety show, which aired for 30 years and stopped showing around 1997 from memory. This thing must of been demonstrated around 10 years ago on public Australian television.
Hint: you couldn't do it if the coin had an even number of sides.
Well, the square wheel was tried, and by golly, in the primordal soup that passed for dirt, the thing was outstanding! Since all the people who were around when dirt was invented were not born yet, then dirt, as we know it today, was not hard, so a "square wheel" worked just fine.
Several trial vehicles were made in 10,000 B.C, one going nearly 300 feet in just under 20 minutes! That one is forever entombed several hundred feet below the Great Pyramid. (Dig it up to prove me wrong).
I remember riding a car with rectangular wheels on an identical "bumpy" road some ten years ago. It was in Heureka, a Finnish science exhibition centre, on a school trip.
This is why people think public research is a waste.
Let's spend gobs of money on making a primitive
proto-gear and call it a wheel except you can't turn
and you have to make a special road.
Someone surprise me with something usefule from this
research, it seems like a bit of a
looking-up-at-the-falling-Daisycutter dead end.
You're forgetting about drift - your assumption is correct if the wheel does not slide across the surface of the material, but as we all know any car can skid or hydroplane across the road surface. This is the basis of my assumption. If you have a wheel that rotates at a constant speed regardless of "actual" velocity, and then move that wheel along a surface faster than the wheel can rotate, you will have drift.
Reminds me of anecdote.. two bicycle designers discussing:
"Hmm.. if we put a circular shape on flat surface we should get smooth rolling action, right?" - "Yes.." - "Well, we put square wheels on our bicycle and the earth is a round.. so why the hell does it not work???"
"the coin will roll smoothly in slot machines etc. Try it!"
/.
casino advertisers have invaded
=)
The problem with potholes... is that they cause wheels with diameter approaching zero to approach asymptotically the meta-location of socks which have been lost in the dryer.
*CLUNK* "Blasted potholes, where'd my wheels go this time?"
"We have to go forth and crush every world view that doesn't believe in tolerance and free speech." - David Brin
relating radius to velocity:
v=2*pi*r
dv/dr=2*pi
Of course inertia means the ride won't be quite as jerky as that would indicate, but the wheels will have to speed up and slow down the rate of turning, and that will cause some jerkiness. It won't be a perfectly smooth ride.
It's going to be fastest with the corners of the wheels touching the track, and slowest with the middle of the sides touching down.
So the answer to my question is yes, the rate of turn of the wheels will change as it rolls along. In relation to your interpretation, there is transfer of kinetic energy between moving the whole bicycle forward and turning the wheels around, so the forward velocity of the bicycle will change.
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