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Can a bicycle create a unicycle track?(19 posts)

Can a bicycle create a unicycle track?ET
Aug 27, 2002 5:48 AM
That is, if you make the usual simplifying assumptions necessary for such a question, is there a path (other than the trivial case of traveling in a straight line) that can be swept out (e.g. through paint or water) so that only one pathline would appear? Yes or No?
Yes, but this is the only way to do it...mr_spin
Aug 27, 2002 6:21 AM
LOL!ET
Aug 27, 2002 6:26 AM
That's cheating. Can it be done with front and back tire remaining on the ground at all times?
Nomr_spin
Aug 27, 2002 6:29 AM
The front wheel will always turn tighter than the back, because the back is stationary. If you had a bike where the back wheel could also turn, you might be able to do it, but you'd probably need to use the fly-by-wire system out of an F-16 to get it perfect.
One example...jose_Tex_mex
Aug 27, 2002 6:01 PM
Sorry if I am being picky. However, I disagree with you use of the word "always." Here's why.

Put your bars at an infinitesimally angle just less than 90 (from straight ahead) and "ride" the bike. Your front wheel will be a big circle and the rear a tiny circle - a dot.

Try 89, 88, 87, 86 and other degrees and you will see that for sometime the front wheel will indeed turn tighter than the front.
... rear wheel will indeed turn tighter than the front ... nmjose_Tex_mex
Aug 28, 2002 11:03 AM
USPS in TdF riding with tennis shoes !?wilsonc
Aug 27, 2002 11:26 AM
look at the shoes...
:)
USPS in TdF riding with tennis shoes !?yeah right
Aug 27, 2002 12:41 PM
when you're taking your victory lap, for all of a mile or two, i guess it's acceptable, right along with ball caps and flags. plus i sure wouldn't try something like that while clipped in.
and the answer is...ET
Aug 27, 2002 10:09 AM
Yes!!

My original post title is the title of a 10-page article by David L. Finn, Rose-Hulman Inst. of Tech, appearing in the September '02 issue of the College Mathematics Journal. Complicated math functions are necessary to generate them, the starting position of the bike is crucial, and the only solutions he found so far all have rather short paths before they necessarily terminate, so if you said No, we won't hold it against you. See his article for further details on how to generate the paths.

In the unlikely event you choose not to look up his article but still wanna see some actual paths, the article provides the following link. Get a load of this (in moving action!!):

http://www.rose-hulman.edu/~finn/research/unicycle/animations.htm
still nomr_spin
Aug 27, 2002 10:26 AM
Not in the real world, which is what I live in and what I assumed you were talking about. Check out his assumptions:

"The bicycle is ridden on a flat surface, and that the bicycle is not banked into the ground, that is the plane of each tire meet the ground in a right angle. We suspect that one can create a unicycle track without these assumptions, but the equations become much more complicated."

There is no way he can be making those kinds of turns without banking the bicycle, or without riding it so slowly it would have to be supported by something or someone, and therefore, not really "ridden" as he claims.

Plus, I still don't buy it. If you magnified the path enough times, you'd probably find some variation. You can probably create a line given that a tire is wide enough to cover up the small variations.
falling means steering but does steering mean falling???jose_Tex_mex
Aug 27, 2002 6:28 PM
Spin,
When you cycle you are riding a series of arcs and are constantly falling, steering, restoring, and repeating. As you cycle your center of gravity is constantly changing and as such as you cycle your CoG is constantly going from side to side of an imaginary perpendicular line. As it goes to one side you begin to fall. A fall causes your bike to steer. As you steer in the direction of the fall your bike experiences a restoring force which puts you back towards upright. However, your CoG now causes you to fall in the other direction and the process is continued.
To not steer causes a crash - thus straight line motion is impossible.

However, does this mean that a steer causes a fall? IMHO, and I could be wrong - No. Somewere in the back of my mind those little voices are saying that for modern frames steering does not have to cause a fall.

From paragraph 3 you appear to be saying that by steering one must bank (fall). Although, this normally happens I will say that it is not a must.

Just my $0.02
and the answer is...jose_Tex_mex
Aug 27, 2002 5:57 PM
I love this sort of thing and although I haven't read through the entire study I do plan on it.

I pretty much agree. I am sure the guy is just trying to show that indeed it can be done. However, not too many of us are likely to trace out those paths - sober!

Still, very cool article it would have "gotten" me as I would never have guessed those paths. I would have tried a simple arc but lean the bike awkwarldy to make the rear wheel follow behind.

I don't think we need to get philosophical or metaphysical on this study.
Cannot ride a straight line...jose_Tex_mex
Aug 27, 2002 10:36 AM
Actually, a bicycle can never really travel in a straight line. I did a study on this in school and showed that the path a bicycle wheel takes while being ridden is a sinous wave. The peaks made by the rear wheel being smaller than the front.

In fact if you wanted to try and ride a straight line you would probably want to weld the headset so that the bars could not be turned. However, you would not be able to ride/balance such a bike.

As for making just one line, I would have to say no. Although, it might be possible by riding in extreme variations by leaning the frame for short periods of time. Your rear wheel likes to follow a shorter route than the front which leads me to believe the routes will be different.
So the stoker on a tandemSpoke Wrench
Aug 27, 2002 1:48 PM
never rides quite as far as the captain? Are you brave enough to try to explain this to my wife?
not truemr_spin
Aug 27, 2002 1:58 PM
The stoker may even travel further because the back of the bike can't turn as quickly as the front. It has to take the long way around, in a sense. But I can't imagine it's by much!
I don't think so.Spoke Wrench
Aug 27, 2002 4:28 PM
It looks to me like the rear wheel cuts every corner more than the front. I know I have to steer wider with my tandem than with my other bikes. I'm beginning to think that you're just trying to make points with my wife.
Wrong "not true" but true "not true"jose_Tex_mex
Aug 27, 2002 5:50 PM
Okay, I just re-read my 1995 study and need to clarify my point. However, no clarification needed here - it is impossible to cycle in a straight line.

There's a lot of variables flying around when we talk about the steerability/stability of bicycles. They include: candence, speed, accleration, and of course the rider's ability. Trying to weed through these is difficult.

However, I will say that the paths the wheels take are largely dependent upon speed. At lower speeds the rear wheel will have more of an opportunity to take a shorter path as it wants to follow the path of least resistance. However, during riding at normal speeds the rear wheel will "normally" display a graph that is greater in amplitude and often more frequent than the front. But this is very specific to the rider - do you spin alot or power? More spin = more motion in the rear.

You cannot say that the rear wheel "always" follows a shorter path. For example, let's take the case where you are standing still and "riding" your bike with the handle bars at a 90 degree angle. Your front wheel traces out a circle where the rear pivots on a dot. Now try 89 degrees - about the same thing and so on and so on. Clearly, the front wheel traces out more distance than the rear.

Of course we rarely ever steer more than a few degrees. However, when we are turning (riding an arc) it does seem intuitive that the rear wheel is more to the inside than the front and is thus taking a shorter path. I just rode through a few puddles and "proved this."

I would also say that the rear wheel likes to follow a shorter path. However, your butt and legs might force it to do something else.

As for the original question - making one line, I agree with the article that it can be done. However, like ET said - only for short intervals.

So, until we get out the motion detectors to view the path the wife and yourself take we cannot really be sure.
Wrong "not true" but true "not true"Spunout
Aug 28, 2002 7:13 AM
I still think you should weld someone's steerer tube, and test this. Please post pictures!
already saw this done...jose_Tex_mex
Aug 28, 2002 7:37 AM
on television with a mtb bike. The guy trying to ride it was a pro trials rider. He could turn the crank maybe once in a low gear and do a bunny hop. Unless you are an ace doing track stands you'ld probably fall pretty fast - just like me!