SELF-HELP: A strange-looking experimental bicycle exhibits self-stability in the absence of the effects most commonly presumed to cause stability.
Image: Sam Rentmeester/FMAX
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Be kind to your bicycle, for you may need it more than it needs you.
Once rolling, bicycles can cover ground just fine on their own—no rider required—thanks to a property known as self-stability. If a bicycle starts to tip over, its front wheel turns into the fall, bringing the bike back into balance, just as a rider would do if he or she were behind the handlebars. Of course, that stability is missing when the bicycle is stationary—bicycles have a limited range of self-stable velocities within which they are able to regain their balance even if knocked sideways [see first video below].
The question of how bicycles work—and what causes self-stability—has been around since the 19th century. Over the years, two main factors have emerged to explain a riderless bicycle's balancing act. One is the gyroscopic motion of the spinning front wheel; the other, a design feature known as trail, is the placement of the bicycle's steering axis so that the axis intersects the ground ahead of the point where the front wheel meets the ground. Both features act to couple the bicycle's steering to its leaning—if the bicycle tips rightward, it will steer to the right—allowing it to turn into a fall and remain upright.
But those two factors are not needed for a self-stable bicycle, as it turns out. In the April 15 issue of Science a team of researchers from the Netherlands and the U.S. describe an experimental bicycle that exhibits self-stability despite having neither trail nor a gyroscopic wheel. "Even though those two effects are important, they're not necessary," says study co-author Andy Ruina, a professor of mechanical engineering at Cornell University. "Just like chocolate cake is important to a nice birthday dinner, it isn't necessary."
The demonstration, Ruina and his colleagues say, shows that a number of parameters contribute to a bicycle's stability, and that more exotic bicycle designs than are typically considered might be surprisingly stable. And the finding serves to underline what complex machines bicycles really are, and how imperfect is the theoretical underpinning of their dynamics.
"Everybody can operate a bicycle, but very few can describe the operations," says study co-author Arend Schwab, a professor of mechanical engineering at the Delft University of Technology in the Netherlands.
"The bicycle has been a perplexing topic for the past century," says Richard Klein, an emeritus professor of mechanical engineering at the University of Illinois at Urbana–Champaign who did not contribute to the new study. "It has so many paradoxes and mysteries and challenges."
One of those challenges, explaining self-stability, even attracted the attention of famed German researchers Felix Klein and Arnold Sommerfeld in the early 20th century. Klein and Sommerfeld advanced the theory that angular momentum from the gyroscopic front wheel keeps the bicycle stable.
The importance of trail was elucidated by British chemist David Jones, who in 1970 recounted in Physics Today his efforts to construct an unrideable bicycle. In his experiments Jones discovered the importance of placing the steer axis so that it points ahead of where the front wheel touches the ground, and built a bicycle with its front wheel extended forward by four inches to demonstrate his finding. The bicycle "crashed gratifyingly to the ground when released at speed," Jones reported.
Schwab says that before undertaking this study, he would not have considered it possible for a bicycle without gyroscopic torque or trail to exhibit self-stability. "Not in a million years," he says. "Before I did this research I was in the group saying, it's the gyroscopic effects and the trail." But by examining the complex mathematical equations that describe a bicycle's motion, the researchers found another route to self-stability. The group designed and built a prototype bicycle (which with its tiny wheels and no place to sit actually resembles a child's scooter more than it does a bike) whose mass distribution causes it to steer toward its direction of tilt in just the right way to stabilize it.
The front of the bicycle, which includes the steering axis, has a lower center of mass in relation to the ground than its rear, so the front falls faster than the rear, much as an upright pencil falls faster than a longer broomstick does. The bicycle's front mass is concentrated forward of its steering axis, so when the bike's front end begins to fall, it turns the bicycle into the fall as needed to stabilize the entire assembly [see video below].
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20 Comments
Add CommentThe writer is leaving out one important detail. Every bicycle in motion carries two gyroscopes of its own. The two wheels of a bicycle tend to act as natural gyroscopes once in motion. I've experimented with the same and there is a definite and noticeable force keeping the bicycle in a constant plane, independent of turning the handlebar.
Reply | Report Abuse | Link to thisThen adding a weighted appendage sticking out above the wheel of a bike ought to increase the stability?
Reply | Report Abuse | Link to thisAs any kid who's ever had a bicycle can tell you, if you remove the front wheel and , holding it aloft by one side of the axle, spin the wheel quickly, a very strong gyroscopic force will become apparent. In the aforementioned configuration, it is about impossible to tip the wheel from it's rotating plane. On another note, perhaps the writer is from another English speaking country. In the U.S., I and all my colleagues have always used the word "caster" to describe what this writer refers to "trail"
Reply | Report Abuse | Link to thisPart of the physics of a gyroscope, which the small wheels and counter-rotating upper wheel, deal with precession and nutation. These two wheels will each resist rotation normal to the direction of motion, that is falling, and will tend to cancel out each other's precession forces. It seems that the point has not been made that although small there are 4 gyroscopes on the frame, and while smaller, they are rotating faster that if they had been the size of a normal wheel. The test then would be to do the same experiment on ice with skate blades. How about a test of that?
Reply | Report Abuse | Link to thisGreat minds think of bike.
Reply | Report Abuse | Link to thisI think that ice is nice and would suffice to answer the question of how important the gyroscopic contribution is to the stability of a bicycle. I can't believe that no one has built a skate- or ski-supported bicycle.
Reply | Report Abuse | Link to thisI have no idea what this means:
Reply | Report Abuse | Link to this[T]rail... is the placement of the bicycle's steering axis so that the axis intersects the ground ahead of the point where the front wheel meets the ground."
Do a Google Images search for "bicycle." You'll see the steering axis is several inches behind the point where the front wheel touches the ground. Sloppy writing.
Oh. Unless you draw a line along the steering column and down the forks, at a slant to the ground. Then it makes sense. I was seeing the steering axis as vertical, not tilted. Still, an illustration would have been nice.
Reply | Report Abuse | Link to thisYou got it.
Reply | Report Abuse | Link to thisThe stability is the same basic principal as the fifth wheel trailer hitch versus the bumper hitch, it moves the point of turn contact over or just in front of the rear axle, the point of motive force.
No. The writer of this article has it backwards.
Reply | Report Abuse | Link to thisWhen the wheel hub is placed AHEAD of the axis of steering, it becomes more stable. If the wheel hub is placed BEHIND the steering axis it becomes less stable.
This is easily verified in any bike shop. Just look at the geometry of the front fork of touring bikes. The for curves forward. If it curved backward, it would not work.
Please fix the article and re-read the original.
Re: "When the wheel hub is placed AHEAD of the axis of steering ..."
Reply | Report Abuse | Link to thisJohn, the article says nothing about the placement of the wheel _hub_. Instead, it refers to the point where "the bicycle's steering axis ... intersects the ground" and "the point where the front wheel meets the ground."
The ski-bike does exist and has been around since the mid 1960s at least. Since they are intended for careening down hill at high velocity, I'm not sure if they would be suitable to testing self stability. The few times I've seen them they had a rider on them carefully controlling them.
Reply | Report Abuse | Link to thisNo, the article is correct. True, the handlebars are behind the wheel, if dropping straight down. But the steering axis is not straight down, it runs from the handle bars down through the shaft and the fork just before the rake. Look at a picture again. Extending this line, it meet the ground just ahead of where the wheel makes contact.
Reply | Report Abuse | Link to thisThe article does not leave out gyroscopic effects, mentioning it something like five times. Sure, this effect is useful for stabilizing a bicycle, but the whole point is that it's not the only way to have a bicycle self-balance. The researchers designed their bicycle to have unappreciable gyroscopic forces, which they did by adding wheels that spin in the opposite direction.
Reply | Report Abuse | Link to thisSo if I understand this correctly, it is the angle of the curve in the front forks that create an imaginary plane to the ground, in front of the point of actual contact of the front tire? Does the angle of the steering hub in the frame also figure into this?
Reply | Report Abuse | Link to thisTalk about re-inventing the wheel! Be advised that nothing new has been discovered! **All of this*** was explained in England 60 years ago. See
Reply | Report Abuse | Link to thisRA Wilson-Jones, Proc. Inst. Mech. Eng. (Automobile division), 1951-52, page 191. 7.
(I met Wilson-Jones when Bill Milliken (still alive now at age 100), I, and other Americans gave papers there in 1956-57.)
Also, Encyclopaedia Britannica ( 1957 edition), entry under "Bicycle. ...
Also, The Physics of sports - Angelo Armenti - 1992
Also, http://www.pdfarticles.com/topic/bicycle+physics+pdf.html.
Furthermore, the statement that “The front of the bicycle, which includes the steering axis, has a lower center of mass in relation to the ground than its rear, so the front falls faster than the rear” is just plain wrong, Given a rigid frame, it all falls as a unit. Silly, silly.
Hi Albert Fonda and others:
Reply | Report Abuse | Link to thisAndy here, co-author of the paper under discussion: "A bicycle can be self-stable without gyroscopic or caster effects." That paper, 2 supporting documents, and more stuff can be looked at here:
http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/stablebicycle/
Or just google ruina bicycle. Have a look please.
Our paper is narrow, it doesn't really go past the title. But I don't think it deserves such easy dismissal as either wrong, unoriginal or unaware
of the literature. That is, I don't think anyone who has looked at what we have has claimed that. Maybe have a look at the paper and the supporting documents and see what you think. (As an aside, we have got permission to post the formerly secret CALSPAN stuff of Milliken and others, some of which is now available to the world on our www sites. And you will see also reference to Wilson-Jones in our stuff also.)
Hi Andy Ruina and others:
Reply | Report Abuse | Link to thisThe link you cited provided lots of information necessarily omitted from the Scientific American article. In particular it provides a quite different meaning for the explanation that “the front of the bicycle, which includes the steering axis, has a lower center of mass in relation to the ground than its rear, so the front falls faster than the rear,”
I took “the front of the bicycle, which includes the steering axis” to mean everything BUT the steered parts; what you meant was ONLY the steered parts. Quite a difference, As I understood it then the description was indeed silly, and I said so = = but that was my mistake. I retract that, and apologize.
The link also provided your extensive bibliography, not omitting Wilson-Jones (as, of necessity, had the SciAm article).
So corrected, now I have much more to study. Your work was scholarly and extensive, and my flamboyant criticism was undeserved.
Nevertheless I am, for reasons too abstruse to recite here, unconvinced that “the two attributes thought to be most important for a bicycle's self-stability turn out not to be necessary,” as the article’s subtitle says. I’m still reserving my opinion on that one.
When I hold my bike upright, standing still, front wheel aligned with the bike, and I push the saddle to the left, the front wheel turns, falls to the left.
Reply | Report Abuse | Link to thisBecause the point of contact of the front wheel with the floor cannot be changed (quick enough), the bike tends to fall.
But when rolling ahead with some speed, this corrective motion CAN and so WILL be done fast enough.
You would expect an violently oscillating behavior, but apparently there is enough dampening in the rubber or something.
Another thing:
When I turn the front wheel, the center of gravity of the bike comes up a bit. So gravity keeps the wheel steering ahead. Try this on an old bike, not a racing bike.
Nice thing is, these scientists isolated another cause/effect of self-steering.
Brilliant observation! LOL!
Reply | Report Abuse | Link to this