We still don't really know how bicycles work
newstatesman.com
newstatesman.com
A bicycle in motion adjusts its center of gravity to remain upright. It's very similar to the inverted pendulum problem.
Look at a bicycle directly from behind with the wheels exactly lined up. Now imagine that you could frictionlessly slide the two tire patches left and right. The similarities to the inverted pendulum become more clear.
Of course, it is more complicated than the classic inverted pendulum. Instead of one point of contact under the mass, there are two. And the two points of contact (i.e. the wheels) have their own complex dynamics.
Having a rake angle on the front wheel makes a bicycle self correcting (if the c.g. is on the right side of where the wheels contact the ground, then a right turn is induced in the front wheel by the rank angle)
There are two major forces that must be in balance to turn a bicycle - the side force from being off center with respect to c.g., and the centripital force in the turn.
Ever watch a cyclist train on rollers? That's much closer to an inverted pendulum. And since there is no forward momentum, there is no centripital force, which makes it more difficult to remain upright on rollers than on pavement.
No. If you actually read the paper linked (and the Supplementary Online Materials, which contains a lot of the actual information), it is shown that rake angle is not necessary for the bike to be self correcting. You can build a bike with a negative or zero rake angle that is still self-stable (at least, according to the bicycle dynamics modelling software they were using, JBike6; they didn't actually build this particular bike, but did build one that had small negative trail and no gyroscopic effects that was still stable).
As they demonstrate in the paper, none of rake angle, trail, or gyroscopic forces are either necessary or sufficient for self-stability. All of them can influence stability, so saying the gyroscopic theory has been proven wrong is not entirely right either; it is a part of the dynamics that adds stability, it is simply not necessary or sufficient on its own. In fact, the paper shows that on the "benchmark bicycle", removing the gyroscopic force makes it unstable, so on that particular design, the gyroscopic force is necessary for its stability (thus explaining why it was believed for so long that gyroscopic force is what provided stability).
What we know is that gyroscopic forces, trail, rake angle, and distribution of the center of mass of the fork and body of the bicycle all influence stability (in particular, the center of mass of the body of the bike being substantially higher than that of the fork); none of them alone are sufficient to provide stability, and likewise none of them alone are necessary as we can build bikes without them that are still self-stable.
> > Having a rake angle on the front wheel makes a bicycle self correcting ..
> No. If you actually read the paper linked ...
(probably going to regret going meta, but the initial 'no' in forums and irc really bothers me)
Also, while a riderless bike is fairly stable, a rider overpowers the autocrorrective nature when they hold the handlebars. So, really bikes are stable in large part because the rider balances for the bike as seen by your ability to keep a bike upright without moving and it becomes far easer to do so at as you speed up.
The takeaway is that there are several factors which influence the stability of a bike. We know of certain designs which utilize one or more of these factors to achieve self-stability (and the conventional bike has all of these factors, hence why it tends to work so well), but we don't know the exact set of conditions on the combination of factors which would allow you to characterize which designs are stable versus unstable, without simply trying out any given design and simulating it.
They very clearly describe (at the end of the video) that even with gyroscopic and tracking forces removed, the two most important factors are where the center of gravity is, and the tendency to turn into a fall (arguably just the second, but it is caused by the location of the center of gravity with regards to the pivot).
[1] http://www.youtube.com/watch?v=YdtE3aIUhbU
Edit: more info on the TMS (two-mass skate) bike at its wikipedia page: http://en.wikipedia.org/wiki/Two-mass-skate_bicycle
It's fairly clear that common two-wheelers are stabilized by the rake and trail inducing a counter-steering effect when pushed horizontally - try to shove over a bicycle and the front of the front wheel will turn in the direction of the push because the point of contact of the tyre with the ground is behind its axis of rotation (the amount of which is the trail). And if the bicycle is moving forwards, this turn of the wheel will cause a torquing effect to roll the bike in the opposite direction of the shove. So long as the correction is somewhat less than the overall shove, the system should be self-damping.
But if the dynamics were fully understood, we'd be less likely to get motorcycles with issues like the well-known Pan Weave[1] and other high speed stability issues. At the limit, things like aerodynamics, chassis rigidity etc. start coming into the equation.
An interesting take on this, with both mathematical modeling and real prototypes, can be found at [1]. Note also that gyroscopic stabilization is not necessary: in the prototypes, a counter-rotating extra wheel cancels out the angular momentum of the front wheel.
According to the authors, it's not yet even proven that a stable bicycle must turn towards a fall. Almost the only sure thing, so far, is that "at least one factor coupling lean to steer must be present". We know a lot of sufficient conditions for stability, but not what is necessary.
The conclusion of the paper: "As a rule, we have found that almost any self-stable bicycle can be made unstable by misadjusting only the trail, or only the front wheel gyro, or only the front-assembly center-of-mass position. Conversely, many unstable bicycles can be made stable by appropriately adjusting any one of these three design variables, sometimes in an unusual way. These results hint that the evolutionary, and generally incremental, process that has led to common present bicycle designs might not yet have explored potentially useful regions in design space."
EDIT: here's a not-paywalled version of the paper linked in the submitted article.
[1] PDF link: https://scholar.vt.edu/access/content/group/141943de-4222-46...
Pretty much anyone can see this for themselves. Walk a bike with your hand holding the back of the seat, not the handlebars. Steer the front wheel by leaning the bike. Lean father to correct faster. If it's a cheap bike, let go and watch this happen on its own till it wobbles too far to counteract.
This is one of those idiotic tropes like bumblebees not being able to fly.
Two of the proposed theories (that it has to do with gyroscopic effects, and that it has to do with trail), have been disproven by creating a self-stable bike with no gyroscopic effects and (slightly) negative trail. The paper introduces one additional factor, the difference in center of mass between the steering assembly and the rigid body of the bike; the steering assembly having a lower center of mass causes it to fall faster, providing the necessary corrective steering to achieve self-stability.
So, there are several factors we know about, which can increase stability. We know how to locally optimize stability for certain designs. But we don't yet have a full set of necessary and sufficient conditions for a bike to be self-stable. We haven't even proven, analytically, the intuitive notion that a bicycle must lean toward a fall, though given our intuition it is believed to be true.
Here are the two necessary conditions that the paper provides:
> To hold a self-stable bicycle in a right steady turn requires a left torque on the handlebars. Equivalently, if the hands are suddenly released from holding a self-stable bicycle in a steady turn to the right, the immediate first motion of the handlebars will be a turn further to the right. This is a rigorous version of the more general, as-yet-unproved claim that a stable bicycle must turn toward a fall.
> Another simple necessary condition for self-stability is that at least one factor coupling lean to steer must be present [at least one of Mδϕ, Cδϕ, or Kδϕ must be nonzero (SOM text S3)]. These coupling terms arise from combinations of trail, spin momentum, steer axis tilt, and center of mass locations and products of inertia of the front and rear assemblies.
That's what is meant when people say "we don't know how bicycles work." We do know some of how they work; we know that the designs that we create steer into a fall, and do so in such a way that damps the wobbles and eventually goes straight again. And we do know some necessary conditions for a self-stable bicycle, like a requirement that something that couples lean and steering must be present; but we don't know if the steering into the fall is absolutely necessary, or if you could build a bike that managed to achieve self-stability without it.
So, I would say that a more accurate summary is "we know how current bicycle designs work, but we don't know exactly what aspects of them are necessary, or how to completely characterize the sets of designs that work or don't work." But that's a bit more of a mouthful than "we don't know how bicycles work", so that's what gets repeated.
I completely understand the point your making. However, at when making a technical argument and then generalizing the end results, we can end up in a situation where the truth of the technical argument no longer strictly implies the truth of the generalized/summarized result. I feel the statement 'we do not know how bikes work' has crossed that line.
Why it works is the open question. We know that it's some combination of gyroscopic effects, rake, trail, and the different centers of gravity of the frame and fork, but we don't know the precise relationship between them that allows it to work.
The issue is that no one has found a way to characterize all possible designs (within certain constraints, such as two wheels each attached to a rigid frame, the frames joined by a hinge) which are self-stable. They know some conditions that are necessary, such as at least one factor linking lean to steering and the design needing a steering force applied to turn in a steady turn. They have not yet characterized what conditions are sufficient for a stable design.
What you want, to say that you fully undertsand how a bicycle works, is a set of conditions which are both necessary and sufficient for a bicycle to be self-stable. If you build a bicycle which meets those conditions, then it will be self-stable (at some speed; certain designs may be self-stable over a wider range of speeds while some may only be self-stable at a narrow range of speeds); if you build a bicycle which does not meet those conditions, it will not be self-stable at any speed.
We've gotten closer over the last century; initially it was believed that gyroscopic force was necessary, but that was disproved. Later it was believed that trail was necessary (or either gyroscopic force or trail was necessary; I haven't read the older paper), but that has now been disproved. We now know a couple of necessary conditions (listed above), but they are somewhat weak necessary conditions, and we don't yet have (as far as I know) a set of sufficient conditions (conditions which, if they hold true, will guarantee that the bicycle will be stable, regardless of other changes to the design), beyond a few known designs which are demonstrably stable.
In fact, if you follow from the paper in Science to the "Supplementary Online Materials" (which is actually the full-length paper; what's published in Science is really an extended abstract), you will see that they prove that "no combination of positive gyroscopic action, positive trail, or positive steer axis tilt are either necessary or sufficient for self-stability over at least a small range of speeds." They construct models of bicycles that lack each of these things but are stable, and have all of these things but are unstable.
I'm pretty sure science still cannot explain how bumblebees would be able to fly a Boeing 747
Also, light does not propagate through glass in a straight line, it diffuses, refracts, and reflects.
This must be what non-programmers feel like when they hear programmers talk about code.
http://www.theregister.co.uk/2002/10/02/mandrake_9_0_vs_mand...
You force yourself to fall and let the bike catch you and damn it is disconcerting the first few (hundred) times.
This is oddly redundant, kind of like saying "primarily by using computers and laptops".
Trail is the tendency of the front wheel of a bicycle or motorcycle to act like a caster. If you change the bike geometry so as to increase trail, the bike will increase its resistance to being turned (steered). This makes the bike easier to handle, particularly at high speeds, and makes it much easier to ride no-hands. But it's not all good: it also makes it very hard to control the bike when the wheel has a lot of load on it (like front panniers) and makes the bike less manipulable.
You can change the trail by changing the angle of the steering column (steeper angle, lower trail), changing the size of the wheels (smaller wheels, lower trail), or adding "rake", which is the forward swoop that many bikes have in their front fork (more rake, lower trail). Though some think rake is to provide a bit of bounce or suspension, it's really not. It's a device used to add trail.
While we might not grok all of the specifics behind the physical dynamics, consider this: We also don't know the specifics of why gravity works. We know enough about it to make practical use of it, it keeps us on the ground and we fall at about 9.81m/s^2, but how we are affected by gravity over vast distances is still a mystery. Why we are attracted.
If we can get along just fine without being blown away by the fact that we don't even know how we stay on the ground, I don't think it's that amazing that we struggle with the dynamics of a particular system of locomotion. We can make it work well enough.
As you say exactly why is still a unknown but then so is everything if you keep reducing the problem.
..or, absent ideological zeal, the number of wheels.
I've ridden adult-sized trikes, and they are fun and relaxing, but they're much less suitable for most serious transport/travel applications.
Cargo bikes often have more than two wheels, but people who don't need to carry significant weight in a basket tend to prefer bicycles as the more practical option. Parents in Copenhagen do often choose the tricycle-with-basket at a moderate speed, as a safer option than putting a kid on the back of a bicycle. But that only works when you have wide bicycle lanes.
http://www.sciencemag.org/content/332/6027/339
And here is a great video by the author:
http://www.youtube.com/watch?v=YdtE3aIUhbU
Short answer: "a bicycle should turn into a fall."
It's so much worse when the ignorance belongs to a "journalist" who really just needed to do a little research before promoting such a poor theme.
Yes, we know how bicycles works. No, it wouldn't be that big of a deal if nobody was working on solving the mysteries of the bicycle in favor of really hard problems like "dark matter".
http://www.youtube.com/watch?v=2Y4mbT3ozcA
It focuses on the question why bikes do not fall, even without a rider on them (spoiler: coriolis is insignificant).
I'm not sure where his fascination with esoteric mechanics comes from, but he has a pretty clever and engaging manner of discussing the stuff.
Edit: Didn't realize that Ruina was a co-author on the paper referenced in the article. Even better. It all goes full-circle.
Now /I/ want to know why the bike do not fall.
If you've read about Einstein's pail-of-milk-on-a-lazy-susan, it's a similarly unintuitive frame of reference. Also, if the experts haven't figured it out: I don't know what I'm talking about.
I find it fascinating that we as a species can observe, define, and exploit Maxwell's law, neutrino physics, etc, but we can't clearly explain bicycles. Or why wings provide lift.
EDIT: forgot the Feynman video
http://bicycle.tudelft.nl/bmd2010/CDProceedingsBMD2010/paper...
I look forward to New Statesman's thrilling coverage of how bumblebees can't actually fly, and nobody knows why duck quacks don't echo.
This seems to suggest that my plan would never work. If gyroscopes don't stabilize, then why are they used on monorail trains etc?
They do, it's just the bicycle's wheels aren't heavy enough to provide enough force to really make that much of a difference.
when you both turn and inclinate the bike, the contact point is more on the side which you turn, balancing the bike.
There maybe a few gaps (particularly for supersonic flight) still being explored, but in general it's inaccurate to claim that we don't know how airplanes work.
The speed explanation is not incorrect, except the REASON for it is.
I learned on school that the air on top of the wing move faster to catch up with the one in the bottom (this never made sense to me...), the air on top indeed move faster, we only don't know why.
Damnit, I should be a physicist, not a programmer :P
We know exactly why. The mass of air above the wing is moving into a larger physical volume, so it spreads out to a lower pressure. Bernoulli showed that pressure and flow velocity are always related (for non viscous flows), so where you get a low pressure you'll also get increased velocity.
The "to catch up" part is wrong, as well as the idea that it's the "longer path" that makes the air speed up. A symmetrical airfoil still generates lift as long as it has some angle of attack.
Now, there is one complexity here in that air isn't totally inviscid. It does have some viscosity, and this creates some complex boundary layer effects and turbulence. So the Bernoulli explanation is a bit of an approximation. The "real" math is Navier-Stokes, but that's not useful to most people for understanding flows based on looking at formulas (it's the math that underlies computational simulation of fluids but nearly useless with pen and paper).
A better "highschool textbook" explanation is the concept of circulation, which captures most of the important details without requiring you to understand tensors and vector calc.
* BLAS (please)
* LAPACK
* memset
* memcpy
* 'Segmentation Fault' is not a synonym for 'exited successfully'.
Next, you'll tell me that 'Thank you for playing Wing Commander' is not a synonym for 'EMM386 exception 006A at 00B8:3128'.