Well, we know enough to know how to increase stability - primarily by increasing trail and rake. Decreasing rake angle is the primary way of making a motorcycle turn faster, with the known risk that it makes it more likely to head shake or even tank-slap.
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.
It's true that increasing trail and rake both increase stability. But curiously, a bicycle can be made stable with both negative rake and negative trail.
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.
Thanks Sharlin, that was not only instructive on the terms, but a great read as well. Now I understand precisely why my uncle can always ride is raked Harley with no hands far longer than I can on my stock bike.
Thank you. We do know how they work, and that it's nothing to do with gyroscopes and everything to do with (what parent said, but simplifying a bit) front fork geometry.
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.
If you read the actual paper referenced, we know some of how it works, but not all.
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.
So we do know how the bikes that actually are 'bikes' work at least to a very large degree (engineering vs math), but we don't know all the possible physics which can enable an arbitrary two wheeled construct to be selfstablize when perturbed while in forward motion.
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.
I suppose it depends on how you look at it, or perhaps on whether you're interested in how a bike works versus why a bike works. How is relatively easily answered; as the bike tilts it steers into the tilt, moving its base back under its center of gravity, in a way which damps itself thus getting back to upright without oscillating repeatedly or falling over.
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.
You could build a bike with no gyroscopic effects, slightly negative rake AND the steering column center of mass at the same height as the rest of the bike. So you could cancel out and test the influence of the last effect.
If that failed to be stable, all that would prove is that particular design was unstable, not that there is no design with those features that is stable. This is a problem of finding a general rule, not just a particular design that is stable or unstable.
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.
>Decreasing rake angle is the primary way of making a motorcycle turn faster, with the known risk that it makes it more likely to head shake or even tank-slap.
This must be what non-programmers feel like when they hear programmers talk about code.
"Here you go. All that was needed was to parse the cat root slash dev etcetera file for eth 0 and pugle the forward identity-locking rehooliginator and symlink it to the libgc perl humongisooler module after a kernel decompile and basic repatch update. Nothing to it, just RTFM and you'll figure it out!"
A slightly mind blowing fact is that if you ride a motorbike at reasonable speed in order to enter a turn to the right you actually turn the handle bars to the left. This causes the motorcycle to lean-over to the right and thus entering a turn in that direction (due to the horizontal component of the weight).
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.
We know quite a lot about how bikes behave, we've been building them for decades, centuries.
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.
Ideological what, now? Bicycles, you may have noticed, are muscle-powered. adding a few dozen pounds' worth of wheels and frame is going to seriously impact acceleration, hill-climbing, and rider endurance, and the increased width will have major effects on hazard avoidance, navigation in narrow spaces, turning radius, and general maneuverability.
I've ridden adult-sized trikes, and they are fun and relaxing, but they're much less suitable for most serious transport/travel applications.
If you want stability above all else, sure; tricycles exist and are more stable than bicycles, and you can go up to 4 wheels, too. They have other downsides, however. More friction, more width needed to both travel and park, and actually worse stability when cornering at speed (they can't lean, so are at risk of flipping in a turn).
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.
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.
[1] http://en.wikipedia.org/wiki/Honda_ST1300#Pan_weave