"Most people have seen a gyroscope in action, so the stability of a rapidly rotating wheel should be fairly intuitive, making this a focus from the start. People have built bicycles with counter-rotating wheels and found that they still remain upright, so that can't be all of the story."
Um, counter-rotating wheels are still gyroscopes. In fact they're extremely stable gyroscopes in that they won't impart rotational velocity on the frame. So by having the wheels on a bike rotate oppositely, you're actually making the gyroscopic effect even stronger.
I think Ars is pulling from this article, which isn't about staying upright but is about the self-correcting steering of a bike wheel (i.e. the fact that you can ride hands-free.) http://www.sciencemag.org/content/332/6027/339.abstract -- in which case the conclusion is correct and likely due to the geometry of the wheel. For example tractors have convex pulley systems that allow leather belts to self-center despite not being perfectly aligned. It's counterintuitive but it works.
> Um, counter-rotating wheels are still gyroscopes.
Um, no. A system consisting of two identical wheels mounted on the same axle and spinning at the same speed in opposite directions has a total angular momentum of zero. It will behave like a solid object of the same mass.
The counter-rotating wheels are not the same as the two that the bicycle rolls on. So there's four wheels, two of which only exist to cancel the rotational inertia of the 'normal' wheels.
This. However I wonder what it would be like to ride a bike on two rolling-roads so that the front and back wheels moved in opposite directions. Or, indeed, a trike/quad with large coaxial wheel separation and contra-rotating rolling-roads.
no, they didn't build it so it has gyroscopic effects in the other direction, they built it so the reverse rotating part would cancel out the forward rotating wheel effect and you wind up with a gyroscopic-ally neutral design.
As you tilt a bike, the effect of trailing on steering increases (i.e. rotational force). This effect is cumulative over time (the velocity of the handlebars turning changes their position in each successive instant; plus the force causes acceleration, increasing the velocity).
Small effects become big effects: I would expect that any trailing would induce sufficient steering effects, and so even 4mm trailing is not "negligible".
Hmmm.... you could test this with a "skate bike" - no wheels, just blades on ice, but with a curved front-blade, free to steer, to facilitate "trailing".
But this seems obvious, and it looks like they have been very thorough, so I'm probably missing something (I haven't read their full paper).
* Stabilization occurs because when the front wheel steers that way, it guides the whole bike in a curve, which creates force tilting the bike in the other direction - therefore righting it.
There goes another traditional physics text-book explanation for why things work the way they do.
Somewhat related, Jef Raskin on how the Bernoulli effect is not really what helps create the lift on a plane's wings (as taught by most physics text-books): http://karmak.org/archive/2003/02/coanda_effect.html
A basic principle of bicycle framebuilding is that if you think you understand bicycle dynamics, you don't. Frame geometries that should ride perfectly develop terrifying handling problems in the metal. Frame designs that are unridable in theory turn out to be relatively practical - perhaps the oddest example of this is the Python recumbent, which steers in the middle, drives at the front and has no handlebars[1]. Bicycles that are self-stable and balance on their own aren't necessarily good to ride and vice versa.
Making sense of bicycle dynamics is particularly bewildering because they are such a natural and direct extension of the rider. Learning to ride a bicycle is a completely subconscious process and what your body is doing runs counter to what your brain thinks is happening. Most people who ride bicycles believe that they steer in the direction of a turn, when in fact the opposite is the case. A child who learns to ride a bicycle with training wheels actually takes longer to learn to ride on two wheels because of this - they have to unlearn steering before they can learn to countersteer.
> This article had zero scientific conclusions (or in fact any science at all)
The article summarizes a piece of scientific work. The work itself does 3/4th of typical scientific work: 1) analyzes the current state of art (previous publications), 2) provides model and expected values, 3) analyzes observational data & deviations from the model. It falls short of 4) providing answer to the final ``why'' -- as the answer is still unknown to the authors. What it does _not_ lack is scientific honesty and integrity.
> To me it sounds like their math is the problem.
Indeed, that's what the article says. ``What their math can't apparently tell them is why so many different bike designs tend to stay upright.'' -- i.e., they haven't found the proper formula(s) yet. They don't blame a compiler (the math itself), but find the mathematical formulas they selected to be not sufficient for creating a complete model.
I think that part of his point was that in this case, intelligent people tried to design unstable bikes, and failed. Even their unstable bikes were stable. He's doing the obvious equating of Intelligent Designer and God. And since "God created the Universe", he made the universe like stable bikes.
Ever since the previous post, I've been wondering where people are getting their bicycles. I've never had a bike that would stay upright on its own at less than ludicrous speed, and the crusty ten speed in the other article had forks that were very obviously bent back, drastically changing the rake and trail.
I also recall an old physics video from High School where the man flipped the fork and handlebars around backwards, specifically so the bicycle would stabilize itself.
How did you test a bike staying upright on its own?
Being stable only requires the bike to resist some reasonable force that would knock it down. It takes much more force to tip a moving bike than a stationary one.
If you have a hill without anything breakable at the bottom of it, and a bike you don't mind breaking, try pushing the bike down the hill. I don't have any hills here in Florida, but I recall that working pretty well as a kid living in more interesting terrain.
Um, counter-rotating wheels are still gyroscopes. In fact they're extremely stable gyroscopes in that they won't impart rotational velocity on the frame. So by having the wheels on a bike rotate oppositely, you're actually making the gyroscopic effect even stronger.
I think Ars is pulling from this article, which isn't about staying upright but is about the self-correcting steering of a bike wheel (i.e. the fact that you can ride hands-free.) http://www.sciencemag.org/content/332/6027/339.abstract -- in which case the conclusion is correct and likely due to the geometry of the wheel. For example tractors have convex pulley systems that allow leather belts to self-center despite not being perfectly aligned. It's counterintuitive but it works.