So it follows that to turn you must establish and maintain a lean - yes?
I suggest another test: Next time you have some snow on the roads, ride straight, then turn. Inspect the tire tracks. I think you’ll find that the front tire track first moves to the opposite direction of the turn.
The same test may be possible on a dry road by first riding through a puddle.
I think this is at least partially a disagreement on terms. Deliberate countersteering may not be occurring, even though some countersteer occurs through the same automatic balance reflex that we don’t consciously track every wiggle of the handlebars, we just ride.
In order to lean, one must push against something - the bike seat and/or pedals. The bike then pushes against the ground. If the force is moving outside of the contact patch to the left, our reflexes will give the subconscious left twist of the handlebars, and then reverse the turn to follow the imbalance created by the lean.
Whereas to ride motorcycles, countersteering is much more pronounced and thus deliberate.
More precisely, looking at torque around the axis through the points where the tires contact the ground.
I don’t think there’s a lot of disagreement at this point is there? To turn left on a bicycle, there has to be a lean to the left (otherwise the rider falls over to the right when the front of the bicycle tracks left). That left lean can be produced through a temporary right turn of the handlebars (‘countersteering’) as part of the turn (typically not consciously noticed by the rider), or possibly an unsteered left lean caused by random bumps. And of course a combination of the two can also create a left lean (including a slight temporary overcorrection to a right lean).
Now, I’m not sure if at this point there’s anyone who disagrees that countersteering happens (unconsciously or not) the vast majority of time someone turns on a bike.
But there’s no fundamental difference between the dynamics of a motorcycle and bicycle. Motorcycles are heavier, probably a relatively lower center of gravity, and possibly a wider contact patch (but maybe not enough to make a difference given the greater weight), but the steering mechanisms are the same.
Yes, a lean can be created by countersteering, but that’s not the only way it can be created, and I maintain that it’s not even the typical way that it’s created on a bicycle.
I guess the question is when you start to lean, how much sideways force is being reacted by the ground against the tires? Is it small enough to be swamped by the friction? Or is it merely the case that it isn’t noticed because it falls into the intuitive corrections you are already making via your internal balance system?
Then what is the typical way to initiate a turn on a bicycle? You reject countersteering as a primary mechanism, but I haven’t heard you offer an alternative.
What’s your theory of two-wheeled vehicle dynamics, and why do you claim it’s a more common way to initiate a turn than countersteering?
Hm. I’d refer you to Vittore Cossalter’s Motorcycle Dynamics for an articulation of the currently-accepted theory.
Section 8.3 (pages 345-350 of the English second edition) has what you’re looking for.
Fajans wrote a very straightforward paper describing these phenomena:
J. Fajans, Steering in bicycles and motorcycles. Am. J.Phys, 68:654, 2000
Specifically, Fajans asserts that there are only two ways to steer a bicycle or motorcycle: countersteering and hip-throwing. But hip-throwing is just hands-free countersteering; turning right requires hip-throwing to the left, which in turn rotates the front wheel to the left. Momentum then causes the rider to fall to the right, and the right turn is initiated.
You seem to be skeptical about whether the field of vehicle dynamics actually exists and whether people in that field have bothered to do any actual work. But if this work existed, it would be directly applicable to mechatronics and robotics, yes? It turns out that control theory from vehicle dynamics is directly applicable to how two-wheeled single-track robots steer. In other words, yes, through countersteering. I would argue that the application to two-wheeled robotics control constitutes a pretty good test of the theory that comes out of vehicle dynamics.
If there’s some other mechanism that supersedes countersteering—the “typical way” bicycles turn, according to you—the robotics researchers are neither using it nor publishing papers about it. You have a real opportunity here to shake up the status quo. What’s your theory?
I maintain that a bicyclist initiates a turn (say, to the left) by turning the handlebars counterclockwise and shifting his weight to lean to the left. And I’ve yet to see any refutation of that hypothesis, just absurdities like the claim that it’s impossible to lean without countersteering.
How do you think the “shift his weight to lean to the left” works? What exactly is supplying the external force to move his weight to the left?
Since we don’t have movable fins or feathers, the only way to push yourself to the left is by applying force through the tires. But how do you push sideways againt the ground, through the tires? Do you think every time you turn, you are pushing sideways on your pedals to move your center of mass?
My preferred answer to this would be to hop on a bike and say “like so” while doing it. I’m not sure where the confusion is arising, so I can’t give a more detailed answer in text.
But perhaps a thought experiment would help. Imagine an object like a bicycle, but with no moving parts: The steering fork doesn’t rotate at all, and the wheels don’t turn. It’s perfectly bilaterally symmetrical. You hop onto the bike while it’s exactly upright, and do your best to balance. We both agree that you won’t be able to balance for very long… but I maintain that you will at least be able to exert sufficient control to determine which direction you fall over. Well, the same motions you make to accomplish that, on a “bicycle” that definitely doesn’t countersteer, you can also make on a real bicycle.
Then describe the simplest model for a bicycle+rider that can have this ability. If we model it as a rigid object with an additional movable weight in the middle (at the CG), would you agree that this system can only exert a small and short-lived force, equal to the mass x acceleration of the movable weight?
So your claim is that this lateral force, which you agree is insufficient to maintain balance, is still sufficient to initiate a turn?
I’m still tired from the discussion we had on steering two-wheeled singletrack vehicles last fall. Rather than contributing anything new here, I’ll just link to my summary from that last discussion.
TL,DR: Countersteering is the only way to steer a two-wheeled (or two-skied/skated) singletrack vehicle. The countersteer may happen directly (with hands on bars), or indirectly (hands-off, shift your weight, bike leans the other way, steering geometry effects a countersteer). On (lightweight) bicycles, the countersteer is often extremely subtle (a fraction of a degree) and can be induced with tiny forces on the handlebar (measured in ounces), so it’s easy to miss.
Dr. Strangelove, I will very much look forward to your rotary encoder measurements.
Ahh great, now I’m on the hook!
I hope the signal is visible through the noise. The encoder is 600 pulses/rot, which with the quadrature encoding means I get 2400 ticks/rot. So in principle, it’s good down to 0.15 degrees. We’ll see if that bears out in practice, and if I can manage to get a stiff enough coupling to maintain that accuracy. The project might take some time if it turns out that I have to 3D print some brackets or such.
Having had my own experiences with riding too close to an object and not being able to turn away from it, I now understand how countersteering is necessary.
The difficulties in balance on the no-moving-parts bicycle are due to the limits of human reflexes, not to the limits of torque that can be imposed. A skilled acrobat could balance on such a bicycle for several minutes.
And I’ve still yet to see an explanation of the necessity of countersteering that’s consistent with my experiments. We all agree that both lean and rotation of the steering column are necessary to turning a bike. The argument for countersteering is that it’s impossible to initiate a lean without countersteering. I do the experiment and set things up so that I can’t countersteer using the handlebars, and still have no difficulty turning. People respond that even if I didn’t countersteer using the handlebars, that I must have initiated countersteering by leaning. But leaning without countersteering is exactly what they asserted is impossible in the first place.
Chronos: Suppose you have (by any method of your choice) established a substantial left lean and thus a brisk left turn on your bicycle. You now choose to stop that turn - also rather briskly.
How do you do that?
The point is that a countersteer happens either directly (with hands pushing on bars) or indirectly (by leaning your body in the direction you wish to turn, which causes the bike to lean in the opposite direction, which induces a countersteer because of the self-stabilizing steering geometry.) I am confident that Dr. Strangelove’s rotary encoder data will show this.
To prove this is true without a rotary encoder, we could instead build a bike with zero rake/trail: the steering axis is perfectly vertical, and the tire’s contact patch is directly below, and perfectly intersected by, said steering axis. This bike would have zero self-stabilizing tendency. You could still ride it with your hands on the bars, initiating/terminating turns with countersteers (though you’d have to pay a bit more attention to make up for the lack of inherent self-stabilization). However, with hands off of the bars, you absolutely would not be able to steer this bike with body english. You’d lean one way, the bike would lean the other, and you’d continue moving in a straight line because the bike would not countersteer when you leaned it.
I don’t think it’s impossible. Just extremely difficult, and not generally done.
The flaw in your experiment is that you are still allowing enough steering input to maintain balance before the turn. Which, by definition, means you are allowing enough input to make a tiny countersteer. The other flaw is that if you anticipate the turn in advance, all it takes is the tiniest counter-steer or balancing to make sure you are leaning when you reach the point you intend to turn.
Is there snow on the ground in your area? Can you do the test I suggested earlier, i.e. ride straight and then turn to the right without the front tire track veering to the left at all? To prove your point, the tire tracks should be right on top of each other, then the front wheel curves to one side, followed by the rear. And you should be able to do this upon request, so you need someone else to tell you when to turn. (Otherwise if you anticipate a turn, you can build up a lean by balancing the bike imperfectly.)
He doesn’t need snow (which creates its own challenges for riding), just dry pavement and a puddle (which can be intentionally created). I’d enhance the experiment by adding a couple traffic cones or other markers that the rider has to steer through, to minimize the amount of waiting for a random lean in the right direction.