Henry Reich Lateral forces only come from being off balance, not from simply leaning. In order to actually start falling, you must have counter steered (perhaps unintentionally) at least a tiny bit. It's very hard to notice sometimes.

July 16, 2015 17:49:27 · Reply

Michael Richters Counter-steering is certainly the usual way of doing it, and it can be very subtle, but it is not the only way to create the lean necessary for a turn. This would be obvious if you rode a bicycle with a passenger (who has no access to the steering mechanism). When they shift their weight around, they transmit forces through the tires, resisted by the road, causing a lateral wight shift. This effect is not subtle, and is completely independent of my steering motions. Also, if you think active counter-steering is the only way to create a lean, how do you explain the fact that people steer bikes hands-free?

July 16, 2015 18:01:39 · Reply

Henry Reich Ah, I see what the confusion is - by "counter steering" I just mean that the handlebars will turn, not that they have to be actively turned by a rider. For a passenger I'm sure they make it harder to steer, and can change the weight distribution considerably, but if the passenger moves to the right, the bike should lean to the left. Which way does it steer then? If you search for "bricycle" you will find videos of a bike that's been modified to make it un-steerable by leaning.

July 16, 2015 18:13:54 · Reply

Henry Reich I guess what I'm trying to say more specifically is that for a balanced bicycle moving in a perfectly straight line to initiate a turn in one direction, the front wheel contact point has to first move slightly (often imperceptibly) in the other direction. This is a mathematically demonstrated fact.

July 16, 2015 18:19:08 · Reply

Michael Richters Oh, yes, I'm familiar with the "bricycle". You're still failing to understand one thing, though. When the passenger moves laterally, he does push on the bike. And the *bike* leans the opposite way, but that's not all that matters. What really matters is not the angle between the ground and the vertical axis of the frame; what matters is the lateral position of the center of mass of the bicycle/rider system and the point of contact at the ground. If I push against the frame, some of that force leans the bike, but some is resisted by the road, because the wheels don't slip. That moves the center of mass laterally without any steering.

July 16, 2015 18:58:36 · Reply

Michael Richters Something you could try that might convince you (or perhaps you'll see a flaw that I haven't) — stand on one foot, and jump to one side. Then do the same and jump to the other side. You didn't have to first move your foot out from under you, did you? The same should be true of a bicycle. The fact that the rider is free to apply forces from many different points in many directions greatly complicates the question, doesn't it?

July 16, 2015 19:04:20 · Reply

Henry Reich A foot is totally different - it has multiple contact points with the ground, allowing you to apply torques at the ground which help you start leaning in various directions. Where is the torque coming from on a bike to move the center of mass away from the contact point? The rider certainly can't create that torque from inside the system just by changing their mass distribution inside the system. An outside torque/force not at the pivot point is necessary. Gravity is this force (hence the unrideability of the bricycle).

July 16, 2015 19:13:30 · Reply

Michael Richters It can be done on ice skates, too, which are even narrower than bicycle tires. But since that doesn't convince you… Let the rider lean one way, the bike the other way, the let the rider exert a force along the rider's axis, which is now not in line with the point of contact. You must see that this force would be resisted by the ground, and allow the center of mass of the system to shift laterally. This is almost identical to a man in a canoe, who moves from the front end to the back end. The canoe moves under him so that their colnective center of mass doesn't move — but only if there is zero resistance from the water. If we replace the water with a more viscous fluid, that center of mass moves more, until that fluid becomes effectively solid, and the canoe doesn't move at all. The bicycle also doesn't have complete freedom of motion. Lateral forces, even internal ones, cause the bike to lean, but they also push the bike's tires against the road, and that resultant force from the road causes the system's center of mass to move.

July 16, 2015 19:36:21 · Reply

Sergio I Montserrat S And this effect is more noticeable in a bike, where wheel mass and rotation are higher, thus the forces involved in keeping the vehicle upright are higher, and thus riders have to consciously apply counterrotation when they are learning to drive. We don't notice in bicicles because forces are smaller.

July 17, 2015 02:04:25 · Reply

Sergio I Montserrat S It doesn't compare, since the foot and ice skates don't have a torque that works as a gyroscope that actively resists a change in inertia. All other examples you gave also fail to include a gyroscopic stabilizing influence.

July 17, 2015 02:08:24 · Reply