Tag Archives: Linear momentum

Ask a scientist at Argonne National Laboratory

In the reply to Ask a Scientist, on Argonne National Laboratory‘s Newton, there are two answers to the question asking what is the relative contributions from angular momentum and counter steering.

The first response, by Unknown, is not too bad. It quickly dispenses with angular momentum as negligible, and then explains how counter steering can work just fine without angular momentum.

The second response, however, by Dr. Ken Mellendorf, is a muddled mess and should be deleted. He first perpetuates the misconception that the spinning wheels somehow resist leaning and steering, and he follows that immediately with the misconception that the frame itself resists steering simply by moving forward.

The wheels are spinning in a vertical orientation, aligned with the path of the bicycle. The faster they spin, the more difficult it is to change them. The bicycle is moving forward. The faster it moves, the harder it is to make the body of the bicycle change direction.

Spinning wheels have no resistance to roll moments if they are prevented from precessing about the yaw axis. Instead, a roll moment causes the front wheel to precess in the direction of the lean, and the rear wheel, which is prevented from precessing by the frame and friction in the two contact patches,  leans exactly as it would if it were not spinning.

Linear momentum is a vector quantity and so the linear momentum in one direction, such as forward, has no effect on linear momentum in an orthogonal direction, such as to the side. Thus the increased linear momentum from going faster is not responsible for the smaller steering inputs required to maintain balance. Instead, it is simply the fact that a give steering input works faster, that is causes a larger lateral acceleration of the contact patches, if the wheels are rolling forward faster.

Then, Dr. Mellendorf tries to tackle counter steering, and things really get crazy.

Once turned, the front wheel moves to the side. The body of the bike, however, tries to keep going forward. The “natural” thing for the bike to do is fall down as the front wheel pulls out from under it. The rider has to lean toward the inside of the turn to prevent this from happening. If the bike “tries” to flip to the right, The rider leans to the left to counter the effect.

If by “the rider has to lean” he means “the rider has to lean along with the bike”, why would the rider have to do anything other than stay with the bike as it does its “natural” thing? Does he also mean to say that the rider cannot lean relative to the bike? Better not tell these guys:

If by “the rider has to lean” he means “the rider has to lean relative to the bike,” better not tell these guys:

The fact is that a rider can stay perfectly in line with the frame of his bike, or lean relative to the bike either into the turn or away from the turn. All that matters is where the combined center of mass is located with respect to the tire contact patches, and the only time a rider must lean to the left if the bike “tries” to flip to the right is when the bike is not moving forward at all.

No, Dr. Mellendorf’s description is most definitely not how a bicycle works.

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What makes for bad bicycle science

As with most endeavors,  there are plenty of ways to make bicycle science bad. There are a few ways, however, that seem to be more popular than others. Here are some of the most common:

1. Ignoring or misinterpreting previous work

Most of the examples itemized in the posts on this site make this mistake. The UW-Madison Physics Department writes as though it were in a vacuum, while Physlink.com cites a useful work and then comes to the opposite conclusion of the author.

Despite flaws in its final analysis, Jones’ 1970 Physics Today article demonstrates the limited role of gyroscopic effect pretty clearly . Thus, anyone writing after 1970 that bike stability or ridability derives solely from gyroscopic effects or that bikes are almost impossible to ride without gyroscopic effects simply hasn’t done their homework.

2. Misinterpreting laws of mechanics

By far, the most popular law to flaunt is that of angular momentum, as demonstrated by Mental Floss.

Spinning wheels have no resistance to roll moments if they are prevented from precessing about the yaw axis. Instead, a roll moment causes the front wheel to precess in the direction of the lean, and the rear wheel, which is prevented from precessing by the frame and friction in the two contact patches,  leans exactly as it would if it were not spinning.

A related misconception is the assertion that angular momentum is somehow conserved when riding a bike and this conservation of angular momentum is why the bike stays upright. Instead, a roll moment from gravity or a steer torque on the handlebars from the rider easily modify the angular momentum.

The next most popular law to flaunt is that of linear momentum, as demonstrated by Rider Education of New Jersey.

Linear momentum is a vector quantity and so the linear momentum in one direction, such as forward, has no effect on linear momentum in an orthogonal direction, such as to the side. Thus the increased linear momentum from going faster is not responsible for the smaller steering inputs required to maintain balance. Instead, it is simply the fact that a give steering input works faster, that is causes a larger lateral acceleration of the contact patches, if the wheels are rolling forward faster.

3. Providing no equations or calculations, no instrumented physical experimentation, or any other sort of validation

This is more of a problem with articles in supposedly peer-review journals, such as in the European Journal of Physics.

Certainly, not every article is intended for a technical audience, but every assertion still needs to be based on reality. Claiming the gyroscopic effect is responsible for so and so without even doing a back-of-the-envelope calculation to show it is possible is just blowing smoke.

Direct human observation is notoriously unreliable, especially of small behaviors combined with large behaviors, such as the steer angle of a speeding motorcycle. Even the Wright brothers observed that most bicycle riders do not realize that they apply a steer torque to the left in order to turn right.

 

Dave Moulton’s Blog: Head Angles and Steering

In an older post, in which he get’s into stability and handling, Dave helps perpetuate two old misconceptions:

Because you are riding straight the gyroscopic action of the spinning wheels, plus your own weight and momentum, is holding you vertical just as surely as if you were physically holding the front wheel.

1. Gyroscopic action simply does not work like this. Instead, either a spinning object precesses in response to an applied torque, as is approximately the case with the front wheel of a bike, or it is prevented from precessing and so reacts to an applied torque exactly as if it were not spinning at all, as is approximately the case with the rear wheel of a bike. Neither holds anything vertical. The front wheel steers to accelerate the contact patches laterally and create a roll moment to counter the roll moment of gravity on the leaning bike, and the rear wheel simply leans with the rear frame.

2. The forward moment of the bike and rider contribute zero resistance to tipping. Linear momentum is a vector quantity and so linear momentum in the forward direction is completely independent of linear momentum in the lateral direction.

3. The mass of the bike and rider resist acceleration due to the force of gravity exactly the same when moving forward as they would when stationary. Whatever velocity they may have makes no difference.

Dave is no longer accepting comments on this post, so I cannot point out these mistakes there. Perhaps he will see them here and make a correction.

European Journal of Physics: On the stability of a bicycle on rollers

Unlike all the previous examples discussed, which are self-published and answerable to no one, the European Journal of Physics describes itself as a peer-review journal, and as such, it should be held to a higher standard. That makes the 2011 article “On the stability of a bicycle on rollers” by Cleary and Mohazzabi all the more troubling.

Jim Papadopoulos and I, with the help of Andy Ruina, responded with “Comment on ‘On the stability of a bicycle on rollers’“, but it was treated as though it were merely the other side of some controversial issue with no clearly correct answer. Instead of trying to paraphrase what we spent weeks polishing to perfection, let me just quote directly from our response:

The two key differences noted in the paper, however, are not correct. The first is the authors’ claim (page 1297) that ‘riding a bicycle on rollers explicitly tests the role of the centrifugal force’, repeated in other words as ‘if the bicycle and the rider both lean to one side, there is no centrifugal force to correct the lean on rollers . . . ’. This claim is most easily refuted for treadmill riding, to which the authors suggest their ideas also apply. Riding a bicycle on a constant-speed treadmill is actually (neglecting wind resistance) mechanically identical to riding on fixed, level ground at a constant speed. The most straightforward explanation for this is Galilean invariance, which says that the laws of mechanics are the same in all reference frames moving at a constant velocity relative to each other. To argue against this invariance, one would have to show that the mechanics have changed at some point in the following short series of experiments.

(1) Ride a bike on the deck of a long stationary ship straight toward the stern at 18 km/h, as indicated by a speedometer on the bike’s handlebars.

(2) Ride on the same ship that is now traveling forward at 18 km/h relative to the shore, straight toward the stern at 18 km/h, and thus remain stationary relative to an observer standing on shore.

(3) Bring the ship back to rest, and ride straight toward the stern at 18 km/h on a deckmounted treadmill whose belt is moving straight toward the bow at 18 km/h, and thus also remain stationary relative to an observer standing on shore.

In a video of just the bike and the surface on which it rides, the scene in experiment (3) cannot be distinguished from the scene in experiment (2) because the mechanics are in fact identical. And those, in turn, are identical to the situation in experiment (1). Thus, riding on a treadmill is mechanically no different from riding on fixed ground, and any differences between riding on rollers and riding on fixed ground are, in fact, differences between riding on rollers and riding on a constant-speed treadmill.

The second issue is the paper’s reinforcement of the common misconception that inertia or forward momentum somehow provides stability. This is indicated by the phrases ‘forward inertia . . . aids in bicycle handling for stability’ on page 1293 and ‘the loss of inertia limits the degrees of freedom in bicycle stability’ on page 1299. This point is again simply refuted by the Galilean invariance: in a frame of reference that is stationary with respect to the ground, a bicycle on a treadmill has no forward momentum, yet it has the same balance dynamics (as argued above).

We could not understand Cleary and Mohazzabi’s reply and so discontinued the discussion.