Mental Floss: Why is it so hard to balance on a bicycle that’s not moving, and easy on one that is?

After a great start, with correct statements such as

bikes are, however, dynamically stable, or stable when moving forward, because steering allows a rider to move the bike’s points of support around under the center of gravity and keep it balanced,

the wheels come of the cart in paragraph 3 with this mess:

Spinning wheels have angular momentum, and when you’re sitting on a bike, you and it and its wheels make up a system that obeys the principle of conservation of angular momentum. Unless torque, or twisting force, is applied from outside the system to change the wheels’ angular momentum, that momentum and the direction of the momentum remain constant. In a nutshell, once the wheels line up a certain way, they want to stay lined up like that. It’s easy for you to move them, but hard for an outside force to do the same, and so the bike is easy to keep balanced but doesn’t topple easily.

1. Unless you and your bike are in free fall in a vacuum, angular momentum will not be conserved.  The slightest lean will allow gravity and the ground contacts to form a couple that applies a large external moment to the system.

2. The wheels do not care which way they are lined up and will easily change orientation in response to external torques, such as the roll torque described in point 1 above or a steering torque.

The rear wheel is generally prevented from presessing in response to a rolling moment, and so will roll with the rear frame exactly as if it were not spinning at all.

The front wheel is generally free to rotate about the steering axis and so gyroscopic pressession will cause it to steer in the direction of an applied roll torque and lean opposite to the direction of the applied steer torque.

It pains me a little to point out this flaw because the article ends with a plug for the wikipedia article and even credits me for the picture I downloaded from elsewhere on wikipedia and cropped to show cyclist performing a track stand, but facts is facts, and this article gets a couple of key facts wrong.

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HowStuffWorks: How Motorcycles Work

At least the explanation of motorcycle steering doesn’t invoke magical gyroscopic stability, but it does assert that countersteering works because of gyroscopic precession.

This motion is called precession, and it’s what causes the steering in motorcycles to be counterintuitive.

No mention is made of roll moments due to laterally accelerating contact patches or gravity, just precession.  Professor Cossalter in his excellent Motorcycle Dynamics, on page 304 of the second edition, calculates the roll moment generated by gyroscopic effect for a motorcycle traveling at 22 m/s (79 km/h or 49 mph) to be 3.5 N-m (2.6 lb-ft) and compares it to the roll moment generated by the accelerating contact patches of 30 N-m (22 lb-ft), which is 8.6 times larger. He concludes with the note that the gyroscopic effect is present from the instant torque is applied at the handlebars, and the roll moment generated by the lateral force of the tires can take some time, ~0.1 seconds in this example, to build up.

So gyroscopic effect is neither necessary nor sufficient for steering in motorcycles to be counterintuitive. Instead, steering in motorcycles is counter intuitive because countersteering is necessary, and countersteering is necessary because motorcycles are single-track vehicles that must lean into a turn. Finally, countersteering works because of the roll moment generated by laterally accelerating contact patches, the force of gravity acting on the center of mass, and to a small amount, if spinning wheels are present, gyroscopic precession.

If you are going to explain how stuff works, it probably helps to learn how stuff works first.

BoomerBiker: Gyroscopic Precession

Boomer Biker tries to get it right, but ends up in a muddled mess anyway, with statements such as these:

“Gyroscopic precession” is the tendency of a rapidly spinning object to resist being tilted.

and

Precession is far more powerful than gyroscopic stability.

Oddly, the first statement is immediately followed by a dictionary definition which contradicts it.

The second statement is one of several that invokes “gyroscopic stability” as though it were some phenomenon different from precession.

What appears to be stability is exactly precession. Spinning objects respond to an applied torque by rotating about a third axis, perpendicular to both the spin axis and the axis of the applied torque and at a rate inversely proportional to the spin rate. That is all. If a gyroscope or a spinning bike wheel is prevented from precessing, as the rear wheel of a bike usually is, it moves in response to an applied torque exactly as it would if it were not spinning. There is no magic stability.

Professor Cossalter, on page 304 of the second edition of his in his excellent Motorcycle Dynamics, calculates the roll moment generated by gyroscopic effect for a motorcycle traveling at 22 m/s (79 km/h or 49 mph) to be 3.5 N-m (2.6 lb-ft) and compares it to the roll moment generated by the accelerating contact patches of 30 N-m (22 lb-ft), which is 8.6 times larger. He concludes with the note that the gyroscopic effect is present from the instant torque is applied at the handlebars, and the roll moment generated by the lateral force of the tires can take some time, ~0.1 seconds in this example, to build up.

C.H.U.N.K. 666: An Introduction to Bicycle Geometry and Handling.

After a great start, with lines such as:

the ability to steer is necessary to keep a bicycle moving under any circumstances,

the author slips in some malarkey like this:

when the bicycle is moving fast, the rider has more momentum, and inertia will exert a greater pull on the bicycle.

Momentum is a vector quantity, and as such, the momentum in one direction, such as straight ahead, is completely independent of the momentum in an orthogonal direction, such as to the side. Therefore increasing momentum in the direction of travel can have no effect on momentum to the side.

Instead, by moving forward faster, a smaller steering angle is necessary to accelerate the contact patches in the direction of lean.

Exploratorium: Science of Cycling

The Science of Cycling article by the Exploratorium does many things well, until it lays this egg:

Interestingly, many scientists are in complete disagreement about even the fundamentals of balancing and steering. Some insist that gyroscopic action is responsible for stability, others say the exact opposite.

Talk about “teaching the controversy.” Please name one “scientist” that is getting articles published about bicycles or motorcycles that would make the claim that “gyroscopic action is responsible for stability.”

Instead, exactly the opposite is true. After the  David Jones Physics Today article in 1970,  it is a well established fact that gyroscopic effects are not necessary for bicycle stability.

More recently, Kooijman, et al., in their 2011 Science article,  demonstrated that neither gyroscopic effect nor trail are necessary nor sufficient by themselves for self-stability.

Is bicycle science now like evolution and the age of the universe, about which some publishers feel the need to appease the religious right?

Rider Education Of New Jersey: Stability And Cornering

While there are several good details in this article, including the observation that the best way to

restore the situation where the contact patch line is under the Center of Gravity

is to

Move the tire contact patch line back UNDER the new Center of Gravity

it does invoke not one, but two common misconceptions:

1. Forward inertia of the motorcycle will tend to keep the bike moving in a straight line.

2. Gyroscopic forces, primarily of the two wheels, but also other components whose axis of rotation is in the same direction as the wheel spindles, tend to resist any change in the angle of lean of the motorcycle.

To understand the problem with the first point, it is helpful to remember that inertia is a vector quantity, and as such, the inertia in one direction, such as straight ahead, is completely independent of the inertia in an orthogonal direction, such as to the side. Therefore increasing inertia in the direction of travel can have no effect on inertia to the side.

Instead, by moving forward faster, a smaller steering angle is necessary to accelerate the contact patches in the direction of lean

The problem with the second point is that gyroscopic forces of the wheels, and any other spinning parts simply do not resist changes in the lean angle of the motorcycle.

Instead, those spinning parts simply move, in response to an applied torque, in a way unlike that of non spinning parts. This is called precession. If a spinning part is prevented from precessing, as the rear wheel and most engine parts are, by the friction of the front and rear tire contact patches, then they roll in response to applied roll torques exactly as they would if they were not spinning.

The two roles that gyroscopic effect can have on the front tire are:

1. to generate a steering torque towards the direction of lean

2. to generate a roll torque in response to apply steering torque.

The first can contribute to the overall tendency of the bike to steer in the direction of a lean, but only if the front wheel is free to steer.

The second can contribute to the desired leaning of the bike in response to an applied coutersteering torque on the handlebars.

TotalMotorcycle.com: Beginner’s Guide to Motorcycling

While it is laudable to try educating new riders, it is never helpful to give them wrong information, as TotalMotorcycle.com does in their Beginner’s Guide to Motorcycling Section Five 1/2: Counter Steering, Push Steering the Easy way.

As the front motorcycle tire spins, the force of the spinning causes the motorcycle body to want to stay upright and be stable.

This is wrong in several ways:

1. inanimate objects, such as motorcycle tires don’t want anything, but that is really a stylistic issue.

2. the bigger problem is the suggestion that the spinning of the tire keeps it upright. If the front wheel can not steer, no amount of spinning could keep it upright, and if it can steer, the rider and at least three other factors, besides gyroscopic effects, tend to steer it in the direction of the lean: geometry, specifically trail; mass distribution; and tire mechanics.

Why go out of the way to invoke some magical property of spinning wheels, when the critical contribution is the ability of the front wheel to steer?

Phys.org: How the bicycle got its spokes

A recent news article on Phys.org tries to present some of the history of the technical development of bicycles. It goes off the rails, however, when it touches on balance:

Then comes the phenomenally complicated bit: not falling off. “Only a few people really understand how balancing a bicycle works,” says Philip Garsed, a PhD student in electronic engineering whose passion for bicycles developed into his recent talk at the Cambridge Science Festival, titled How the Bicycle Got Its Spokes. “There are lots of effects interacting with each other. One of the most interesting is the gyroscopic effect. If you have a wheel spinning around an axle and then try to tilt the axle from side to side, you get this weird effect that makes it resist that change. On a bike, that tends to keep you upright and for quite a long time it was thought that this was the reason why a bike can be balanced. It was then proved that it was not actually necessary – someone stuck a flywheel that rotated in the opposite direction on to the wheel and eliminated the effect, but the bike was still rideable. I have a book that explains the details of bicycle balance. It’s hundreds of pages thick and it helps to have a physics or engineering degree to get your head around it.”

1. It is not phenomenally complicated: bikes balance by being steered in the direction they are leaning.

2. Anyone who has read the second paragraph of the Wikipedia article knows this.

3. Spinning bicycle wheels do not resist change, they merely change in a way unlike non-spinning bicycle wheels. They cannot keep a bicycle upright unless at least one of them is allowed to steer.

It would seem that if you thought something was phenomenally complicated, you would avoid speaking publicly about it, or at least check with someone who does understand the topic before you do.

I posted a comment at the bottom of the article and emailed Philip Garsed at the University of Cambridge, but have received no reply.

PhysLink.com: Do gyroscopic forces from the wheels make any significant contribution to the rideability of a bicycle?

PhysLink.com tries to answer the question, and the author of the reply does not beat around the bush:

Yes, the gyroscopic forces, better known as the angular momentum, of the wheels on a bike allow us to ride a bike. … The reason that you stay up on a bike is that angular momentum, like regular momentum, must be conserved if no external torques act on the object. … When you are riding a bike forward, the right hand rule gives the direction of angular momentum to be to the left, perpendicular to the wheel. This direction does not want to change, therefore the wheel wants to stay upright and it makes the bike very ridable.

Wow. Flat out wrong in many ways and no mention of steering at all.

1. The  David Jones Physics Today article from 1970,  demonstrates that a bike is quite ridable if the gyroscopic forces are canceled.

2. Gravity acting on the center of mass and the ground reaction forces create a couple that acts as a large external torque. If there were no external torques, bikes wouldn’t tip over at all and there would be not need for a way to balance them

3. The direction of the angular momentum vector can easily be changed by the application of an external torque, such as the one described in the previous point.

The author even goes so far as to suggest that he has seen Jones’ article but comes to the opposite conclusion that Jones does.

However, when the extra wheel was spun backwards, the bike became almost impossible to ride because the vectors for angular momentum cancelled each other out. It was like trying to balance a bike that was not moving.

Instead, a main point of Jones’ article is how hard it was for him to make an unridable bike.

The Straight Dope: Why is it easier to balance on a moving bike than a non-moving one (original and revisited)

The original response to this question was just terrible.

Because modern bicycles are equipped with a pair of  gyroscopic stabilization devices that require the motion of the bike in order to operate. These devices are known as “wheels.”

It implies that the reader is a dummy for not knowing this obvious “fact” and that non-modern bicycles maybe didn’t have a pair of wheels.

The revised response is better but it merely discards one misconception for another. After citing the David Jones Physics Today article from 1970 , the author writes:

So why do bikes stay up? The answer is: trail.

While it is true that both trail and gyroscopic effects can contribute to the self-stability of a bike, it has been demonstrated, by Kooijman, et al., in their 2011 Science article,  that neither trait is necessary nor sufficient by themselves for self-stability.

Instead, the simple answer is that when a bike is moving forward, it can be steered to keep the wheels under the center of mass. More correctly, by steering in the direction of a lean, the tire contact patches accelerate in the direction of the lean causing a moment about the center of mass to counter the moment created by gravity.

The steering torque necessary to steer in the direction of the lean can be provided by the rider, or, in some cases, by some combination of mass distribution, geometry, gyroscopic effects, and tire properties.

The revised response ends with

On the bike path of progress, you have to expect the occasional bum steer. 

They have provided two bum steers so far. Perhaps they can get it right on the third try.

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