Speed 101: Motorcycle Racing as Real-World Physics Lab at edutopia

The number of errors in this article by Owen Edwards, apparently aimed at educators, helps explain perhaps why so many misconceptions persist in the public mind.

The first misconception is that forward motion somehow causes a bike to resist turning:

In fast turns, lean angle and forward motion counteract the powerful pull toward the outer edge of the track.

and

the initial physics lesson to be learned watching a racing bike hurtle into a tight turn is Newton’s first law of motion: “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it,” explains Falco. To a rider, this means that the faster a motorcycle is going, the less it wants to turn.

The truth is that a a bike’s inertia, the property which does resist acceleration according to Newton’s 1st law, is constant, and a lateral force, such as friction between the tires and pavement, will cause the exact same lateral acceleration when the bike is racing down the track as when it is stationary at the start line.

Mr. Edwards follows up immediately with another common misconception that countersteering works because of gyroscopic precession:

Because the wheels act as gyroscopes, this countersteering leans the bike in the opposite direction (into the turn).

As already discussed repeatedly here, 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.

There’s a little more mumbo-jumbo about contact patches:

the tires at an angle, narrowing what engineers call the contact patch and making the bike easier to turn.

But there really isn’t even enough information there to decide what is wrong with it.

The article subtitle is

Isaac Newton hops aboard a two-wheeled teaching tool,

but it appears Mr. Edwards was left standing at the starting line.

A Motorcycle is a Gyroscope in the SPS Observer

This article by Dwight E. Neuenschwander, a professor in the Physics Department at Southern Nazarene University appears to have been published in the SPS Observer, the quarterly magazine of the Society of Physics Students (SPS) published by SPS and the American Institute of Physics (AIP). No publication date is given, but the article is currently hosted on the SPS Observer web site, which also hosts issues back to 2002, but no way to search them for a particular article or topic.

In any case, Prof. Neuenschwander makes the astounding claim that simply leaning a motorcycle will make the entire motorcycle precess in the direction of the lean:

If you lean to the left, the motorcycle turns left (likewise on bicycles). Why is this so?  … This induces a nonzero torque … Hence the angular momentum vector L rotates about a vertical axis, and the motorcycle precesses to my left.

Not just the front wheel precesses, but the whole motorcycle. No mention is made of steer angle, steer torque, or even friction between the tires and pavement. The whole bikes just yaws by the magic of gyroscopes!

Of course, no such thing happens. Instead, there are two possibilities. Either the front wheel is free to precess about the steering axis, does so to steer in the direction of the lean, and the friction between the tires and the pavement generate a yawing moment on the bike. Or the front wheel is not free to precess and the roll moment generated about the contact patches by the force of gravity acting on the center of mass simply causes the bike to roll until it strikes the pavement. Gyroscopes are not magic after all.

Near the end of the article, Prof. Neuenschwander writes

Hmmm… further research is needed….

We don’t need any further research like this.  What is really needed, instead, is reading up on the topic before writing about it. Sharp’s seminal paper on the Stability and Control of Motorcycles has been available since 1971, so the information is out there.

The Motorcycle as a Gyroscope by Higbie in the American Journal of Phyics

This article was published in 1973, a full 3 years after Jones’ Physics Today article, so there really is no excuse. If Higbie didn’t catch it, then the editors at the American Journal of Physics should have. Their current statement of editorial policy includes

Technical correctness is necessary, and contributions should … significantly aid the learning of physics.

Higbie’s contribution, however, meets neither criteria. He leads off with

As I was riding my 650 cc motorcycle, I discovered a curious fact which might be useful to those who would like to have an everyday example of gyroscopic action.

The curious fact he discovered is that is necessary to countersteer his 650 cc motorcycle, and the rest of the article is devoted to explaining what countersteering is and how gyroscopic precession works. No mention is made of any other phenomenon.

Thus, without so much as a back-of-the-envelope calculation or controlled physical experiment, he asserts that gyroscopic precession is how and why big bikes such as his 650-cc machine countersteer, and even goes so far as to call it gyroscopic turning. This implies that single track vehicles without spinning wheels can’t or don’t countersteer. How does he propose that such vehicles generate the roll moment necessary to negotiate a turn?

Well, if Higbie had done a little math after his exciting ride and before dashing off his manuscript , he would have discovered that gyroscopic effect makes a small contribution to the total roll moment which is quickly overwhelmed by the contribution from the lateral acceleration of the tire contact patches and then from the contribution from gravity acting on the center of mass which is no longer over the contact patches.

As I have written before, there is a nice example provided by Professor Cossalter on page 304 of the second edition of his excellent Motorcycle Dynamics. He 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.

Higbie concludes that

This example of gyroscopic motion is sufficiently involved and “relevant” that it could be useful in first-year college or high school courses.

Sure, unless anyone checks the math and discovers that gyroscopic precession is neither necessary nor sufficient for a bike to countersteer. Then this becomes an example of how misconceptions get perpetuated.

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.

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.