Tag Archives: roll moment

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

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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.

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From Stargazers to Starships at NASA.gov

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In answer to a question about balancing a bicycle on NASA’s (yes, that NASA) “From Stargazers to Starships” site by Dr. David P. Stern we are treated to this gem:

By slightly turning the handlebars right or left, you impart some of the rotation of the front wheel (“angular momentum”) to rotate the bike around its long axis, the direction in which it rolls. 

That’s it, the whole story.

While it is true that the precession of the spinning front wheel in response to an input steer torque is about the roll axis, this effect is minuscule in comparison to the roll moments generated first by the laterally accelerating contact patches and then by gravity acting on the center of mass that is no longer directly above those contact patches. Dr. Stern’s explanation also implies that gyroscopic effect is necessary for balancing a  single track vehicle by steering it, which will come as quite a shock to the guy riding this thing:

As for the actual magnitude of the contribution to the overall roll moment on a bike from the precession of the front wheel, we can refer to the nice example provided by Professor Cossalter in his excellent Motorcycle Dynamics.

On page 304 of the second edition, 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. We should expect the gyroscopic effect on bicycles, with lighter wheels and lower speeds, to be proportionately smaller.

There is a little more nonsense at the end of Dr. Stern’s reply about how bikes with straight forks, such as motorcycles, have no fork offset and so more trail, more stability, and less agility.

The design of the front wheel “fork” is quite interesting, turning forward like the letter j. This is an “inverse caster” which makes the ride less stable–but allows a skilled rider nimble moves. If you ever look at a motorcycle, or at the bikes used in a circus on the high wire, they lack this “letter j” feature, the wheel axis is always in line with the handlebar shaft. That helps stability but reduces agility. 

Can you imagine how much better these guys would be if there were some way to reduce trail and increase agility without curved forks.

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Of course curved forks is only one of several ways to generate fork offset and thereby alter trail.

No, bicycle science is not rocket science, but it still requires that you do your homework.