# Balancing a Bicycle

Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."

## Question

Paul Cook <cmd@plantaganet.com> remembers a Marilyn column from about two or three years ago, in which Marilyn explains why it is easier to balance a moving bicycle than a stationary bicycle. According to Paul, Marilyn claimed that precession occurs in spinning bodies as a result of external forces acting upon them due to the spinning, and that these forces become stronger as the speed of rotation increases. She also suggests that it would be easy to remain aloft if you were able to sit on a giant gyroscope and steer it to avoid tipdowns.

If you have this column, please send it to me.

## Paul Responds

Apparently she thinks that the "external forces" are "due to the spinning" and that the faster the spin, the stronger the external forces. She thinks that as a gyroscope slows down, it tips more and more. (Actually, it remains upright as long as the rotational speed is great enough that the gyroscope is in a "sleeping" state. Below that critical rotational speed, it will begin to undergo nutation and will eventually fall over. But this ain't what she said.)

As for her comment about sitting astride a giant gyroscope and steering it just a little to avoid its tipping -- I really am not sure what to say, except that I know that she is confused.

## An Explanation

Jeff Kaylin <jkaylin@aol.com> offers the following explanation:

The gyroscopic force is responsible for the bike staying up, but not in the sense of holding it up. Although the force is strong when we think about turning, it is very minor compared to gravity and your weight. What happens is that when the bike tips to the left, the gyroscopic force twists the wheel (and handlebars) to the left. Therefore, the bike is steered in a direction to put the wheels underneath the weight. This happens because the steering is in the front of the bike. If the steering were in the rear, the bike tipping to the left would have the rear end of the bike steering to the left which in effect makes the motion turn to the right and you are down on the ground.

However, motorcycle riders have a tougher time with those larger tires. The trick is to turn in the opposite direction at first so that the cycle tips into the desired direction and then skillfully steer in the correct direction, maintaining a reasonable bank. The ending of the turn is just the opposite.

I've heard of people trying to ride their bicycles with their arms crossed. The trick is to lock the arms and steer with the shoulders. Now let's have someone try to ride backwards! I bet the falls will be slammers.

## The Role of the Fork

John Dunn writes:

I remember when MvS did the balancing a bicycle column. Her answer was wrong, but your revised answer is not much better. The fork design has a greater deal to do with the stability of the bike. The angle that the fork makes with the road, and the bend of the fork affect it far more than any possible gyroscopic effects. The "contact patch" of the tire is ahead of the line that the fork makes due to the bend in the fork. As the handlebars are turned, the wheel is steered underneath the direction of the fall. For a real demonstration of this, if your bicycle is capable, turn the handlebars completely around. You will find that it is almost impossible to ride. Examine children's bikes, and you will see that they have a greater bend in the fork, so their bikes will be easier to keep upright.

## The Contact Patch

Ben Lien <lienb@asme.org> disagrees:

Actually, the contact patch is behind the line of the fork, despite the bend in the fork that places the patch farther forward than would otherwise be the case. The angle of the head tube causes the contact patch to be behind the line of the fork. The bend in the fork is there to reduce that distance. This gives the bicycle more maneuverability.

The farther the distance between the axis of the fork and the contact patch, the more stable the bicycle is (and I'm sure there is a limit somewhere). The bend in the fork helps the rider steer by making the bicycle less stable (more maneuverable).

## Precession and Bicycle Geometry

Ben Lien <lienb@asme.org> also provided the following information:

The explanations of gyroscopic forces are valid for high speeds, where gyroscopic precession is more of a factor. At low speeds, balance becomes more a factor of geometry of the frame. You will notice that when a stationary bicycle is held upright on a flat surface, and then tilted slightly to one side, the front wheel will tend to steer itself into the turn. This is due to the amount of "trail" in the frame.

To find the trail, measure the distance along the ground from the extended centerline of the head tube to the point of contact of the wheel. This distance acts as a moment arm, which turns the front wheel when the tilt of the bicycle causes the upward force from the ground to be out of plane from the axis of the head tube.

A good reference for the subject is Bicycling Science, by Frank Whitt and David Wilson, published by MIT press. The book contains a chapter on balance and steering, complete with bibliography. It cites a study by David Jones, who cancelled the gyroscopic forces in the wheel with a counterrotating wheel to try to make an unridable bicycle. The result was only a small difference in handling characteristics.

I tried to think of a good example of dynamic stability that doesn't use any wheels, and the best I can come up with is standing on one ice skate - it is easier to do when moving. The problem is, the skate doesn't steer for you as the bicycle does.

http://www.wiskit.com/marilyn/bicycle.html last updated July 19, 1998 by herbw@wiskit.com