Subject: Gyroscopic Forces
From: Jobst Brandt
Date: September 16, 1997
The question is often asked and, as often as not, is an introduction to expound on the gyroscopic forces of the rotating wheels that make bicycling possible. This claim is as accurate as the one that authoritatively explains that spokes support the bicycle wheel by hanging the hub from the upper spokes. They don't and it doesn't.
Some who propose the gyroscope theory, also explain that the advanced skill of making fast turns on a bicycle involves a technique they call countersteer. In fact, a bicycle cannot be ridden without countersteer, commonly called balance, and it is this balance that is used to keep the bicycle upright, just as one does while walking, running, ice skating or roller skating. To say that the gyroscopic forces of rotating wheels keep the bicycle upright, ignores that roller skates are operated the same way and have so little gyroscopic moment that one cannot detect it. On ice skates the argument fails entirely. Besides, a bicycle can be ridden at less than three miles per hour, at which speeds there is no effective gyroscopic reaction.
Those who ride no-hands sense and make use of the small gyroscopic effect of the front wheel to steer. This, together with trail of the steering geometry stabilize steering. Without trail, the bicycle would have poor straight ahead preference and would riding no-hands difficult. Many bicyclists never master riding no-hands because the gyroscopic forces are too small for them to detect. Hands on the handlebars completely obscure these forces.
For those who ride no-hands, countersteer should be visible and obvious because the bicycle must be leaned away from the preferred lean angle and direction of a curve so that the turn can be initiated. With hands on the bars, although the opposing lean is unnecessary, countersteer is still needed and can be done without counter-leaning.
That there are gyroscopic forces is evident from the riderless bicycle test in which a bicycle is shoved at a brisk speed (from another bicycle) and allowed to coast on its own. If the initial course is straight, the bicycle will continue this path until it slows to a speed where gyroscopic forces are too small to correct steering. Then the bicycle takes a steep turn as it falls.
Gyroscopic forces are also used to walk a bicycle, holding it by the saddle and steering it to either side by quickly tilting the bicycle. The effect can be observed by resting a road bicycle (with a horizontal top tube) on the shoulder tilted forward just enough to make the front wheel aim straight ahead. Spinning the front wheel by hand forward will make it steer as one expects, left for a left tilt, right for a right tilt, all moves performed in less than a second. With the wheel spinning backward, all responses are reversed.
A good example of a bicycle with no gyroscopic forces is the ski-bob, a "bicycle" with short ski runners in place of wheels. This bicycle, having no rotating parts, is ridden downslope easily by anyone who can ride a bicycle.
Although the gyroscopic effect of its wheels is not what keeps the bicycle upright, as is often claimed, it is essential in riding no-hands, or to walk the bicycle while holding only onto the saddle, as is often done. The belief that leading the bicycle while walking next to it holding onto the saddle is effected by the lean of the bicycle and trail of the front wheel is often mentioned as a mechanism and it seems possible that this is true. However, there are a few effects that make this not the case.
Separating the variables of this effect is difficult unless a good diagnostic method is used. The tests proposed rely on leaning the bicycle near to reality, that is, the bicycle must lean laterally about an axis about as near to the axles of the wheels as it does on the road. This means that hanging the bicycle from high above will cause much translation to achieve lean. This causes lateral accelerations that interfere with the accuracy of the simulation.
There are three effects that interact when walking the bicycle, hand on saddle only. They are:
- Gravitational force of leaning, bearing on the trail of the wheel.
- Inertial force of the center of mass of the wheel and handlebar acting on steering when the bicycle is rapidly tilted.
- Gyroscopic moment about the inclined axis of the fork when the frame is tilted about its horizontal long axis.
The suspended bicycle test works as described below if the head bearings are properly adjusted and the tilt motion is executed in less than a second about an axis near the wheel centers. When done slowly over several seconds the gyroscopic moment is too small to overcome the gravitational moment. If the tilt is induced rapidly, in a small fraction of a second, "countersteer" is induced through inertial moment about the steering axis.
- With the bicycle suspended in a vertical plane, tilted just enough forward to make the front wheel stably align straight ahead:
- With the wheel not rotating, the wheel will steer toward the direction of lateral tilt if the tilt is induced in more than a half second. If the tilt is done rapidly, the wheel will steer in the opposite direction before steering to the direction of tilt.
- With the wheel manually spun forward, its steering response becomes faster but behaves largely the same as with the non-rotating wheel.
- With the wheel manually spun backward, steering response to frame tilt is opposite to the direction of tilt when induced in one second or less. The effect diminishes as rotation slows.
- The effect is best observed if the bicycle is tilted back and forth, equally to both sides of vertical in a one second period. In this mode, steering will nod from side to side, toward the direction of lean if the wheel is spinning forward and opposite to the direction of lean if spinning backward.
The experiment of riderless bicycle stability has been discussed here and bears on this thread because the riderless bicycle has no gravitational lean steer, there being no side loads on the trail of the front wheel. This occurs because the bicycle is balanced. A plumb bob hanging from the top tube will remain pointing to the downtube during the entire run. In this case the bicycle uses only the gyroscopic moment of tilt to stay upright. That is, it steers into the slightest lean that would make it fall. The bicycle finally falls when speed becomes too slow... or it runs off the course.
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