A motorcycle will only remain fairly stable in an upright position when it is moving forwards. We can attempt to demonstrate what centrifugal forces are, by carrying out an imaginary experiment. Let's assume that you have removed a (bicycle) wheel and are holding it, with both hands, one on each side of the axle, in front of you, while it is rotating. It is then quite easy to move the wheel up- or downwards and to the front- or the rear.
However, if you attempt to copy the movement of the handlebars, by tilting the axle out of the horizontal position (from figure 1 to figure 2), you'll notice that the centrifugal forces make it difficult and that surprisingly, they influence the wheel vertically as well. If you tip the wheel, looking at it from above, to the right, it will tip, looking from behind, to the left. This effect only occurs when the wheel is rotating and, the faster it rotates, the stronger the effect is.
To express this in a formula, the generated momentum is the same as the sum of the inertia momentum of the wheel and the velocity at which the wheel is rotating and also how quickly it is shifted from it's stable- to a different postion. The more rapid the steering movement, the stronger the wheel will tip over. In the absence of a driven distance, in this case, the velocity is represented by the angle degree over the time-unit (angular velocity ?).
A motor cycle which is directed into a curve without the necessary preparation being taken, would thus, tip over in the opposite direction. This is why motorcyclists subconciously steer, depending on their curve-entrance speed, first of all, slightly in the counter direction, before leaning into the curve. This is the point when the stabilizing effect of the centrifugal momentum counteracts against the motorcycles tendency to straighten up. The faster one corners, the more difficult it is to maintain the angle.
One can hardly believe it but also other rotating parts in the motorcycle have an influence. Thus, a higher idling RPM can help to balance a motorcycle when it's standing still.
It should be noted, that up to now, we've only dealt with the gyroscopic effects. Of course the construction itself can also influence the stability. So, let's start with the axle, in a four-wheel vehicle it's called the pivot- and in a two-wheeler, the steering axis. We'll ignore the three-wheelers with two front wheels for the moment. The dimensions of the steering axis are described here. The steering head angle (No. 3 in figure 1), is thus formed by the steering axis (No. 1) and the perpendicular (No. 4). The offset (No. 2) results because the steering axis often doesn't run through the center-plane of the front wheel. The relatively large amount of over-run with this vehicle is the reason why the center of the wheel/road contact area trails behind the track-point, an important element for the stabilization of the steering. The above shown trike, which is not very good at cornering anyhow, manages quite well with this stabilization, whereby, with a motorcycle, it would be very restricting.
Through riding over a hump vertically, the track-point can suddenly find itself behind the center of the wheel/road contact area, which cancels out the stabilising effect. It is said that the over-run becomes positive and that the handle-bars have to be held very tightly. Of course, the smaller the diameter of the wheel is, in relation to the height of the hump, the stronger the effect is.
With an increasing wheel diameter, the over-run also becomes greater. The positive offset shown in the above picture also influences the over-run. Whereby however, although a greater over-run, through offsetting, will increase the re-centering forces in the steering, these will be negatively influenced by a greater steering head angle. 06/12