CHAPTER VII.
BALANCING, AND SOME QUESTIONS OF POTENTIAL ENERGY—HILL-CLIMBING.
It seems pertinent at this point to make some further distinction between two distinctive classes of road wheels. The conception in the mind of man of road carriages which require an element of balancing was a recent event in the development of vehicles in general, and the similarity of the words bicycle and tricycle, together with the fact that both are included in the generic term velocipede, has led many to overlook a distinction of balancing, which should class them under very different heads. Both are velocipedes if we mean machines run by foot-power; both are man-motors in the light that human force or energy actuates them; but the two-wheel single-track machine must employ a particular faculty on the part of the rider, not required in running one of stable equilibrium.
It seems superfluous at this stage of development of the art to enlarge upon the fact that a bicycle has to be balanced by a particular action not required in any other form of carriage; but when inventors will keep on getting up means to lock the steering device, and riders will persist in reminding us that the steering head “moves too easily,” it is severely pertinent to remark that while a certain law of whirling bodies might show us that a wheel will not fall over quite so quickly when rolling as when standing still, yet it is not this law so much as the action of steering that differentiates the bicycle, or single-track carriage, from other machines. The action of the handle-bar while in motion does substantially, in balancing the bicycle, what you would do if you were balancing a cane vertically on the end of your nose: if the cane starts to fall, you run in that direction with your nose till you get under the centre of gravity again. But the bicycle can only fall sideways, so, when it tends to fall in that way, or when the centre of gravity gets to one side of the vertical line from the point of support on the ground, you cannot run directly sideways with the support as you would in the cane illustration, but you can run indirectly sideways, nevertheless, with the point of support, the only difference being that you must run considerably forward at the same time in order to shift the lower extremity, or point of contact and support, in that direction.
After considerable discussion of this apparently simple subject with eminent gentlemen well qualified to speak on such topics, the following appeals to my mind as a more definite and complete explanation than that given in the nose and cane case, bringing in an element of the problem omitted above, to wit: in running the point of support of contact across and under, as it approaches the vertical plane of gravity and general forward momentum, the steering wheel lies slightly across this plane, and its own plane is still out of vertical, leaning a little, as it did before, with the centre of gravity back of the point of support; the forward momentum then throws the entire system upright. In rapid running this momentum does a large proportion of the work, and it has been vigorously maintained that all balancing is due to this element; for small motions, however, the cane explanation is quite sufficient.
The foregoing explanation of uprighting the bicycle is, to my mind, almost entirely independent of any law of whirling bodies as generally understood.
An article showing that this subject is not devoid of interest or obsolete is given below from the Bicycling World, in which I think the law of whirling bodies will apply. “The Rochester wheelmen debated the question, ‘Why does a bicycle stand up while rolling and fall down as soon as onward motion ceases?’ The answer decided to be correct was, that ‘the bottom of the wheel can have no side motion because it rests on the ground; and since the bottom is constantly becoming the top and the top the bottom, if the upper part of the wheel gets any lateral motion, it is checked by being brought round upon the ground again before the motion has too much influence.’” I do not suppose this ingenious decision, rendered by the high and mighty Solons of the Rochester Club, was a serious one; however, we do find that just such logic is quite common.
It is not plain whether the question discussed was that of a bicycle with or without a man upon it, but I take it to be the latter. Some of the gentlemen had no doubt noticed that to give the machine a shove it would keep upright for a longer time running than when standing unsupported. This is purely a case of the law that whirling things tend to keep their own plane, as illustrated in the gyroscope and the spinning top. In the running bicycle without a man upon it to constantly rectify its position, the principle is simply one of the parallelogram of rotations. If the wheel from any external force starts to fall over, or, in other words, to revolve around a horizontal line normal to its geometric axis, then, since the wheel is already revolving about its axis in the axle, the resultant of these two rotations will be a rotation about an axis inclined to the former axis of the wheel, which means that the wheel will begin to circle around a centre at some distance from the wheel on the side towards which it starts to fall. This new axis about which the wheel revolves will of course be in a plane perpendicular to the new plane of the wheel, and will be inclined downward from the horizontal plane through its centre, so that the wheel is no longer running in a vertical plane. The rotation about the centre outside of the wheel, towards which centre the wheel leans, brings into play a centrifugal force acting to upright the wheel; that is, to bring it back to a vertical plane. Now, if the wheel be run along a straight groove, so that circling around a centre is prevented, then it will fall as quickly as when standing still; or if, in the bicycle, the steering-wheel be locked so that it will not turn out of the plane of the two wheels, there would be no uprighting resultant, and the machine, according to Newton’s law of independent forces, would fall.