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, almostentirelyindependent 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 theBicycling World, in which I think the law of whirling bodieswill 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.
When a cyclist climbs a hill, he not only overcomes the friction which would be generated if he travelled over the same length of level road surface, but he ought to be supposed to establish a certain amount of potential energy, or energy against gravity, and therefore should lose none. Yet he does lose considerable somewhere or he would not dread the hilly road as he does. In this matter of potential energy in hill-climbing upon a cycle, the subject assumes a different aspect from that of rolling on or off obstructions, as in rough-road riding treated of elsewhere. In climbing a hill there is no loss of momentum from a too sudden change in its direction; the matter of inertia does not figure in the case in any way, and we have a mere question of the rise and fall of a weight under certain modifications, said weight being the rider and his machine, said rise the ascent of the hill, and the fall the descent thereof. In a purely physical sense, then, we store up a certain amount of energy, or, in other words, put so much energy to our credit as against gravity, and theoretically we have a right to expect to get the benefit of it.
To illustrate this potential energy, suppose we placea pulley at the top of a hill and a rider at each end of a rope running over the pulley, with one man at the bottom starting up and the other at the top starting down the same hill. The descent of one man would draw the other up, excepting that each would have to work only just enough to make up the loss from friction, as he would in case the road were level and of equal length. I have little doubt that in such a pulley arrangement there would be much less loss of power and energy than riders now experience in the actual practice of hill-climbing. To illustrate with one man how the potential energy should be returned and thereby benefit the rider, let us place him at the top of a hill at the bottom of which another hill of the same height begins, whence, by the acceleration of gravity, the rider ought to find himself at the bottom of the first hill with an amount of momentum acquired that would send him to the top of the next; in other words, we might naturally expect when we roll down one incline to roll just as far up another of the same grade, or of the same vertical height regardless of the grade, or else we should expect a return of the energy in sending us capering over a level road without further labor, until the kinetic energy is exhausted. We find, however, that such a desirable result does not appear, and we notice that, however long, beyond a certain limit, the hill may be, we have no more momentum or kinetic energy at our disposal than we would in the case of a shorter hill. To what can this loss be attributed? There is but one visible cause,—to wit, our work against the air.
If all riding were done in a vacuum, we would more nearly get back our energy, but somehow or other the vacuum is generally in the rider and doesn’t count, so there is an end to that. The rider, then, loses the momentum he would acquire from gravity because the friction of the air is resisting his progress at the rate of, or according to, the square of his velocity. Inorder to store up all the energy in a falling body we must allow gravity to increase the velocity as the square root of the distance. But it is easily seen that a rate of speed will soon be reached such that the air by impact will entirely annul all increase of velocity, and therefore all of the momentum we can expect to have at the bottom of the hill is just that which was acquired at the time and point at which the impact of the air balanced the accelerating force of gravity. This will soon come to pass, even omitting other friction, which, in connection with hill-climbing, we can afford to omit with good reason, because we should expect to have that to overcome if the road were level. The mere difference in the length of the surface travelled over will not bother a cyclist if it be a good level road, so we must blame it all on the air; I see no other way out of it. No manner of springs or anti-vibrators will help us out of this difficulty. If our rider puts on the brake, then of course there is no question as to where the work goes; but, as we all know, with a safe machine and an expert rider this is not often done in an ordinary country.
In defence of our theory of loss of energy on very long hills, observe the fact that a mere rolling road is not generally despised by the cyclist; in fact, many prefer it to a dead level, the writer being decidedly one of their number. The short intervals of labor and rest, the continual barter and sale with gravity, in the transfer of energy to and fro, is not by any means an uncomfortable diversion to either our minds or bodies; but when we come to suffer the usurious interest demanded by the action of the air against us, we simply draw the line, and go by another road, even though the surface thereof be not of the most inviting character.
Some ingenious mechanics have devised mechanism whereby they propose to store up the power lost in the brake action; but it is doubtful if any riders would care for it after they become expert and daring, whichthey all do in course of time in spite of all admonition against undue risk.
Speaking of potential energy and momentum, we naturally come upon the question of machine weight. It is a peculiar fact that the weight of the man does not form so important a part in the bicycle exercise as that of the machine, so that if a rider be heavier by twenty pounds than another, it will not generally count against him; but if that weight is in the machine, competition is out of the question. Nature seems to make up in muscle, or supply of energy in some way, for the extra weight in the man, but said nature is not so clever when this weight is outside of him.
It is sometimes thought that a heavy man or a heavy machine will descend a hill faster than a lighter. This is not reasonable. The accelerating force of gravity being independent of the mass, the heavy system will have the same velocity at the bottom, and momentum being represented by mass, times velocity, the increased mass will increase the momentum; but the speed is the same: this extra momentum is required in raising the heavier system to the same height as the lighter. But even if the rider should get the benefit of all the energy he stores in climbing a hill, there is still an indisputable objection to a heavy wheel,—to wit, a man can labor long and continuously at a strain within reasonable limits, and can do a large amount of work thereby; but to strain the system beyond those limits, and attempt to store up too much energy in too short a space of time, is to make nature revolt, resist the imposition, and refuse to be appeased for some time to come and often not at all; in short, an overstrain is bad, and by a heavy machine, no matter what amount of energy you may store up at the top of the hill, if in so doing nature has been overtaxed, it will result disastrously. So we see that, outside of all mechanical questions of momentum and potential energy, there is a vital objection to heavy machines on purely physiological grounds.