Cycling art, energy, and locomotion

by Robert P. Scott

SOME QUESTIONS OF POTENTIAL ENERGY, MOMENTUM, AND HILL-CLIMBING.

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 place a 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. In order 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, which they 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.