Cycling art, energy, and locomotion

by Robert P. Scott

The diagrams show the paths of the point in the various machines passing over a four-inch obstruction; F designates the front and R the rear wheel, and the arrows indicate the direction of translation,—that is, the way the machine is running. The degrees designate the angle between lines from the drive-wheel axle, one extending vertically and the other through the saddle; sometimes also expressed in inches of horizontal distance between verticals through the rear axle and saddle. The heights or top points of the curves from the base line show the amount the machine is raised at the saddle as each wheel passes over the obstruction; these heights give inferentially the position of the saddle between the wheels, or, rather, between the vertical lines through the respective axles thereof, since the nearer over a wheel the saddle is placed the more it will be elevated when the wheel passes over the obstruction. Again, from the location of the saddle with reference to the axles we can determine the amount of weight carried by each wheel, the weight each carries being proportional to the respective distances from the saddle horizontally. The sum of the heights of the two curves from the general level will be the height of the obstacle.

Theoretically there is no difference in the amount of work required to pass over an impediment, no matter where the saddle is placed, as the man must be raised in all to the height of the same, and it does not matter whether he is lifted up half way twice or all the way once in so far as the amount of labor is concerned. The man and the machine must be lifted up to a certain height in some way; as it happens, it is more comfortable to be lifted twice through half the distance than all at once; but this should not affect the actual work done nor the energy expended.

Our scale in the study of this question is one-sixteenth of an inch to the inch; therefore in these diagrams one-eighth of an inch represents two inches in the full-size bicycle. In this connection also it must be taken into consideration that the effect upon momentum is not shown entirely by the contour of these lines; the sudden stoppage or checking of the system is generally shown by a vertical tendency in the curve, but a very disagreeable shock to the body may occur and momentum be lost without any deviation in the curve whatever when, for instance, in the most pronounced case, the saddle goes straight back upon its course. This is shown by means of the short vertical or diverging lines upon the curves. These short lines show the distance forward the point in the saddle travels in proportion to the advance of the wheels in a forward direction in space; each short line indicates an advance of two inches in the wheels. When the lines are below the curve, the saddle has actually dropped backward,—that is, it has been directly reversed in its course.

When the short lines upon the curve are close together, it shows that the saddle and rider are being checked proportionately as these lines are less than one-eighth of an inch apart. On the other hand, when the normal pace of the momentum of the heavier parts is slower than that of the wheels, it is shown by the lines being more than an eighth of an inch apart. In this case there is a tendency to increase the momentum instead of decreasing it,—a state of affairs not so much to be deplored if it were not evident that it is equally checked at some other point.

We know, in practice with the Ordinary, that the loss of momentum by sudden checking can only happen to the full extent when the pace is reasonably slow; should the momentum be too great it will simply refuse to be interfered with in its forward course, and the rear wheel will leave the ground with a result and in a manner quite well known.

In the safer forms of bicycles,—those from which a header is improbable,—without proper springs, the rider will simply slide forward on the saddle, causing considerable loss of momentum besides that due to vibration, since he must afterwards slide himself back again.

Referring to the diagrams, [Fig. 1] shows the Ordinary bicycle with a fifty-two-inch front and an eighteen-inch rear wheel. The front wheel mounts the obstacle with some difficulty, the curve upward being rather sudden in its change of direction from the base line, thus showing that the momentum is checked very rapidly; see the short vertical lines upon the curves, which are about one-half the distance apart of those on the base line between the curves and at the ends. Also notice that F (the front wheel) carries three-fourths of the weight, one curve being about three times as high as the other.

Particular attention is called to the easy and gradual curve shown by the mounting of the small rear wheel R; it would seem to show that the great clamor of theorists for large rear wheels in the Ordinary is somewhat unwarranted; the drop down and back in rolling off the obstacle will be seen to be quite sudden, but notice not very much more so than in [Fig. 2], which shows the Rational, so called, with a fifty-two-inch driver and twenty-four-inch rear wheel. The large rear wheel affects the drop to some extent, but in all obstacles under four inches in height there is no perceptible benefit derived, at least not such as to warrant the extra weight and disarrangement of the steering.

[Fig. 3] shows a machine with a fifty-two-inch rear driver, R, and an eighteen-inch front steering wheel, F, with the saddle twenty degrees in front of the vertical line through the driving axle. The curves are just the reverse of the Ordinary; in the latter the quick drop, down and back, of the rear wheel in leaving is comparable to the backward thrust of the front wheel in [Fig. 3] running upon the obstruction. No machine in the market at present makes exactly the curve of [Fig. 3]; it is about that which the American Star would make with its saddle a little farther forward, and that of a recent rear-driving crank machine called the “Eagle.”

[Fig. 4] shows the American Star, as commonly seen, with a fifty-two-inch rear driver and the saddle directly over the driving axle. This curve shows no elevation of the saddle as the front wheel mounts the obstacle, but a radical check to the momentum is shown; observe the curve (F), and note that the saddle is forced back in the order of the small numerals, advancing to 1, going back to 2, then on to 3 and 4, which shows that the momentum is not deviated up or down, but is directly reversed in its course.