CHAPTER VIII.
COMPARISON OF THE CURVES OF TRANSLATION, IN MACHINES OF WHICH THE DIAMETERS OR COMBINATION OF WHEELS DIFFER, OF A POINT TAKEN IN THE SAME RELATIVE POSITION ON THE SEVERAL SADDLES—CONSEQUENT CONCUSSION AND EFFECT UPON MOMENTUM.
In discussing this matter it has been taken for granted that the proper point upon which to base calculations is that point in the saddle at which the motion of the machine may be supposed to be transmitted to the rider; this happens to be very near the centre of gravity of the system, and is also quite near the centre of gravity of the man. The motion is of course partially transmitted to the rider at the pedals, but we will for the present waive that modification.
Simple as the running of two wheels over an obstruction seems to be, there are some interesting points to study. It was a surprise to the writer, and it is his hope that it may be of interest to others, that the saddle, and of consequence the rider, actually goes backward at times when the wheels are running forward; as, for instance, when the machine rolls slowly from a four-inch obstacle, as shown by the curve of the point in the fifty-two-inch Ordinary given below, and also particularly in the advance upon the same of the Star rear-driver. This reversion of momentum sometimes results in a drop of the rear wheel, but it is always an actual reacting force in the front. We feel the curves very plainly on a rigid machine, but it is a satisfaction to know exactly what they are and what the springs must overcome.
Fig. 1.Ordinary, 52 F., 18 R.; 4-in. obstruction; saddle twenty degrees back.
Fig. 1.
Ordinary, 52 F., 18 R.; 4-in. obstruction; saddle twenty degrees back.
Fig. 2.Rational Ordinary, 52 F., 18 R.; 4-in. obstruction; saddle thirty degrees back.
Fig. 2.
Rational Ordinary, 52 F., 18 R.; 4-in. obstruction; saddle thirty degrees back.
Fig. 3.Lever Rear-driver Star, 18 F., 52 R.; 4-in. obstruction; saddle twenty degrees forward.
Fig. 3.
Lever Rear-driver Star, 18 F., 52 R.; 4-in. obstruction; saddle twenty degrees forward.
Fig. 4.Star, 20 F., 52 R.; saddle vertically over axle.
Fig. 4.
Star, 20 F., 52 R.; saddle vertically over axle.
Fig. 5.Star, 24 F., 39 R.; saddle over axle.
Fig. 5.
Star, 24 F., 39 R.; saddle over axle.
Fig. 6.Kangaroo, 40 F., 18 R.; saddle twenty-five degrees back.
Fig. 6.
Kangaroo, 40 F., 18 R.; saddle twenty-five degrees back.
Fig. 7.Rear-driver Rover, 30-in. wheels, eleven inches apart; saddle forty inches high, twelve inches forward.
Fig. 7.
Rear-driver Rover, 30-in. wheels, eleven inches apart; saddle forty inches high, twelve inches forward.
Fig. 8.Rear-driver, 30 F., 24 R.; saddle forty inches high.
Fig. 8.
Rear-driver, 30 F., 24 R.; saddle forty inches high.
Fig. 9.Dennis Johnson, 30-in. wheels; saddle thirty inches high, midway between wheels.
Fig. 9.
Dennis Johnson, 30-in. wheels; saddle thirty inches high, midway between wheels.
The diagrams show the paths of the point in the various machines passing over a four-inch obstruction;Fdesignates the front andRthe 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 inthe 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 considerableloss of momentum besides that due to vibration, since he must afterwards slide himself back again.
Referring to the diagrams,Fig. 1shows 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 thatF(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 wheelR; 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 inFig. 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. 3shows 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 inFig. 3running upon the obstruction. No machine in the market at present makes exactly the curve ofFig. 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. 4shows 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.
Fig. 5shows a new machine of the Star pattern, with twenty-four-inch front steerer,F, and a thirty-nine-inch rear driver,R. The check in the momentum is not so radical as that shown inFig. 4, as the front wheel mounts the obstacle. The one short line below the curve shows the backward thrust.
The sudden check in striking an obstacle, with the machines last referred to, shows the necessity and enormous advantage of a forward give to the saddle support adopted in some of those patterns. This arrangement is not so necessary in the Ordinary, yet it would do no harm, for it will be seen that the large front wheel of the latter strikes the obstacle with quite a sudden upward curve and check in the momentum sufficient to justify its use.
In the Star, Eagle, and such other types the man is raised upon the obstacle entirely by the large rear wheel, which carries nearly all of the weight, as shown by the height of the curve; it raises beautifully upon the obstruction with little or no check in the momentum, the diverging lines showing about the same distance apart as at the base. It has been thought to be an advantage to reduce the weight upon the front wheel, but the importance is very much exaggerated; it will reduce the impact in dropping down from an obstruction, and will thus cause less annoyance in rough-road riding;still this does not alter the fact that the momentum in the man and part of the machine is not only stopped, but reversed backward, as shown in the diagrams. If the wheel were lifted entirely free from the ground before advancing upon the obstruction, it is obvious, then, that no harmful result would ensue, not so much because the jolt and impact in dropping off is obviated, but for the reason that the momentum forward is not interfered with. If the rider should run full force against a wall with his forward wheel, it would be of little consequence to him whether there was any weight upon it or not; it is not always a question of vertical disturbance or of the action of gravity that is of annoyance to the bicycle rider; it is sometimes better to have a heavy weight upon a wheel if it can be kept in contact with the obstruction, as, for instance, upon the front wheel of the Ordinary when it rolls off, as it will be seen that the curve shows a splendid contour by which to give a good pull on the machine.
Fig. 6shows the Kangaroo type, with a forty-inch front driver and an eighteen-inch rear wheel; this curve presents very little change from that of the Ordinary.
Fig. 7illustrates the Rover type, having two thirty-inch wheels with their centres forty-one inches apart, the saddle forty inches high and twelve inches in front of the vertical through the rear axle. The mere contour of the curve in the last figure mentioned would be somewhat misleading did the diverging lines not show that in the rolling off of the rear wheel the momentum is considerably checked,—that is, the saddle moves more slowly forward than the normal forward pace of the wheels, though there is no direct reversion of the momentum, as occurs in the Ordinary and some others.
In this connection let me call particular attention to a cardinal distinction with reference to the action in rolling upon and from an obstruction. If the wheelsin descending hold the man back in order to remain in contact and thus roll off, it will, of course, result in a check of momentum exactly equal to that which would occur in such advance upon an obstacle, as would be shown by a similar curve in the opposite direction; but, as a matter of fact, the momentum being a certain amount, the effect is to cause the wheel to leave the obstruction entirely and not roll, but jump off, which result causes a great loss of energy and is sure to occur in rapid running. In this case the forward momentum gets no benefit from the potential energy acquired in mounting the obstacle, which shows the great necessity of proper springs such as will enable a man to swing forward slightly without rigidly drawing the machine after him. The object of the springs in this connection should be to hold the wheel in contact and permit it to roll instead of forcing it to jump off; if it rolls and is not carried off by the force of momentum, the energy will be given out in driving the machine forward instead of being lost in the vibration caused by impact when the machine strikes the common level. That is to say, the machine should roll off, but not hold the man back in order to do so; by proper springs the wheels remain in contact, while the man goes on at the regular pace of momentum. The liability of the rear wheel to jump off is a serious difficulty in the present Rover type of rear-driver; there is no reversion of the momentum, nor such a tendency to drop perpendicularly, as in the Ordinary, yet it drops a greater distance and is charged with more weight. This objection cannot be entirely remedied by any springs we now have in use; it requires a lively vertical as well as a horizontal amplitude in the motion of the springs, and they should be placed at the hub of the rear wheel in a manner similar to those used of late in connection with the front wheel. It will be seen from the diagrams that the curves shown by the front wheels leaving the obstructions are never such as would show any liabilityto jump off; advancinguponthe obstruction must, in them, be mostly provided for.
InFig. 8we have a machine provided with a thirty-inch front and twenty-four-inch rear driving-wheel. This is a modification of the Rover type recently favored by some English makers. The drop of the rear wheel is more radical than that of a full thirty-inch.
InFig. 9appears a Dennis Johnson machine, with two wheels of the same size, having the seat low down and exactly midway between them. This is perhaps the easiest riding contrivance in so far as vibration, jolt, and shock are concerned. Observe the equable motion it displays. This machine was patented in England, as spoken of in an early chapter, seventy years ago.
It will be seen, from a general observation and study of all of the diagrams, that the best and most gradual curves are made by the front wheel in descending from, and by the rear wheel in advancing upon, the obstacle; hence it follows that the front wheel works against momentum more in ascending and the rear wheel more in descending.