CHAPTER VI.

GRAPHIC ILLUSTRATION OF THE APPLICATION OF POWER TO CYCLES—KINEMATICS.

The manner in which the construction and general arrangement of the driving mechanism, the road surface, and other conditions control the application of power is a curious study. In connection with it I have made an instrument to illustrate the same graphically, which, for the sake of a name, we will call the “Cyclograph,” an engraving of which will be found below.

The Cyclograph.

A frame,A A, is provided with means to attach it to the pedal of any machine. A table,B, supported bysprings,E,E, has a vertical movement through the frameA A, and carries a marker,C. The frame carries a drum,D, containing within it mechanism which causes it to revolve regularly upon its axis. The cylindrical surface of this drum,D, is wrapped with a slip of registering paper removable at will. When we wish to take the total foot-pressure, the cyclograph is placed upon the pedal and the foot upon the table. The drum having been wound and supplied with the registering slip, and the markerCwith a pencil bearing against the slip, we are ready to throw the trigger and start the drum, by means of a string attached to the trigger, which is held by the rider so that he can start the apparatus at just such time as he desires a record of the pressure.

The following are a few sample sections cut from registering slips illustrating some of the points discovered in these experiments. Only a few strokes of the crank or lever can be shown; it is evident that great space and expense of reproduction would be required to give the entire record for even a small part of a mile. It will be understood, I think, without further explanation, that these curves show the extent and variation of pressure of the foot upon the pedal in order to drive the respective machines under circumstances named and described by the figures and thereafter.

52-inch Ordinary; race-track; getting up steam.

52-inch Ordinary; race-track; speed, eighteen miles per hour.

52-inch Ordinary; race-track; speed, ten miles per hour.

52-inch Ordinary; up hill, grade, one foot in twenty-five; speed, about eight miles per hour.

52-inch Ordinary; starting up hill.

52-inch Ordinary; up hill, grade, one foot in ten; stalled at four miles per hour.

52-inch Ordinary; up hill, grade, one foot in twenty-five; curves of both pedals superposed.

52-inch Ordinary; back pedal; down hill, grade, one foot in twelve.

Rear-driver Rover type, 54-gear; up hill, grade, one foot in twenty; speed, nine miles per hour.

Rear-driver Rover type, 54-gear; up hill, grade, one foot in twenty; continuation of No. 10.

Rear-driver Rover type, 54-gear; up hill, grade, one foot in seven; speed, ten miles per hour.

Lever rear-driver, 30-inch wheels, gear about 50; up hill, grade, one foot in twenty; speed, eight miles per hour.

Lever rear-driver, 30-inch wheels, gear about 50; up hill, grade, one foot in twenty; speed, twelve miles per hour.

Lever rear-driver, 30-inch wheels, gear about 50; up hill, grade, one foot in twenty; continuation of No. 14, over top of hill.

A six-inch crank was used upon the machines in these experiments, and the lever action was such as to be comparable to a fifty-inch gear. The height of a point on the curve shows the extent of and variation in power upon the pedal, and the translation from left to right the time. In consequence of the limit of pressure occurring but once in each stroke, the number of undulations determines the speed, since it would show the number of strokes in a given time, and we know the number that make a mile.

The number of pounds’ pressure at any point on a curve is shown by the figures upon the perpendicular line, as, for example, inNo. 1the apex of the curve just to the right of the scale is about even with the hundred-and-fifty-pound point; this pressure was maintained for a very short space of time, since the curve travels a very short distance to the right at this point; in other words, it is quite sharp at the top.

Stronger springs were used on the Cyclograph in testing the safeties, as I found myself liable to compress them beyond their limit; hence the scales must be closely observed in making comparisons. Among the interesting results noticeable in these experiments I find, for instance, in Nos.3and4, an abnormal deviation in the height of the curves at the same speed upon the same track at nearly the same time, though running in opposite directions. Finding this strange difference of some fifty pounds in pressure, I noticed an almost imperceptible breeze against me in the one, and in my favor in the other, direction.

No. 12illustrates how a hundred-and-fifty-pound man gets up a pressure of two hundred and forty pounds presumably by a ninety-pound pull on the handle-bar.

InNo. 9we see how one hundred and fifty pounds pressure is applied in back-pedalling down a grade of one foot in twelve. That the curve would not be very regular is easily impressed upon the mind of the average rider.

One part of curve (not shown), of peculiar contour, terminated experimentNo. 9at a rut a little farther down the hill, with dire results to the operator and provoking influence upon the running gear of the ’graph, which has been making some erratic curves of its own, now and then, ever since.

Comparing Nos.5,10, and13, the curve of the lever machine (13) indicates that, while pressure is not so great as in the others, it is held for a longer time, shown by the greater height and sharper tops to the curves of the crank machines.

The short cross-lines about three-fourths up on the left sides of the undulations in Nos.10,11, and12designate the points at which the crank crosses the perpendicular at the top. There is quite a pressure, and it is a little odd that it should be found at this point; it can only be attributed to ankle-action back of the natural dead centre.

InNo. 6, and to some extent in all the others, observe the jagged appearance in the general advance of the curves, which must be due to vibration: these results were all obtained upon tolerably smooth roads, mostly in Druid Hill Park, Baltimore.No. 6was taken upon a road perhaps a little rougher than the track around the lake, but still upon an unusually smooth surface, and it was a surprise, not to say an alarming discovery, that this vibration should occur under such circumstances.

The lake track, upon which results2and3were found, was in perfect condition, smooth as a surface-plate, and without the customary sprinkling of pebbles so common when dry weather has loosed the settings of these tiny obstructions and suffered them to roll out upon the roadway; yet these figures show the saw-teeth, and I have been unable to find a road smooth enough, or jointed machine frames and springs good enough, to make unwavering symmetrical lines. These little deviations in the curves always seem to show themselvesto the extent of several pounds in height in spite of all alleviating conditions, suggesting that we have much to strive for in the construction of the ideal wheel free from all concussion. In order to judge accurately of the total amount of power to turn the wheel, we have to consider the register of both pedals superposed, as inNo. 8, but the curve made upon one generally answers all purposes. The possibilities in this study are unlimited, and, with a perfectly-accurate instrument, it strikes me, the results of much more definite bearing than those acquired in the silly practice of testing machines by the strength of men.

I have refrained from giving any tests as to the comparative power required to drive machines of the same type and of different manufacture, differences being liable to result from a bad condition of the machine, such as the want of oil, or from happening to get hold of an unusually bad sample, making the liability to do injustice too great. The writer does not feel himself called upon to judge of or express differences in quality of workmanship in general, if for no other reason than that by the time the matter goes to press, such merits or defects as he might have discovered may change. Workmanship does change, principles never can; and, what is more, the hypotheses and conclusions in regard to principles, treated of in this or any other book, are always open to contradiction; if injustice is done to any maker of wares in a matter of principle, said maker always has a remedy in defence, and if he can disprove assertions made his justification is complete, whereas if a mistake of fact is recorded, such as the operation of a certain machine, and the machine upon which the alleged fact is based happens to disappear, the party interested is denied a just remedy. There are of course certain criteria of good workmanship, and the same should be touched upon in order to teach the reader how to judge of it; but beyond this no writer should be allowed to go,unless at least he has been paid for advertising competing wares at regular rates.

The cyclograph attached to the revolving pedal shows the total amount of pressure required to do a certain work on a machine; but if it is desired to ascertain the track resistance or the friction of parts alone, it is necessary to so place the instrument as to register the tangential resultant in turning the crank, taking no note of any power thrown away by indirect application; that is, if we wish to register the circular or tangential resultant, the cyclograph is attached by its frame rigidly to the crank or lever of a cycle, and the revolving pedal, which has been detached, is hung upon the spring platform. This last arrangement is used in experimenting to ascertain the extra power available by ankle-motion, as will be shown hereafter.

Throughout this work a slight tendency to urge the element of dead centre as against the crank-cycle may have been discovered. Makers and riders who find fault with this apparent praise of lever and non-dead-centre devices can derive considerable comfort by the study of ankle-motion. No better introduction to our diagrams, showing the possibilities arising therefrom, can be given than the following extract from theIrish Cyclist, viaThe Bicycling News and Wheelman’s Gazette:

“ANKLE-ACTION.“Among the many thousands of riders in this country, says theIrish Cyclist, very few have any desire to improve their style or realize for a moment the vast importance of correct ankle-motion. You meet a rider plodding along, working his legs like pistons, with a heavy, lifeless motion. Remonstrate with him, and see what he will say: ‘Oh, he can go well enough; he does not believe ankle-action makes such a difference, and he does not want to “scorch” in any case.’ Now, we want our readers to grasp these facts. Any rider can acquire a tolerable ankle-action by careful practice, and the acquisition of such will increase his power by nearly one-fourth, and will enable him to ride hillsnever before attempted, and to keep up a better pace at the expense of the same amount of energy. This being so, the acquisition of such art should be asine quâ nonto every rider. That it is so can very easily be proved. In following the pedal the foot describes a complete circle. Suppose the circle to be divided into eight segments, taken in order from the highest point.[5]With a rider who does not use his ankles, force is applicable only through segments 1, 2, 3, 4, and in segments 1 and 4, the force not being applied at right angles to the end of the crank, a large proportion is wasted, and consequently it is only thoroughly effective through segments 2 and 3, or during one-fourth of the revolution. The rider who has mastered the mysteries of ankle-action will drop his heel as the pedal approaches the highest point, and he can apply a certain amount of force through segment 8. After passing the so-called dead point, his heel being still dropped, the force is applied at right angles to the crank, or nearly so, and consequently he can utilize his full power through segment 1. By rapidly straightening the ankle when entering segment 2 an additional impetus is imparted, and, as before, full power can be applied through segments 2 and 3. Entering segment 4, the heel should be raised and the pedal clawed backward, and this clawing action will enable the rider to work past the dead point and well through segment 5. Consequently, the man who rides with his ankles stiff can only work through segments 1, 2, 3, 4, or half the whole circumference, and his work is thoroughly effective only through segments 2 and 3, or one-fourth the circumference, whereas the man who utilizes his ankles can work through segments 8, 1, 2, 3, 4, and 5, or two-thirds the whole circumference, and his work is thoroughly effective through segments 1, 2, 3, and 4, or one-half the whole circumference. The advantage gained in the latter case is self-evident. The acquisition of the art is often tedious and troublesome, but if cyclists only knew the enormous increase of power which results they would not be content until they had mastered it. From the cycling volume of the Badminton Series, written by Lord Bury and G. Lacy Hillier, we take the following instructions:“‘Seated either on a bicycle slung so that the wheel may revolve, or upon a home-trainer, the beginner should raise the pedal to its highest point, and then, steadying the wheel with the brake, place his foot upon the pedal, carefully fitting the slots in his shoes into their places, and seeing in any case that the foot is straight. Then, using the thigh muscle for the most part, let him thrust the foot (and pedal) forward in a horizontal direction; in fact, a sort of sharp forward kick, having the heel dropped as low as possible, the toes well up, and the foot firmly set on the pedal, which will be at an angle. This should be practised carefully with the brake slightly on, and for this purpose, though a bicycle may be used, a tricycle will be foundmuch handier. If no home-trainer is available, the brake can be put slightly on by means of a piece of string or strap to the lever, tied to any convenient point, and the novice can spend a few minutes daily practising this exercise; in carrying out which programme the left foot should at first be used more than the right. As soon as the usual awkwardness of the ankle-joint has been worked off this action will be found remarkably effective in starting the machine; after a time the ankle muscles, and those of the calf, will become stronger, and a sharp straightening of the ankle, as the pedal passes through segments 1 and 2, will materially aid the propulsion of the machine. This straightening of the ankle will be continued until the foot is brought into a position at right angles to the leg, the muscular effort of which should now have by equal gradations become directly downward. The pedal will now assume a horizontal position, and the power of the leg with the weight of the body and the pull of the arms will all be exerted to force it downward; at this point the crank throw is in the most effective position, and the hardest work is put in. When the pedal begins to follow a backward course, the ankle-action becomes of the greatest value. The toe is gradually dropped, and the heel raised as the pedal gets nearer and nearer to the lowest point, the action having at length reached the backward or “clawing” stage. To secure the full advantage of ankle-work, this “clawing” action must be very carefully practised; the toes should be sharply pressed upon the sole of the shoe as if they were trying to grasp something, whilst the ankle should be straightened as much as possible, the foot being almost in a line with the leg, the calf muscles being strongly retracted, and the backward pull (which of course requires fitted shoes) can be made practically effective through segment 5, and also of service well into segment 6. The ineffective portion which exists on either side is soon reduced to a very small part of the circle, for as soon as segment 7 is entered upon the heel should be sharply dropped, and an upward and forward kick or thrust, as described in the directions for the first position, will lift the pedal forward and upward through segment 8, when, of course, the whole series of actions will be repeated.’—Bicycling News.”

“ANKLE-ACTION.

“Among the many thousands of riders in this country, says theIrish Cyclist, very few have any desire to improve their style or realize for a moment the vast importance of correct ankle-motion. You meet a rider plodding along, working his legs like pistons, with a heavy, lifeless motion. Remonstrate with him, and see what he will say: ‘Oh, he can go well enough; he does not believe ankle-action makes such a difference, and he does not want to “scorch” in any case.’ Now, we want our readers to grasp these facts. Any rider can acquire a tolerable ankle-action by careful practice, and the acquisition of such will increase his power by nearly one-fourth, and will enable him to ride hillsnever before attempted, and to keep up a better pace at the expense of the same amount of energy. This being so, the acquisition of such art should be asine quâ nonto every rider. That it is so can very easily be proved. In following the pedal the foot describes a complete circle. Suppose the circle to be divided into eight segments, taken in order from the highest point.[5]With a rider who does not use his ankles, force is applicable only through segments 1, 2, 3, 4, and in segments 1 and 4, the force not being applied at right angles to the end of the crank, a large proportion is wasted, and consequently it is only thoroughly effective through segments 2 and 3, or during one-fourth of the revolution. The rider who has mastered the mysteries of ankle-action will drop his heel as the pedal approaches the highest point, and he can apply a certain amount of force through segment 8. After passing the so-called dead point, his heel being still dropped, the force is applied at right angles to the crank, or nearly so, and consequently he can utilize his full power through segment 1. By rapidly straightening the ankle when entering segment 2 an additional impetus is imparted, and, as before, full power can be applied through segments 2 and 3. Entering segment 4, the heel should be raised and the pedal clawed backward, and this clawing action will enable the rider to work past the dead point and well through segment 5. Consequently, the man who rides with his ankles stiff can only work through segments 1, 2, 3, 4, or half the whole circumference, and his work is thoroughly effective only through segments 2 and 3, or one-fourth the circumference, whereas the man who utilizes his ankles can work through segments 8, 1, 2, 3, 4, and 5, or two-thirds the whole circumference, and his work is thoroughly effective through segments 1, 2, 3, and 4, or one-half the whole circumference. The advantage gained in the latter case is self-evident. The acquisition of the art is often tedious and troublesome, but if cyclists only knew the enormous increase of power which results they would not be content until they had mastered it. From the cycling volume of the Badminton Series, written by Lord Bury and G. Lacy Hillier, we take the following instructions:

“‘Seated either on a bicycle slung so that the wheel may revolve, or upon a home-trainer, the beginner should raise the pedal to its highest point, and then, steadying the wheel with the brake, place his foot upon the pedal, carefully fitting the slots in his shoes into their places, and seeing in any case that the foot is straight. Then, using the thigh muscle for the most part, let him thrust the foot (and pedal) forward in a horizontal direction; in fact, a sort of sharp forward kick, having the heel dropped as low as possible, the toes well up, and the foot firmly set on the pedal, which will be at an angle. This should be practised carefully with the brake slightly on, and for this purpose, though a bicycle may be used, a tricycle will be foundmuch handier. If no home-trainer is available, the brake can be put slightly on by means of a piece of string or strap to the lever, tied to any convenient point, and the novice can spend a few minutes daily practising this exercise; in carrying out which programme the left foot should at first be used more than the right. As soon as the usual awkwardness of the ankle-joint has been worked off this action will be found remarkably effective in starting the machine; after a time the ankle muscles, and those of the calf, will become stronger, and a sharp straightening of the ankle, as the pedal passes through segments 1 and 2, will materially aid the propulsion of the machine. This straightening of the ankle will be continued until the foot is brought into a position at right angles to the leg, the muscular effort of which should now have by equal gradations become directly downward. The pedal will now assume a horizontal position, and the power of the leg with the weight of the body and the pull of the arms will all be exerted to force it downward; at this point the crank throw is in the most effective position, and the hardest work is put in. When the pedal begins to follow a backward course, the ankle-action becomes of the greatest value. The toe is gradually dropped, and the heel raised as the pedal gets nearer and nearer to the lowest point, the action having at length reached the backward or “clawing” stage. To secure the full advantage of ankle-work, this “clawing” action must be very carefully practised; the toes should be sharply pressed upon the sole of the shoe as if they were trying to grasp something, whilst the ankle should be straightened as much as possible, the foot being almost in a line with the leg, the calf muscles being strongly retracted, and the backward pull (which of course requires fitted shoes) can be made practically effective through segment 5, and also of service well into segment 6. The ineffective portion which exists on either side is soon reduced to a very small part of the circle, for as soon as segment 7 is entered upon the heel should be sharply dropped, and an upward and forward kick or thrust, as described in the directions for the first position, will lift the pedal forward and upward through segment 8, when, of course, the whole series of actions will be repeated.’—Bicycling News.”

Using the arrangement of cyclograph spoken of, by which ankle-motion may be shown, I find that I can begin to get a tangential resultant force on each crank at an angle of eighteen degrees back of the vertical line through the axle of the drive-wheel, beginning atdand ending ate,Fig. 1,—in all, thirty-six degrees over a half-circle on each crank.

Fig. 1.Ankle-power.

Fig. 1.

Ankle-power.

The diagram shows the sections 1 to 8, and alsogives an idea of the extra power. To see the direct circular resultant force to turn the wheel, imagine the length of a crank frommtonwithout ankle-motion and thenm nplusn ofor the length of the crank with ankle-motion added. I have been able at each of the pointsaandito get thirty pounds when the crank crosses the vertical line at the top and bottom. Thus it is discovered that by means of this ankle-motion on both cranks simultaneously, I can get a force of sixty pounds in the direction to turn the wheel, at a time when absolute dead centre would otherwise occur, amounting to two-fifths of the maximum pressure resulting from my entire weight on one crank at the best possible point, directly out in front, going down.

I have more than verified the results shown by the cyclograph by suspending a fifty-four-inch bicycle, with six-inch cranks, above the floor, placing myself in the saddle, and having an attendant attach a twenty-pound weight at a point on the rim, ninety degrees from the bottom. This weight I was able to raise at the dead-centre point of both cranks,—that is, vertically up and down,—which shows a real power at thepedals of ninety pounds, or forty-five pounds on each, and I do not suppose that I am by any means an expert in ankle-motion. The above ninety pounds is a much greater showing than I made on the cyclograph in actual running, but it is reasonably certain that, by practice, even such an amount could be obtained.

In the case of no ankle-motion,—that is, with a direct downward pressure on the crank,—a tangential force in the direction available in turning the wheel begins as the crank crosses the vertical at the top, and then increases as the sine of the angle the crank makes with the vertical, until such angle reaches ninety degrees or extends out horizontally, after which the power decreases as the sine of the angle the crank makes with the vertical below the centre until the crank crosses at the bottom, at which point the power ceases.

To represent this variation of power by actual length of lines, appended will be found a diagram,Fig. 2, showing the tangential resultant or force to turn the wheel, imparted by a one-hundred-and-fifty-pound man with and without the use of ankle-motion.

A Ais a line showing the divisions of the angles through which the crank passes in its revolution around the axle. The linea f iis a sine curve.

Using the middle section and beginning at the pointa, which is that at which the crank crosses the vertical above the axle, making a zero angle therewith, we have a direct downward pressure and, without ankle-motion, zero power. Now, by means of ankle-motion on one crank at this point we get thirty pounds of power, represented by the length of the line fromatob; and by ankle-motion on both cranks we have sixty pounds, represented by the total length of the line fromatoc. After the crank has advanced forward fifteen degrees, we have thirty-nine pounds of direct power (m n), and then adding the ankle-power of twenty-three pounds (n o), we have a total resultant of sixty-twopounds, represented by the length of the next line (m o), and so on up, the direct power increasing and the ankle-power diminishing till we come to the top of the curvef, when we have one hundred and fifty pounds of direct power. Passing through the angle of ninety degrees, and now counting from the vertical below the axle, we decrease in power inversely as we increased before.

Fig. 1will show a little more graphically to the eyes of some casual readers how the power expands. Taked a f i eas the regular swing of the crank with no power ata, thend b f h eas the increase of power on one and the dotted linescandgas the auxiliary ankle-power on the other crank added.

Fig. 2.Ankle-power sine curve.

Fig. 2.

Ankle-power sine curve.

[5]Observe Fig. 1, p. 58.

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