Bramley & Parker’s Specification. English patent. No. 6027. November 4, 1830. See [page 211].

CYCLING ART,
ENERGY,
AND
LOCOMOTION:
A SERIES OF REMARKS ON THE DEVELOPMENT
OF BICYCLES, TRICYCLES, AND MAN-MOTOR
CARRIAGES.

BY
ROBERT P. SCOTT.

ILLUSTRATED.

PHILADELPHIA:
J. B. LIPPINCOTT COMPANY.
1889.

Copyright, 1889, by J. B. Lippincott Company.

DEDICATION.

THIS WORK
IS
RESPECTFULLY DEDICATED TO THE MEMBERS INDIVIDUALLY,
AND AS A BODY CORPORATE,
OF
THE BALTIMORE CYCLE CLUB.

PREFACE.

The average intelligence of the Cycling fraternity can, with justice, be said to be above that of any other association of men and women, devoted to pastime, sport, and exercise, in the world; yet withal it is with some considerable feeling of anxiety that this book is sprung upon them. There can be no question but that we are a reading community, and yet all attempts catering to our wants, in the way of books, seem to have met with a less hearty support than should have been expected. The author of one of the greatest works connected with Cycling has recently informed us that he is still many hundreds of dollars behind, and other authors have good reason to complain that their books can be searched for even at club-houses, where they surely ought to be found. Books consisting largely of advertisements have, no doubt, paid the compilers, as have also the numerous periodicals, but when we ponder over the colossal efforts of Kron and Stevens, and think of the poorly-rewarded devotion of Sturmey, “Faed,” the Pennels, Stables, Cortis, and others, the encouragement is not at all stimulating to writers; especially since all books of these authors are of the most attractive character and easily comprehended, whereas a large portion of this work is written with a view to inspiring a close study of the art, and for that reason, if for no other, is liable to be dry reading. However, it is too late now to swerve from the task; if one more must be added to the procession of dejected, empty-pocketed venturers, “so mote it be.”

No petition is made to the Fraternity to read this book in particular, but it is hoped that all cycling books and periodicals will be patronized, hereafter, with the usual liberality so characteristic of wheelmen in connection with other matters, and if this work should, in any way, foster this hope, its mission will be more than filled. In one way the writer has already been amply repaid; if he had never undertaken this task it is just possible that he, like many others, might never have followed a cycler through India, or have made the acquaintance of “The Best of Bull-Dogs.”

The nature of this book has drifted, to some extent, from the rigid mathematical character originally intended, partially because it just drifted, and also perhaps intentionally, in order to give it a more popular bearing. If some severely practical readers should notice an attempt at humor, or an amusing turn given to what should be stern mathematical or mechanical reasoning, it is hoped that it will not be considered undignified or trivial, for it is done with an object; and if the popular reader should be averse to running off into abstract theories, let him but remember how little we realize that everything we do, or make, in our daily experience rests upon some fundamental principle which we ought to know and be able to explain. Who would have thought that the principles underlying the simple matter of balancing a bicycle would confuse even a school-boy? Perhaps it ought not; nevertheless, the article on that subject is cut rather short, for the reason that the writer, even with the help of others more competent, was unable to definitely determine all points in regard to it. My thanks are due to Prof. E. W. Davis, of Columbia, S. C., Gustav Bissing, Ph.D., of Baltimore; Prof. Robinson, of Columbus, Ohio; F. R. Smith, A.M., of Cambridge, England, and others, for valuable assistance courteously rendered.

Respectfully,
R. P. Scott.

Baltimore, 1889.

CONTENTS.

Cycling Art,
ENERGY, AND LOCOMOTION.

PART I.

Cycling Art,
ENERGY, AND LOCOMOTION.

CHAPTER I.

INTRODUCTORY.

Locomotion as applied to the question of transportation of matter in all its varied forms has always been, and will always continue to be, one of the great problems of advancing civilization. To such an extent does the element of transportation enter into our highly organized system of society that it is said to be the most powerful factor in the evolution of man. So confidently is this believed, that a great genius has been led to promulgate the theory that at some future time man will consist of a head and trunk; that all use for the limbs being entirely dispensed with in the art of moving and manipulating matter, these will gradually shrivel up and drop off, as it has been said the tail did when we no longer used it for swinging our bodies from tree to tree, like the proverbial monkey, or as a projectile force so valuable to the locomotion of the kangaroo.

The development of mechanical means for transporting and manipulating all matter has, to a wonderful extent, excused the use of man’s legs and arms: and the facility with which a great mass is loaded for transportation, delivered at its destination, and there manipulated with scarcely the touch of human hands has, it must be admitted, greatly diminished the labor otherwise delegated to the limbs. It is possible that almost all matter could be moved, moulded into desirable form, and utilized by civilized man for all his requirements, by the use of mechanical means, and man could no doubt transport himself by the same means, without using his limbs, and thereby reach a very high state of civilization; but such means must include a great amount of mechanical appliance accompanying the transportation, the more in proportion to each as the number of travellers is less in the same circuit.

Now, I think we can well admit that the very highest state of advancement will be marked by the greatest facility each man has to go his own way, and when we come to think of the world crowded as it must eventually become, does it not seem apparent to the reader that, since the natural energy now encompassed within our system is sufficient to carry us about, it will be for the best to continue to use this energy in our locomotion and make our improvements with the view to such a use, not for the purpose of dispensing with the many mechanical conveniences that now subserve our demands, but in order to add a simple and convenient means of unit transportation over reasonably long distances in a reasonably short space of time and accomplish the same with the least possible increase of mechanism? Humanity without the power to transport itself is to us an almost incomprehensible idea, and at the present day it is almost equally hard to conceive the state of society in which the movement of large masses over even small distances was impossible; yet there was a time when man could do no more than transport himself, together with such articles as he could carry upon his back or hold in his hands. It was probably not till long after this that he constructed a sled from the bark of a great tree to receive his chattels, and pulled it along by some rude vine; still nearer to our own time comes the invention of the wheeled vehicle or wagon, and when we come to that marvel of modern inventive genius the railway and steam-driven locomotive we are within a period yet personally known to our oldest fellow-citizens.

So much inventive ingenuity, so much marvellous energy has been expended upon the solution of the problem of transporting large masses, in which we see the wheel has finally played an important part, that the question of the individual transportation of individual men has received comparatively little attention, and it is only within the last twenty-five years that an amount of labor and thought has been given to this problem at all commensurate with its importance. This recent labor and thought has not been expended in vain; it has placed the man, too, upon the wheel, which has done so much towards developing the use of other energy, and at last there spreads out before him a beautiful vista of independent locomotion unexampled in all the previous experience of his race.

As wheel suggests the name “cycle,” let us call this art, appertaining to the man and the wheel, “The Cycle Art,” or, more definitely, if we wish, the art of “Man-Motor Carriages.”

CHAPTER II.

THE CYCLE ART.

Posterity will always consider this the embryo generation of the cycling art; it might well be termed the “living wheel age.”

A number of valuable books have been written on the fundamental principles of locomotion by means of walking, riding upon animate beings, flying and creeping, and also upon all kinds of inanimate or mechanical motors, but little has been said about physical properties underlying the intervention of a wheel between the body of man and the surface to be travelled over, the motor being man himself.

The interesting art of man-motor carriages has already developed an industry of such great importance that the certainty as to its permanency is beyond cavil, and, believing that it will yet assume much greater proportions and become of more and more absorbing interest, there seems to be some excuse for an attempt to place even a limited amount of personal information before those connected with the industry and before the admirers of the art. There are few industries the product of which is dispersed among so varied a class of patrons, and scarcely none in which the patron takes so lively an interest in the respective articles produced.

In most industries, where a machine is the product, the consumer is expected to be an expert in the art to which the industry appertains, and is therefore supposed to be capable of individual judgment as to the merits of what he acquires; if a steam-engine is the object of the purchase, it is expected that an expert of some ability in the art will judge of and afterwards run and repair it; but how could this be expected with a bicycle?

There is probably no other machine used by mankind, with the possible exception of the watch, that does service to such a variety of individuals as the cycle. Now, it would be of little use to write a book for popular reading on the mechanical construction of a watch, because from its very nature none but an expert could appreciate the facts, if any were given; but greater hope might be entertained in regard to a larger machine, because the buyer can at least see what he is about. You never heard of a bicycle-rider blaming his repairer for stealing the wheels out of his machine and substituting others, because he can see, however inexperienced he may be, that this has not been done. Now, if we all could, by a little observation, learn one-half as much about our watches as we can about our bicycles, the poor watch-maker would never suffer the indignities so universally and unjustly heaped upon him. The primary knowledge above hinted at as possible, among the hoped-for patrons of this work, seems to be an auspicious circumstance in connection with an effort to teach them a little more.

CHAPTER III.

CAN WE IMPROVE UPON THE CREATOR’S METHODS?

“We find in a great number of standard treatises a sort of accusation brought against nature for having entirely wasted a great part of the force of our muscles by causing them to act under a disadvantageous leverage.”—E. J. Marey.[1]

À propos of fundamental principles, what are the requirements needful for the most successful means of man-motor locomotion? In more homely phrase, how can a man, without calling upon the storage of energy other than that inherent in his own body, propel himself from place to place with the least amount of physical exertion? It is evident now, that under very many circumstances the means provided us by the Creator for such purposes are not the most economical; that is to say, it has been found that if we employ a medium through which to transmit our energy, the energy will be more economically expended, in carrying our bodies from place to place, than if we apply the force directly to the work as nature seemed to intend in presenting us with a pair of legs. The writer cheerfully concedes, for one, that for almost all purposes the legs are very practical; as, for instance, in climbing a tree or a pair of stairs, a rail fence, or even a very steep hill, or when, as in some of our early travels, we are compelled by an embarrassing paucity of funds to take to the cross-ties of a poorly ballasted railroad. And further, we admit that the invention of a pair of legs, if properly claimed in a patent, would, with perfect justice, have entitled the inventor to all uses to which they could be put, including the pumping of a bicycle. But we are perfectly willing to infringe the leg patent, provided we can improve upon it even for certain purposes, as we have in adopting the modern bicycle, in its use, for instance, upon a reasonably smooth level road. Why we have been able to thus improve upon nature’s device is not quite clear. Undoubtedly, however, there is some unnecessary friction in the leg method; it cannot be on account of impact with the air, because a man on a bicycle certainly catches as much air himself, in addition to that of the machine, as he would do in walking. Evidently, then, there must be more motion or extra friction or both in the body, in the leg method, than is really essential in conveying one over a good road. Probably the main cause of this friction is that the rider’s body is supported differently; it requires less muscular strain to sit than to stand. We not only know this from experience, but it is proved by the fact that the temperature of the body is lower while sitting than while standing; also still lower when lying down, showing that less energy is being expended and less muscle consumed. Since the spirit of the writer began to wrestle with the foregoing leg versus cycle controversy, by happy chance he fell upon an estimable work[2] of which a careful perusal would almost make us think that nature really had an embryo cycle or wheel method in view when we were planned for legs. The great interest attaching to the above-mentioned work arises from the fact that the book was written before the cycle was at all broadly known to be of any assistance to the self-propulsion of man under any circumstances. This work must be read to be appreciated. I give some quotations, the application of which shows that, in the minds of some, the Creator had an idea of a wheel within a wheel; in short, that nature seemed to want to roll.

Let us quote from page 51, “Animal Locomotion.”

“When the right leg is flexed and elevated, it rotates upon its iliac portion of the trunk in a forward direction to form the arch of a circle which is the converse of that formed by the right foot, if the arcs alternately supplied by the right foot and the trunk are placed in opposition, a more or less perfect circle is produced, and thus it is that the locomotion of animals is approximated to the wheel in mechanics.”

Hence we roll,—but not far enough,—we approximate in nature, but reach the goal by man’s genius; shown in the full circular wheel.

It will be seen from the following (p. 51) that the bones in man are not arranged for high speed; hence we must make up for this deficiency.

“The speed attained by man, although considerable, is not remarkable; it depends on a variety of circumstances, such as height, age, sex, and muscular energy of the individual, the nature of the surface to be passed over, and the resistance to forward motion due to the presence of air whether still or moving. A reference to the human skeleton, particularly its inferior extremities, will explain why the speed should be moderate.”

Page 52. “Another drawback to great speed in man (as distinguished from animals) is, ... part of the power which should move (serve as a motive power) ... is dedicated to supporting the trunk.”

Now, in the cycle method we support the trunk all right, but should apparently make more use of the arms,—inventors take notice.

Page 56. “In this respect the human limbs, when allowed to oscillate, exactly resemble a pendulum.”

Here is the trouble with nature; there is too much oscillation instead of continuous rotation; nature does not go far enough.

Page 58. “The trunk also rotates in a forward direction on the foot which is placed on the ground for the time being; the rotation begins at the heel and terminates at the toes.”

Thus the rotation is all right so far as it goes.

Page 60. “The right side of the trunk has now reached its highest level and is in the act of rolling over the right foot.”

Hence see the effort of nature to roll.

Page 61. “In traversing a given distance in a given time a tall man will take fewer steps than a short man, in the same way that a large wheel will make fewer revolutions in travelling over a given space than a smaller one. The nave of a large wheel corresponds to the ilio-femoral articulation (hip-joint) of the tall man, the spokes to his legs, and portions of the rim to his feet.”

We thank nature very much for this suggestion of the wheel; without it perhaps we should never have conceived of the veritable wheel itself.

I also find from another work:[3]

“Living beings have frequently and in every age been compared to machines, but it is only in the present day that the bearing and the justice of this comparison is fully comprehensible.”

Page 67. “One might find in the animal organism many other appliances the arrangement of which resembles that of machines invented by man.”

Page 91. “Let us examine from this point of view the articulation in the foot of man: we see in the tibio-tarsal articulation a curvature of small radius.”

Page 112. “In addition to this the body is inclined and drawn up again; at each movement of one of the legs it revolves on a pivot.”

And so on in all works on animal locomotion will ever be found a continual reference to radius, roundness, and rolling.

These quotations show that while we must acknowledge that the fundamental principles involved in the cycle were anticipated, to a certain extent, by nature, we may yet take great credit upon ourselves for developing the new or improved method to such a perfect and useful degree.

To the oscillating features found in the human organism the genius of man has added a full circular revolving mechanism, pushing further nature’s aspiration to roll. Nature rolls a little, and then rolls back again; man has so improved upon himself by the addition of a wheel that he can roll on forever. It is quite evident that by such means he saves much energy; let us now determine if possible how this saving can be still further increased.

The whole question of the advantages of the cycle method or wheel locomotion must resolve itself into one of reduction of organic friction as shown by fatigue in the body. All inorganic friction, such as metallic friction in the machine and upon the road, must be finally overcome at the expense of organic friction due to the exercise of the muscles in man. Without stopping to discuss such profound questions as to just what organic friction is, or as to how the display of energy creates friction, we will confine ourselves to the more tangible problem,—to wit, improvements upon the improvement; that is to say, granting the cycle method to be an improvement upon the leg method, we will discuss improvements in the cycle method.

We feel perfectly justified, from our own experience and observation, in adopting, as a basis upon which to build all future improvements, the broad principle underlying the intervention of continually rolling wheels between the rider and his road-way. Now, we ask, what are the requirements appertaining particularly to this wheel method?

In order to approach the subject logically, I repeat that the fundamental requirement is the reduction of organic friction or fatigue of the body.

The above requirement is met in two ways: First, directly; that is to say, by working the muscles of the body to the best possible advantage; secondly, indirectly, by reducing the inorganic friction such as is found in the machine and in its action upon the road.

We shall attack first the reduction of direct organic friction by discussing the manner of applying the energy of man to revolve the wheel; his position and economy of power; and secondly, the reduction of the indirect or inorganic friction in the machine by regulating the size of the wheels and weight thereof, the jolt or jar, the friction of the parts one upon another, loss of momentum, and such other problems as may present themselves in the course of our discussion.

The terms used in this book hereafter will be largely arbitrary. Man-motor and locomotive carriages, velocipedes, unicycles, bicycles, tricycles, tandems, and all such terms will be included more or less in the broad terms “cycle” and “cycle-method.” Wherever any distinctive feature is to be made prominent, then such qualifying adjuncts or special terms will be used as express it.

In speaking of different styles of bicycles, we will adopt the name “Ordinary” for the prominent form of machine which is provided with a large wheel fifty to sixty inches in front, with a crank movement, and the usual fifteen- to twenty-inch rear wheel. The recent rear-crank driver, with the two wheels of about equal size, we will recognize as the “Rover” pattern, in deference to the people who first pushed it into the market and so named it. Other terms will be adopted which will be self-evident to all acquainted with the art.

Attention is called to the engravings in Part II. of this book, which will give an idea of the different forms of machines used in the art.

[1] Animal Mechanism, 65.

[2] J. Bell Pettigrew, M.D., F.R.S., F.R.S.E., F.R.C.P.E., “Animal Locomotion.”

[3] E. J. Marey, College of France, Academy of Medicine, “Animal Mechanism,” 1887, p. 1.

CHAPTER IV.

THE DIRECT APPLICATION OF POWER.

It is evident that one of the greatest, if not the very greatest, of the requirements of a practical road wheel, or a man-motor carriage, is that the power of the rider shall be transmitted to the said wheel in the most direct manner possible; that is, by causing the strain to come upon the muscles in such a way that these muscles shall be placed in the best possible position to overcome such strain, and to take advantage of such conditions as nature has already provided for, in training our muscles to the work we have had to do under the old régime, without the wheel.

The muscles of man are best adapted to a direct pull or push. If we push upon a weight with the muscles at an angle to the direction in which we want the weight to move, the effective power is limited in the same way that the effect upon a weight is limited if we push at it in a direction at an angle to that in which we wish to move it; that is to say, not the total, but only a portion of the power will be effective in moving the weight.

The above facts apply particularly to our subject when we desire to transmit motion to a wheel by means of the weight or gravity of our bodies. Gravity acting downward in a vertical line, if we are not placed over the resistance, the resultant effect is in proportion to the cosine of the angle at which we work, as follows:

Let W = the weight of the man and a be the centre of gravity and also the location of the source of power of said weight, and let c represent the point at which it is desired to apply the power to turn the wheel.

Power angle.

Now, it is known that the weight W, acting by gravity in the direction ab, may be taken as proportional to the length of the line ab, and the portion of the pressure P in the direction ac, which will be effective to turn the wheel, may be taken as proportional to the length of the line ac; that is, ^P _W = ^ac_ab, or P = ^ac_abW, where ^ac_ab is evidently always less than unity. Now, if the angle bac is thirty degrees, and W = 150 pounds, W times ^ac_ab is 130 pounds. Or, by trigonometry, the weight W, acting in the direction ab, by gravity as in working a cycle, will have a resultant in the direction ac representing the power acting to turn the wheel equal to W cos bac. If the angle bac is thirty degrees and W = 150 pounds, then W cos bac = 130 pounds. Now, in order to still get one hundred and fifty pounds of force on the wheel, a pull on the handle-bars would have to be given sufficient to make up the lost twenty pounds, which the rider would get without any pull on the bars if placed directly over the work. This pull, while not fatiguing to the legs beyond the necessary requirement of power, is an entire loss of work in the arms, and must tell on the system. This is all an additional loss to that which ensues from the fact that nature has fitted us to stand upright and not to work in an angular position; our every-day experience in walking gives us practice in a direct vertical strain on the muscles of the body, and we should make it a point to apply our force as nature intended, in so far as it is applicable to our wheel method. These conditions apply more or less to any form of locomotion, and particularly to the cycle.

From the foregoing remarks we are amply justified in drawing the conclusion that the resultant force available in the application of the physical power of man is in proportion to the cosine of the angle at which he exercises this force. We are well aware that many apparent variations will occur when so rigid a mathematical fact comes to be applied to the exercise of man’s energy in driving a bicycle; but all we care for is to lead the reader well up to the point by means of reasoning, which we hope will give at least a partial hypothesis for a conclusion well demonstrated by practical experience. We assert that when we consider the application of the gravity of the body to work on either a bicycle, or to other work of similar requirements, our mathematical demonstration is strictly true. It is justifiable, therefore, from a purely theoretical stand-point, to say that the rider of a bicycle wants to get directly over the work; let us see how our experience demonstrates this conclusion.

Take first the differences between a modern ordinary bicycle and the old velocipede, or “bone-shaker,” so called. The former is lighter and better made; but the one great difference is that the rider is more nearly over his work. It was this one advance which encouraged the development of other minor differences which had been roughly thought out before. In fact, the Patent Office shows that many of these improvements were on record, but there would have been little use for them if the rider had not worked himself up into a place where he could do something. Just who raised him up from a midway position between the two wheels, the saddle seventy-five degrees back of the vertical through the drive-wheel axle, as in the old bone-shaker, to nearly the top of the forward wheel, working at an angle of thirty degrees, as in some ordinaries, we will not attempt to say; but when he got there he has been willing, for a long time at least, to try to stay there, even at the expense of frequently going down on the other side, much to his annoyance, particularly as the general construction of the thing compelled him to go down the other end up, which end nature did not intend for terrestrial impact. It may as well be stated just here, however, that when our rider raised and moved his saddle forward he would have gone clear up to the vertical had it not been that it was absolutely impossible for him to stay there at all without hanging a heavy counter-balance somewhere in the neighborhood of the rear wheel, a scheme which, by the way, has been really recommended in modern cycle history.

One excuse for dwelling upon the foregoing dissertation is that many casual observers and some riders, strange as it may seem, assert that in the development of the modern rear-driving Rover pattern, we have been retrograding to the old velocipede, whereas, in fact, we have made another step forward of a similar nature to that spoken of before in raising the rider up above the point of application of power. In the Rover machine we have landed the rider practically where, as before said, he could not remain at all before; but in this new machine he has gained the advantage of being able to stay there.

Thus our rider has been gradually getting up and over the work. Various devices have been used in order to facilitate this operation, but, unfortunately for our power-development theory, many of the changes have been coupled with the safety feature so prominently that, in efforts by makers to place the rider in the best possible position for work, the safety feature is all that the casual observer has been able to see; therefore it is that in several machines, such as that called the “Extraordinary Challenge,” the sales have been made more on the strength of safety than on their other great point of real merit, the advantage in power. In such machines, the rider has often been surprised to find that he had more power than he supposed, but having bought his mount with a view to safety, and it being still found to contain almost as great an element of risk as he before incurred, considerable disfavor has been the result. Had the element of increased power been thoroughly understood and appreciated, such machines would, in spite of the great deterioration in appearance, have been regarded more kindly.

No better illustration in other arts of the desire and tendency of the operator to get over his work can be had than in that of the ordinary foot-lathe. No maker of lathes would think of attaching a treadle in such a manner that the workman could not perch himself directly over it. In some experiments on foot-lathes, the writer found that he could run at a given speed and resistance three times as long when over the work as when standing some twelve inches back and he had to reach out for it; in fact, it seems quite evident that our theoretical conclusion is fully established in actual practice.

Granting then that the direct vertical application of power by the rider is a desirable acquisition, let it be called a fundamental requirement. It must not, however, be supposed, in this connection, that the foregoing in any way justifies the swimming position, or kicking back, which some experimenters have of late been prone to adopt. We must approach but never get beyond the vertical limit.

Since this manuscript has been ready for the publisher, articles in the Bicycling News by “Warrior” and “Semi-Racer” have come under my notice, from which I clip sections, appertaining to this subject, as follows:

“If, as ‘Crawler’ says, it is a very great improvement to have the saddle well over the pedals, how comes it that the contrary is now so universally advised, and as much as four inches recommended between the line of saddle-peak and the line of crank-axle? There never was a greater mistake made than when the saddle was generally placed in advance of the crank-axle. Apart altogether from its effect on the steering or easy running of the machine, there are two very strong reasons why the saddle should be kept well back. In the first place, it is quite impossible to sit upon the tuberosities designed by nature to carry the weight of the body unless the legs are flexed at the hip-joints. The parts resting upon the saddle are, otherwise, soft and delicate structures, liable to injury from the violence of the saddle. Were it for no other reason, this is enough to determine the position well to the rear of the crank-axle. But another reason: it is not a fact that one has greater power with the saddle, as suggested by ‘Crawler.’ One may certainly throw his weight alternately upon either pedal readier, because he is nearer a standing position; but, on the other hand, with the saddle well back and the handles well forward, the purchase so obtained gives far greater power from muscular contraction than the mere weight of the body gives, and, indeed, many more muscles are called into action when the saddle is kept back.—Warrior.”

“With regard to gearing, I consider that the position of the rider has much to do with this also. A rider sitting well back can use his ankles much more effectively than one right over the pedals, and can consequently exert a driving force through a considerably greater part of the stroke, whereas the vertical rider depends chiefly upon the weight of his body during a comparatively short portion of the down stroke for propulsion, and upon the momentum of the machine to carry him over the dead centre. It will be found, therefore, that the rider using his ankles properly will be able to drive at least three inches higher with the same amount of force, and, at the same time, there is much more equable strain on the machine.—Semi-Racer.”

The quotations show one great trouble in writing a book: such a long time elapses between writing and publishing, that new facts and opinions come up in the mean time which demand attention and suggest alteration, as, for instance, my former paragraph in regard to the swimming attitude should have been expanded.

“Warrior” carries his theory to extremes. He is all right in cautiously avoiding an unduly-forward saddle, but when he places the front tip back of the vertical through the crank-axle, he goes too far and is utterly wrong.

The cause for such diversity of opinion in this matter is that it is tested under different circumstances. In riding over an easy, slightly rolling country, the tendency to get back on the saddle is indisputable, for reasons noted by “Warrior” and fully treated of in my chapter on “Saddles and Springs in Relation to Health;” but notice how we slip forward, almost off the saddle, when we have any work to do, as in mounting a difficult hill; and also notice that the farther forward we get, and the less the angle at the pedals between the saddle and the vertical, the less will be the pull on the handle-bar. (See early part of this chapter.)

In this connection the very long saddles, largely adopted in America, are of great advantage, since, when not working hard, the rider can sit well back and then slide forward when occasion demands. What “Warrior” means by “greater power from muscular contraction” is rather ambiguous. I may admit that more power can be consumed when the saddle is back, but I deny that more effective power to turn the wheel can be maintained. The rider may get more exercise from “muscular contraction” than from the effect of his weight, but he will cover less distance with equal fatigue.

As to “Semi-Racer,” his statement, that more ankle-motion is available when sitting back, is absurd. Will he not lose in “clawing” force below what he gains above?

In my chapter on “Ankle-Motion” I would say that the wonderful power therein asserted as possible was attained by having the saddle well over the work. Before disposing finally of this digression, let me express my pleasure that these subjects are meeting with general and enlightened discussion. However much opinions may differ, I regret, as a loyal Yankee, that we in America have to depend so largely upon cross-water importations for the initiative; but it is hoped that such importations may always be on the free list, maugre the high-tariff proclivities of the writer and many others like him on this side.

The next point of importance is the mechanical means whereby the rider transmits a revolving motion to the drive-wheel, and to lead up to this let us discuss the evolution from walking to riding. The actual development has been of a legitimate character; first, walking; second, walking with the trunk supported on rolling mechanism; third, propulsion by means of mechanical things like legs, the entire body supported upon rolling mechanism; fourth, propulsion and support all by means of, and upon, rolling mechanism.

The Dennis Johnson wheel.

The early bicycle, such as that of Dennis Johnson, patented in England, No. 4321, 1818, did not support the rider entirely free from the ground. It consisted in a pair of wheels placed under him, constituting a sort of third or rolling leg, the feet, though not for support, still touching the ground. This machine is a fair sample of an intermediate stage between the era of oscillating devices subjoined to the trunk by nature—to wit, the legs—and that of the present cycle. In the Johnson machine the legs are used for projectile force only, and serve as a motor, the weight of the body being supported on rolling mechanism as aforesaid; hence it was a more natural and palpable sequence to walking than other prior contrivances in which the rider was raised upon a platform such as shown in the machine of Bolton, patented in the United States, September 29, 1804.

The Bolton machine.

The Bolton and similar machines really belong to a different class from that of Johnson, but if we confine ourselves to our bicycle or balancing-machine, thus throwing out the Bolton class, the development from the leg to the wheel method proceeded in order, for we have next the Lallement crank-wheel, United States patent, November 20, 1866, which represents substantially the present single-track type.

The Lallement machine.

One illustrious gentleman, Croft by name, patented a machine in the United States, August 21, 1877.[4]

The Croft machine.

In the Croft machine a pair of bars held in the hands are used with which to propel by pushing against the ground, instead of using the legs as in the Johnson. By supporting the body entirely free from the roadway, Croft takes a step in advance of Johnson, but he still retains his propulsive power by means of oscillating devices having contact with the ground, and in this respect might be said to use a pair of mechanical legs. He combined a walking method with that of rolling, as was the case with Johnson and Baron Draise, but he seemed to think a mechanical extension to the arms a better medium through which to pass his energy than nature’s own devices for that purpose. Quite a number of inventors have gone astray on this question of the power of the arms in these manumotors. No doubt the arms could be made to help, but our present physical development suggests the legs as better; especially if one or the other plan is to be used alone. True, the Croft machine could use the entire body, as in the case of a man shoving a flat-boat or scow upon the water, but the inventor’s engraving does not show any such effort as necessary. What a pity that we did not have a single-track machine, propelled by the Croft process, between the time of Johnson and Lallement; how nicely it would have helped us out in our chronological development. We of the wheeling fraternity may, however, take a crumb of comfort from the fact that the two bicycles, or balancing machines, did make their appearance in respectful logical order.

In naming the Bolton, Johnson, Lallement, and Croft machines, I have not taken the trouble to ascertain whether they all were the very first machines of the kind in the art, nor would it matter whether they were or not, unless it could be shown that others were of equal prominence. We should not recognize mere vagaries as an advance in the art: the above gentlemen patented their machines, and it is therefore reasonable to suppose that they were real workers, and not simply chimerical characters flitting about in the minds of recent explorers. The famous Draisaine is worthy of mention, but our man Dennis will answer all purposes of illustration. Galvin Dalzell is now reputed to have been the first to raise himself from the ground on a single-track machine, and back as far as 1693 one Ozanam, a Frenchman, is said to have made a four-wheeled vehicle of the Bolton type, but driven by the legs.

Blanchard, about 1780, did some work in connection with the subject, and one Nicephore Niepse, we are told, made a machine of the Johnson type about the year 1815. For further information on this subject, see “Sewing-Machine and Cycle News,” in Wheelman’s Gazette, September, 1888.

In quite a recent edition of The Wheel the editor gives us a little foretaste of a book to which we look forward with interest. In it he mentions improvements by Gompertz in 1821, Mareschal, Woirin, and Leconde as having worked on cranks in 1865, and David Santon as having brought a wheel to America in 1876.

L. F. A. Reviere, of England, is said to have made the large front and small rear wheel; C. K. Bradford, of America, the rubber tire; E. A. Gilman, of England, anti-friction bearings, and A. D. Chandler, of Boston, is mentioned as an importer and rider of 1877.

[4] This is not a misprint for 1777.

CHAPTER V.

THE CONNECTING LINK BETWEEN THE LEGS OF NATURE AND THE WHEEL OF MECHANICS.

We now proceed to compare the different modes which have been devised to transmit power from the rider to revolve the wheel; of these there are two principal classes, the simple crank and the lever and clutch. These devices or connecting links relate to the motion of the legs as well as to the power transmitted through them. It is not necessary to treat of the horizontal motion of the limbs, as it is of little consequence provided the rider remains substantially over the work. Power is applied mainly through the vertical resultant, and the consequent fatigue is the effect of the amount of energy given out in a vertical direction. Crank riders acquire a horizontal power, or resultant force, by what we call ankle-motion, which has, to quite an appreciable extent, overcome the most serious inherent defect of the crank device; without this force the dead centre appertaining to the crank, in which the vertical resultant has no power to turn the wheel, would have made it a prey to the champions of other contrivances.

The above remarks in regard to horizontal motion and resultant force apply equally well if the rider is not over the work, except in that the phraseology would be different. A man in straightening out his leg can apply power in a certain direction or in a certain line; now, if he is not over the work, this will not be a vertical line; hence the term horizontal motion would have to be called motion at right angles to the line of transmission of power.

The importance of the dead centre is too great to be passed over without some further discussion. It would be a source of great satisfaction if a general conclusion could be reached in this crank versus lever and clutch controversy, but aside from the difficulty of drawing our conclusion there is a lack of a specific hypothesis in regard to an important element of the problem,—to wit, that as to the nature of the road and other resistance and consequent speed attainable or usually desirable. There is little doubt but that, so far as present developments show, the crank machine has excelled upon a smooth road and at high speed; yet this very fact leads us to suspect that perhaps for rough roads and at slow speed it might be objectionable, for it is easy to see that all questions of dead centres would eliminate themselves at high speed. Taking a steam-engine, of the crank and pitman type, for example, there is no trouble so long as speed is kept up, but it is well known that a certain velocity must be maintained or the crank will stop at the dead centre, even when provided with a heavy fly-wheel. Now, in a bicycle there is practically no fly-wheel at all, and, to pursue the comparison still further, we know that if the fly-wheel of an engine were removed great trouble would ensue; still it might be possible to keep running if the speed were great enough. It is evident, from common observation, that for intermitting slow and high speeds an engine, or any other machine, constructed without a fly-wheel must be provided with some means for continuing the power or carrying it over what would otherwise be dead centres. Multiple cylinders and rotary engines are made to serve this purpose.

The commonly accepted idea that a cycle for racing purposes upon a smooth road is a certain guide as to the requirements under other conditions is therefore hardly justifiable. For best results the form of mechanism used as the connecting link between the legs of nature and the wheel of mechanics must be determined, or at least be modified, by the conditions under which we intend to work. This problem is not at all confined to the art of cycling, it appears in many departments of mechanics. The same question has been mooted in respect to sewing-machines, and non-dead-centre attachments have been made and used upon them, but naturally the demand was not urgent, as this machine comes within the realm of high-speed devices with fly-wheel and evenly-running resistance. In scroll sawing by foot-power and in portable forges, non-dead-centre clutches are used with great effect. Hence our general mechanical experience makes it safe to say that such modes of continuous application of power have valuable uses applicable to this problem. It is not attempted to set up a definite unequivocal comparison or dictum in this matter as applied to cycles, for it is the desire of the writer and his right to make conclusions comparable only to the proofs recognized in practice, which in this case, in the cycle art, appear to be in favor of the crank machine. However, the writer’s opinion, based upon his theory and individual experience, is that we have more to fear from the weight, complication, and friction of parts in the lever and clutch than from the inherent principle of transmitting power upon which it works, and that some non-dead-centre device will finally prevail in the best all-around road cycles, if it can be relieved of purely mechanical objections which somehow seem to be naturally coupled with it. If the writer’s conclusion in this respect is tenable, the induction would follow that such a system, or connecting link, forms the most economical mode of applying power. The body can stand a steady, even pull upon its energy better than uneven intermitting jerks, and I feel sure new riders who have not acquired the ankle-action on the crank cycle will agree in this. This theory will apply to hill-climbing, in which lever and clutch machines have made so enviable a reputation. The rider has in clutch machines an even, steady resistance during the entire downward thrust, and he does not have to get all his power doubled up into a few inches of motion.

The two principal classes of connecting links, the crank and ordinary form of lever and clutch, need no explanation or discussion beyond their fundamental characteristics, but there are several combinations of lever and crank which are of interest and properly come under the head of modifications of the crank. These modifications are numerous in the market, and there exists cardinal distinctions between them. We annex diagrams of five distinct types which fall into two groups, the first group being a combination of lever and crank, in which the foot has an oval motion, as shown by Figs. [1], [2], and [3], the arrows showing the direction of progression.

GROUP I.

Fig. 1.

Fig. 2.

Fig. 3.

GROUP II.

Fig. 4.

Fig. 5.

The second distinctive arrangement of lever and crank is where the lever is pivoted so as to return over the same track in which it descends, as shown in Figs. [4] and [5]. The first group, with its oval motion, has a decided advantage in regard to dead centre or continuous power; since by an ankle-motion the rider can transmit some power in a circular direction to the crank; that is to say, he can actually push to some extent in a forward horizontal direction. But it will be seen that the pivotal connection shown in Figs. [4] and [5] does not allow of any such possibility; the rider must have momentum enough to throw the cranks over the dead centre or he is lost. In [Fig. 4], which represents a form of pivoted treadle used on a reputable make of front-driving machine, it will be noticed that the rider has less than one-half of the revolution of the crank in which any power can be transmitted at all, which becomes apparent in observing a pedal in such devices while in motion, from the fact that it descends more rapidly than it ascends, thus giving the rider less than half the time in which he can transmit any power. We are now speaking of one side only of the machine; taking both sides together, there are two short arcs of a circle in which there can be no propulsive power transmitted to the wheel on either side. [Fig. 6] illustrates this as follows:

Fig. 6.

In the descent of the lever from b to c the power will only be transmitted through the arc between d and e; taking an equal arc from f to g for the power given on the other side, we have the two small arcs f d and g e, all of whose points are dead points, and we might say we have a dead line. Upon the other hand, if the machine happens to be driven in the opposite direction from that of which we have been speaking, or, in other words, if the pedal is in advance of instead of in the rear of the driving-axle, as seen in [Fig. 5], we have an advantage, since the arcs f d and g e would represent arcs in which the rider has power on both treadles instead of on neither, and it might be said that, instead of having an arc of dead centre or no power, we have considerably less than no dead centre at all. The lever and crank, [Fig. 5], is a device used on some rear-driving machines,—the pedal descends slowly and ascends rapidly; certainly a desirable arrangement. That is to say, if the arc d e raises and d f g e lowers the pedal, it will then raise quickly and lower slowly; whereas, if d e lowers and d f g e raises the pedal, it will raise slowly and lower quickly.

The study of wheels in the market made with front-driving mechanism, on the plan of [Fig. 4], suggests an incontrovertible argument in favor of getting over the work, in spite of the difficulty noticed in respect to dead centres; such machines actually have a creditable reputation as powerful hill-climbers and rough-road machines, which can only be explained on the theory that the vertical application of power more than makes up the deficiency caused by the arc of no power at all.

In speaking of the second group, Figs. [4] and [5], it must be understood that the matter of driving from either the front or the rear wheel has nothing to do with the principle, except in so far as it regulates the arrangement of the pedal and the direction of translation appertaining thereto. The difference in principle depends on whether the driving or the returning arc of the crank is towards or farther from the pedal. It strikes me that the style of lever and crank of the first group is a kind of cross between the direct crank and the pivoted lever and crank of Group II., and especially of [Fig. 4] of that group, since it possesses some of the advantages and some of the objections found in both.

I find from observations, which will be spoken of later, that the ankle-power in the direct crank is very considerable, and that it is diminished in the oval-motion lever, Group I., and that it disappears absolutely in the pivoted lever, Group II. These facts are really evident, but as they came within the domain of other experiment, I merely state the result.

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 by springs, E, E, has a vertical movement through the frame A 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 marker C with 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; 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, in [No. 1] the 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. [3] and [4], 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. 12] illustrates 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.

In [No. 9] we 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 experiment [No. 9] at 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], and [13], 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], and [12] designate 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.

In [No. 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. 6] was 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 results [2] and [3] were 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 themselves to 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 in [No. 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.

ANKLE-MOTION AS SHOWN BY THE CYCLOGRAPH.

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 the Irish Cyclist, via The Bicycling News and Wheelman’s Gazette:

“ANKLE-ACTION.

“Among the many thousands of riders in this country, says the Irish 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 hills never 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 a sine quâ non to 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 found much 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 at d and ending at e, [Fig. 1],—in all, thirty-six degrees over a half-circle on each crank.

Fig. 1.

Ankle-power.

The diagram shows the sections 1 to 8, and also gives an idea of the extra power. To see the direct circular resultant force to turn the wheel, imagine the length of a crank from m to n without ankle-motion and then m n plus n o for the length of the crank with ankle-motion added. I have been able at each of the points a and i to 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 the pedals 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 A is a line showing the divisions of the angles through which the crank passes in its revolution around the axle. The line a f i is a sine curve.

Using the middle section and beginning at the point a, 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 from a to b; and by ankle-motion on both cranks we have sixty pounds, represented by the total length of the line from a to c. 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-two pounds, 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 curve f, 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. 1] will show a little more graphically to the eyes of some casual readers how the power expands. Take d a f i e as the regular swing of the crank with no power at a, then d b f h e as the increase of power on one and the dotted lines c and g as the auxiliary ankle-power on the other crank added.

Fig. 2.

Ankle-power sine curve.

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

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, almost entirely independent 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 the Bicycling World, in which I think the law of whirling bodies will 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.

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.

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.

MOTION AT THE SADDLE AS WHEELS ROLL OVER AN OBSTRUCTION.

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. 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. 5.

Star, 24 F., 39 R.; saddle over axle.

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. 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.

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.

[Fig. 5] shows 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 in [Fig. 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. 6] shows 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. 7] illustrates 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 wheels in 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 liability to jump off; advancing upon the obstruction must, in them, be mostly provided for.

In [Fig. 8] we 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.

In [Fig. 9] appears 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.

CHAPTER IX.

SPRINGS IN RELATION TO THE CURVES OF TRANSLATION, MOMENTUM, AND CONCUSSION.

It was a pet scheme of the writer’s to treat of the matter of the annoyance to the rider resulting from a shock or jolt and change in momentum in the various styles of bicycles in a purely mathematical form, and to some extent it can be done; but it is found that so many considerations enter that the question becomes almost interminable. The aim was to find a formula with the sizes of wheels, distances between centres, and position of saddle as variables, which would, when applied, give us a result representing the sum total of annoyance felt by the rider in passing over an obstacle or any depression, rut, or ditch of given height or depth on any combination of wheels likely to be used in one machine. The difficulty in the question is in determining just what that annoyance results from or consists in; no doubt the initial impact, change of direction, and sudden reduction of momentum, and also the duration of the shock, all enter into the grand total.

From a theoretical stand-point there need be no loss of power and consequently no annoyance in running over an obstacle, since all the momentum lost in a forward direction ought to be transmitted vertically in mounting the obstacle, thereby establishing a potential energy which would again be transformed into momentum forward as the wheel rolls down from the elevation. Neither should a rut have to be avoided, since by running into it we gain a momentum that should carry us out; hence, as per theory, the cycler should not worry about riding over rough roads, for in mounting each obstacle he only loans a bit of power in going up, which will be returned to him in going down, and in running down into a rut momentum will be loaned to him sufficient to bring him out. But, alas! he does not fancy the thing; somehow he has a like prejudice against rough roads that he has to hills, and as this prejudice cannot arise from purely theoretical considerations, we must look for some violation of nature’s laws, or some cause why such laws are not directly applicable. In my judgment there is a reasonably definite connection between the annoyance felt by the cycler in riding over a rough road and the actual loss of energy, though not a similar one in all respects to that which applies in regard to hills. A shock produced by a sudden check or deviation of the momentum is not only hurtful in causing a direct loss of kinetic energy, which the rider has stored up and to regain which he must afterwards do work, but also in contusing and jarring the muscular system, which makes him less able to do the work. In so far as the machine is concerned, the loss of energy goes into vibration and into extra friction of the machine; we cannot see any other means by which it can escape; but as to the rider, while energy is of course similarly lost, the motive power is also interfered with. Now, the application I wish to make of this fact, i.e., that the annoyance or shock felt by the rider in wheeling over rough roads is comparable to an actual loss of kinetic energy, as well as in addition thereto, is that the nearer we can approach to an even rolling motion affecting the rider least disastrously, the nearer we will come to a perfect road bicycle without loss of momentum. In other words, the dynamical and physiological considerations lead us to the same end,—to relieve the annoyance by means of proper springs, and to so distribute the inequalities of the momentum and modify the change in direction thereof as to minimize the loss of energy. From experiments tried with properly-constructed springs, I find that momentum can be diverted in striking the obstacle into its required new course, upward and forward, with very slight loss indeed, and that much waste of power in rolling off the obstacle can also be saved, the desired conditions and effect being as follows:

The wheel strikes the obstacle, springs back a little, and begins to rise upon it; at the same time an upward thrust is given, additionally compressing the vertical components of the springs, the man going on forward at the usual pace of momentum and being gradually raised. When the top is reached and the wheel starts down, the weight of man and machine causes the wheel to spring forward a little at first, and then, when the weight would drop too slowly and the momentum would otherwise pull the wheel bodily off, the vertical spring, being compressed, will, by its quick action, together with the pressure backward of the horizontal spring against the obstruction, hold the wheel in contact and make it roll off. This action is reversed in the case of a rut, and is quite similar in either fore or hind wheel.

The principle is to avoid a too sudden attack upon the inertia, to change the course of momentum gradually, and to avoid concussion against inelastic parts.

The direct vertical amplitude in the springs of a cycle is of most benefit in regard to momentum in giving the vertical power time to act; that is, if the wheels are raised quickly the momentum is transmitted to and stored up in the springs and allowed to act gradually in raising all the parts without violent concussion or vibration and consequent loss of power. When the machine drops suddenly in descending from an obstacle the springs will act more quickly than gravity can overcome the inertia of the system, and the wheel will then remain in contact with the obstacle; that is to say, sufficient spring acting horizontally in the direction of the acquired momentum, together with the necessary amount of vertical spring, will store the energy otherwise lost in riding suddenly upon an obstacle; said energy will then be given time to act and be utilized in raising the rider and such parts of the system which the springs control to a certain height, establishing a potential, which will be given out in increasing the forward momentum as the wheel rolls down to the common level.

Springs having a horizontal movement relieving only the saddle can prevent loss of momentum in the man, but cannot prevent the weight of the machine from being thrown dead against the obstacle. This can only be remedied by elastic connections of a kind that prevent the shock from ever reaching the heavier parts, which condition would save almost the entire work lost against the obstacle.

We see, then, that the subject of springs comprehends not only the question of comfort in regard to the shock sustained by the body, but also the most serious and interesting factor in relation to the economy of power; nor is this a theme at all confined to cycles; it has been egregiously overlooked by makers and riders of many other vehicles. No better illustration can be had of man’s selfishness, as against the brute creation, than the fact that now, in machines in which we have to pull our own load, we are just beginning to contrive and apply all possible means to prevent a loss of momentum, whereas in all our carriages drawn by horses we looked only to the ease and comfort of our bodies, and provided good springs with a vertical give for that especial purpose, having little care for any loss of power, to avoid which loss we should also use horizontal springs so placed as to relieve the entire weight of the heavy running gear, as well as that of the man, from forward concussion. I know full well, even then, that a horizontal spring has still some little to do with the ease of riding, but with a heavy conveyance the advantage to the rider is slight as compared with the advantage that it would be to the horse which furnishes the power. The time will come when the evil will be remedied in general carriages, if only for the gain it will be to the comfort of the man. There would be little hope, indeed, if the poor horse were the only party interested, but when man is directly concerned we can expect more rapid development.

When we start our machines for a run it is considerable work to get up an initial velocity or momentum; however, after that there should be only the friction of the machine within itself and upon the road to be overcome, together with the friction against the air; that is to say, if inequalities in the road could be run over without a loss of momentum being caused thereby, there would not be nearly so much work in travelling upon the cycle as is now necessarily required.

The principal parts of the cycle should be as rigid and firm as possible, so as not to respond at random in vibration to every little shock they should chance to receive, for the spring or elasticity wants to be such as can be controlled,—that is, made to store energy in the right way and give it out at the proper time with a desired effect upon the momentum.

It must be remembered in this connection that useful energy can be stored in the machine only in the plane of horizontal motion and gravity; in other words, vertically and horizontally. Any elasticity at an angle to this plane can only be of use in reducing the concussion upon the rider in a lateral direction; and since, upon a single-track machine, but little if any shock can occur in such direction, it should be seen to that no undue side motion is permitted.

In order to fully comprehend the loss of power that it is possible to save by proper springs, observe as a particular case the annexed diagram showing two thirty-inch wheels arranged substantially as in the present rear-driving Safety.

Let c be the centre of gravity, and let the line c o, drawn to the obstacle, pass through the centre of the front wheel and make an angle of forty-five degrees with the horizontal.

Rover momentum.

The momentum c l is split up into two equal components, one acting in the direction c o, and the other in the direction c k perpendicular to c o, tending to turn the system about o as a centre. The numerical value of the c k component, calling m the momentum, is ^m_√2, and its value in the forward direction c o is ^m_√2 cos 45° = ^m_√2 ¹_√2 = ^m₂, which is the forward momentum retained, showing that in this case one-half of the forward momentum is saved and the other half lost.

It is scarcely necessary to say that the use of an imaginary four-inch obstruction, in our study of momentum and concussion, is entirely arbitrary. Of course obstructions of all heights will evolve proportional results. This proportion would not, however, be linear; the nearest we can come to it is to say that the annoyance begins with an obstruction of zero height, and increases about as a trigonometrical sine increases when the angle grows larger.

It is evident that all this theory applied to one obstruction is simply repeated in a number of them, and a number of them make up a rough road, bearing in mind that a rut is but one form of an obstacle.

Some makers of late seem to realize the importance of springs which will allow of a horizontal as well as a vertical motion, and have in them not only provided against the loss of momentum in the man, but also in the entire machine exclusive of the front wheel. This has apparently been done with another object in view,—i.e., that of relieving the annoyance to the hands and arms by reducing the vibration in the handle-bar. This object, though worthy, is far short of the ideal. Such springs might properly be called storage springs or power economizers; they are, however, generally nominated Anti-Vibrators and Spring Forks.

CHAPTER X.