10
ENERGY IN PROPELLING A BICYCLE. 269 to make me the offer, sir; but you see it’s no sort of use.” And Mr. Cubb climbed softly into his sad- dle. and silently melted away in the dark- ening night, leaving the major gazing after him in a state of miserably collapsed aston- ishment and indignation. “This is extraordinary—most extraor- dinary!” finally observed the major, turning to the president, and blowing out his breath like a diver just coming to the surface after a plunge into the water. “Very extraordinary,” drily replied the president. “D—n it! it’s infamous!” continued the major, indignation rising above aston- ishment. “Yes, I think it is,” acquiesced the president, severely. “Never saw such infernal impudence in my life!” said the major. “Nor I, either,” agreed the president. “The d—d scoundrel! Do you consider it possible that he could suppose that I offered him my daughter’s hand—that my daughter would look at him for a moment, sir?” “Possible?” replied the president, with calm severity; “why, Major Podswell, I heard you say to him plainly that your daughter wanted him: I was astonished at you, major; for a gentleman of your age and your standing in the community, Major Podswell, to interfere with the honest love of a young couple, and try to break it up by openly soliciting the young man to visit your own daughter—well, in any way hereafter. That's my advice as sir, I can’t properly characterize it. I a friend, Major Podswell, and I sincerely couldn’t possibly have believed it if I hope you will follow it.” hadn’t heard it with my own ears.” So saying, the president gravely touched “What, sir!” roared the major, “do his hat, shook his head solemnly and you mean to say that I offered my daughter to that young jackanapes?—my daughter, sir!” “You certainly did, Major Podswell,” calmly replied the president, “if my ears are good for anything. And I must say it was the most impudent performance I ever witnessed.” “You—you—damnation!” spluttered the major, now thoroughly bewildered and choking with passion; “do you pretend to say I did that?” “Exactly that,” very coldly replied the president, who all this while had been secretly noting the fact that Mrs. Major Podswell and Miss Cleopatra Podswell were at the window listening; “and if you will allow me to express an opinion, sir, your offer to this honest young man, which he so nobly rejected and spurned, has put your daughter in a very cruel situa- tion. Fortunately for your family, major, I happen to be the only witness to this ex- traordinary affair, and I pledge you my word that it shall never be repeated, pro- vided you and your family drop it, and let the young man and Miss Margery alone after this; but, sir, if you or your daughter interfere with them and pursue or annoy the young man any more, I shall feel it my duty to give my evidence in corroboration of any statement Mr. Cubb may see fit to make public about it. Think what society will say to such a statement, sir! As a man of the world, Major Podswell, you cannot help seeing that the best thing to be done for all concerned is to bury this affair in oblivion as soon as possible; let the young people alone to manage their own affairs, and caution your daughter and your wife to be very careful not to take any notice of their proceedings, or meddle with them walked slowly away, as if pondering deeply upon unfathomable mysteries, leaving the major the most thoroughly dejected, for- lorn, and utterly crushed statue of collapsed pomposity I ever saw in my life. on the energy expended in propelling a bicycle. by. g. johnstone stoney, d.sc., f.r.s., vice-president of the royal dublin society; and g. gerald stoney. The magnitude of the effects produced endurance have travelled considerably more by human muscles acting upon bicycles than two hundred miles in one day, along and tricycles is well deserving of attention. common roads; another has twice main- Several riders of exceptional strength and tained an average speed of more than President Bates.

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ENERGY IN PROPELLING A BICYCLE. 269

to make me the offer, sir; but you see it’sno sort of use.”

And Mr. Cubb climbed softly into his sad-dle. and silently melted away in the dark-ening night, leaving the major gazing afterhim in a state of miserably collapsed aston-ishment and indignation.

“This is extraordinary—most extraor-dinary!” finally observed the major, turningto the president, and blowing out his breathlike a diver just coming to the surface aftera plunge into the water.

“Very extraordinary,” drily replied thepresident.

“D—n it! it’s infamous!” continuedthe major, indignation rising above aston-ishment.

“Yes, I think it is,” acquiesced thepresident, severely.

“Never saw such infernal impudence inmy life!” said the major.

“Nor I, either,” agreed the president.“The d—d scoundrel! Do you consider

it possible that he could suppose that Ioffered him my daughter’s hand—that mydaughter would look at him for a moment,s i r ? ”

“Possible?” replied the president, withcalm severity; “why, Major Podswell, Iheard you say to him plainly that yourdaughter wanted him: I was astonishedat you, major; for a gentleman of your ageand your standing in the community,Major Podswell, to interfere with thehonest love of a young couple, and try tobreak it up by openly soliciting the youngman to visit your own daughter—well, in any way hereafter. That's my advice assir, I can’t properly characterize it. I a friend, Major Podswell, and I sincerelycouldn’t possibly have believed it if I hope you will follow it.”hadn’t heard it with my own ears.” So saying, the president gravely touched

“What, sir!” roared the major, “do his hat, shook his head solemnly andyou mean to say that I offered my daughterto that young jackanapes?—my daughter,sir!”

“You certainly did, Major Podswell,”calmly replied the president, “if my earsare good for anything. And I must say it

was the most impudent performance I everwitnessed.”

“You—you—damnation!” splutteredthe major, now thoroughly bewildered andchoking with passion; “do you pretend tosay I did that?”

“Exactly that,” very coldly replied thepresident, who all this while had beensecretly noting the fact that Mrs. MajorPodswell and Miss Cleopatra Podswellwere at the window listening; “and ifyou will allow me to express an opinion,sir, your offer to this honest young man,which he so nobly rejected and spurned,has put your daughter in a very cruel situa-tion. Fortunately for your family, major,I happen to be the only witness to this ex-traordinary affair, and I pledge you myword that it shall never be repeated, pro-vided you and your family drop it, and letthe young man and Miss Margery aloneafter this; but, sir, if you or your daughterinterfere with them and pursue or annoythe young man any more, I shall feel it myduty to give my evidence in corroborationof any statement Mr. Cubb may see fit tomake public about it. Think what societywill say to such a statement, sir! As aman of the world, Major Podswell, youcannot help seeing that the best thing to bedone for all concerned is to bury this affairin oblivion as soon as possible; let theyoung people alone to manage their ownaffairs, and caution your daughter and yourwife to be very careful not to take any noticeof their proceedings, or meddle with them

walked slowly away, as if pondering deeplyupon unfathomable mysteries, leaving themajor the most thoroughly dejected, for-lorn, and utterly crushed statue of collapsedpomposity I ever saw in my life.

on the energy expended in propelling a bicycle.by. g. johnstone stoney, d.sc., f.r.s., vice-president of

the royal dublin society; and g. gerald stoney.

The magnitude of the effects produced endurance have travelled considerably moreby human muscles acting upon bicycles than two hundred miles in one day, alongand tricycles is well deserving of attention. common roads; another has twice main-Several riders of exceptional strength and tained an average speed of more than

President Bates.

270

twenty, miles an hour along a preparedpath or a whole hour; another has riddenfrom the Land’s End to John o’ Groat’s, adistance of almost one thousand miles,in thirteen days, averaging more thanseventy-six miles a day. These astonishingfeats have been accomplished upon bicycles,and the tricycle does not fall far behind. Atricycle has been ridden a distance of onehundred and eighty miles in one day; andhundred-mile journeys on both classes ofmachines have become frequent. It is per-haps quite as striking that average riders,who are not athletes, even including thosewho are between fifty and sixty years ofage, usually in touring make from thirty tosixty’ miles a day without pressing them-selves, going on day after day without in-termission and without fatigue.

Such an astonishing efficiency ought tol be capable of explanation; and as it isplain that no sound knowledge on the sub-ject can be gained without first ascertainingexperimentally the amount of energy act-ually expended in propelling a bicycle, wehave endeavored to make this determina-tion.

The machine known as the “Xtraordi-nary” offers facilities for attaching an indi-cator diagram apparatus to it, and was thatupon which the experiments were made.It is represented in Figure 1. Indicatordiagrams were obtained in two differentWays; which furnished independent seriesof observations, adapted to test eachother. Further to confirm our results, weendeavored to measure the energy by akinetic method, by taking the feet off thetreadles when the machine was running athigh speed, and leaving it to advance byits own impetus (i.e., kinetic energy) untilthe rate was too slow for the rider to main-tain a steady balance. After some prac-tice the skill required to carry out this pro-gramme was attained, and the observationswere made by an assistant noting the timesoccupied in performing successive sets offive revolutions of the wheel. Startingwith a speed of about fourteen miles anhour, four, and in some cases five, suchsets could be observed before the motionbecame unsteady. From these data theenergy required to drive a bicycle at the

deduced. The results which we were ablespeed successively passed through could be

to obtain by this method, so far as they go,seem to confirm the more reliable deduc-tions from the indicator diagrams; but wedo not believe them to be worth publishingas we had not adequate appliances for

measuring fractions of a second of time,which would have been necessary to givethe observations a satisfactory amountof accuracy. The method, however, isgood, and, as we have found that otherpractical difficulties can be overcome, itwould probably be worth repeating1 theseobservations with the assistance of a chrono-graph.

The first apparatus which we made forfurnishing indicator diagrams was attachedat the top of the right-hand lever of thebicycle. The link which trammels thetop of the lever was removed, and a spiral.spring substituted for it, which was com-pressed when the right foot acted on thepedal. To the lever a vertical flat boardwas fastened to carry the paper on whichthe diagram was to be produced; and thediagram was drawn by a pencil connectedwith the inner end of the spring. Thusthe pencil was relatively at rest and thediagram paper was moved past it in twodirections,—in the arc of a circle corre-sponding to the up-and-down motion of thelever, and radially corresponding to theforce applied. The apparatus is repre-sented in Fig. 2, and the diagram it pro-duced in Figure 3. This may be calledthe crude indicator diagram, from whichthe true indicator diagram represented, inFigure 4, has to be derived.

This was accomplished by hangingknown weights on the pedal to representthe pressure of the foot, and moving thewheel round so as to get the lines corre-sponding to known forces exerted on thepedal. The successive dotted lines of Fig.3 were in this way drawn, when one, two,three, four, five, stones were successivelyhung on the treadle. In the reduced indi-cator diagram (Fig. 4) these become par-allel equidistant lines, and are the dottedlines of that figure. Horizontal distances, inFig. 4, would be strictly proportional tothe forces applied by the foot if it had actedvertically; but if the foot acts obliquely theforce as registered in this way may besomewhat greater than the actual force ex-erted. Hence the energy as indicated inthis way might slightly exceed the truevalue, though, as the result proves, it hasdone so either not at all or but little. Itwas chiefly to detect and avoid this possibleerror that the second series of indicatordiagrams, described on p. 278, was under-taken, contrived so that the indicated energymust fall somewhat short of the true value.

1We have since made these observations—see theAddendum to this paper.

ENERGY IN PROPELLING A BICYCLE.

271

comparison of the two series shows that These on the “reduced” diagram (Fig.any such excess or defect is small in eitherseries.

4) are made proportional to the net verti-cal descent of the foot in its oval motion.

To return to Fig. 4. Vertical distances The area of the “reduced” diagramon Fig. 4 have been made proportional to (Fig. 4) will then be the energy suppliedthe net vertical distances through which by the right foot of the rider during onethe foot descends. This was accomplishedby the help of Fig. 5, which represents

revolution of the bicycle wheel, on thehypothesis that he presses vertically on the

the oval curve through which the foot treadles; and the whole energy exerted bytravelled before the indicator apparatus both feet will, of course, be twice this.was attached, with points marked on itcorresponding to the points numbered in

The following results were obtained with

the same way on the circle of the figure,this apparatus in the winter of 1881-82, and

which is the curve through which the endthe diagram represented in Fig. 3 is copiedfrom that produced in Experiment 6.

table i.

Series I. of Observations made in Winter with the Recording Spring attached to the Top of theLever of the Bicycle.

of the crank of the bicycle travels. And,again, the same numbers on Fig. 3 markthe points of the indicator diagram corre-sponding to those positions of the crank.

1By the net descent of the foot is to be understoodthe distance through which the foot would descend ifthe spring were not compressed. The additional dis-tance through which the foot descends owing to thecompression of the spring, represents additional energyexerted by the rider on the down stroke, which, how-ever, the spring restores to the foot on the up stroke,when by its resilience it assists the lifting of the leg:It accordingly is not work done on the bicycle, and

should not be counted in.

In the other series of experiments madein July, 1882, a spring was placed directlyunder the treadle, so that its compressionwas proportional to the vertical componentof the force exerted by the foot. It movedthe pencil horizontally by a bell-crank leverwhile the paper was carried up and downby a secondary crank fastened to the end ofthe crank of the bicycle. Thus the dis-tances in one direction on the indicatordagrams represent the vertical force of thefoot, and distances at right angle resentthe vertical heights of the end of the bicycle

ENERGY IN PROPELLING A BICYCLE.

272 ENERGY IN PROPELLING A BICYCLE.table i.

Series II. of Observations made in Summer with the Recording Spring attached to the Treadle.i

table I I . – Part I I.

Experiments made on Hills with the same Apparatus.

273

crank. The apparatus is represented inFig. 6, the diagram it produces in Fig. 7,and the reduced indicator diagram in Fig.6. The reduction was erected as before bythe help of Fig. 5. It will be observed fromthe position of the rider, and since thevertical component of the foot’s pressure iswhat is registered, that the results furnishedby this method cannot exceed the truth.They are as follows. No. 29 of the seriesbeing that represented in Fig. 7. That continuance does not seem to reach muchthe results of this series are so close tothose of Table 1. shows that both must benear the truth.

In order to appreciate the foregoingresults, it will be well to compare themwith the annexed table of the foot-poundsof energy expended per minute when work-ing with certain fractions of a horse-power.

It thus appears that the power exerted inseveral of the experiments (see Experi-ments 19, 22, 28, 31, 35) amounted tobetween a quarter and a third of a horse-power,1 while the average furnished by allthe experiments on nearly level ground—

1This is the maximum attained in our experiments,which were limited by the range of the spring of theindicating apparatus; but in actual riding this maxi-mum is often largely exceeded for a short time, as in

sions.spurting up a short stiff hiss, and on other like occa-

which we believe to be close to the averagein ordinary road riding—amounts to be-tween a seventh and a sixth of a horse-power.This is very sensibly more than the workwhich the muscles of a man seem capableof effecting in other applications of them.Thus in rowing, or in raising one’s ownweight, which are supposed to be two ofthe best ways of employing the muscles,the power which it man can exert for any

beyond the eighth of a horse-power. Thisin part accounts for the extraordinary featswhich are daily being performed onbicycles, but it does not appear to give thewhole account of the matter, for which wemust look to physiology and psychologyas well as to mechanics.

In fact the real comparison to be madeis not so much a comparison of the featsaccomplished with the energy expended aswith the fatigue incurred. And this inriding a bicycle is small, not only from themechanical efficiency which the foregoingexperiments show the machine to possess,but also for other reasons. Part of theseare physiological. The rider is seated onthe machine, and thus relieved from whatis the chief source of fatigue in walking,the weight of his own body on his limbs.He is in the posture best adapted to thehealthy play of the vital organs in thechest, and the constant slight movement ofthe muscles of the trunk contributes to thishealthy play. Again, while the arms per-form some of the work, the principalpart is relegated to the most powerfulmuscles of the body, those of the leg. It isalso material to observe that these limbsare left very unusually free in their move-ments, and that the choice of what lengthof stroke he will employ, what force hewill exert, and at what speed he will movehis limbs, is left to the rider, who canadjust these details to what best suit hisown body. How much depends on theseadaptations will be appreciated by any per-son who has ridden far with a saddle toolow for him. The fatigue then ex-perienced is sometimes accounted for bythe supposition that the greatest pressureis exerted when the leg is nearly straight.and that the rider loses this most valuablepart of the stroke: but all our experiments

1The contribution made by the arms when pullingon the handles often seems to the rider out of pro-portion to the force they exert. Perhaps in suchcases their chief office is to stiffen the trunk, and sogive firm points of attachment to the upper ends ofthe great muscles of the legs.

ENERGY IN PROPELLING A BICYCLE.

table i .i i

274

concur in showing that this is not the case(see Fig. 4 and Fig. 8), and that, on thecontrary, the greatest force is exertedalmost exactly at the middle of the stroke.The reason seems rather to be that, unlessthe knee is periodically straightened, thetendons, nerves, or blood-vessels whichpass it are subjected without intermissionto some restraint which incommodes them.

But, besides the mechanical and thephysiological elements, there is a third,—an emotional element. This is the exhila-ration felt in riding the bicycle, which,in addition to that caused by the scenerypassed through and other collateral circum-stances, arises also from the mere exercise,and with most riders is of somewhat thesame kind, but greater and more lastingthan that experienced in riding on horse-back.

It is obvious to remark, that our experi-ments seem to show that an economy maybe effected in workshops where humanmuscular power is employed, wherever itis possible to apply it in the same way ason the bicycle, and with the adjustmentswhich the bicycle-rider has at his disposal.It is plain, from the experience of bicycle-riders, that most work can be done with agiven expenditure of fatigue, when thepressure against which the feet move ismuch less than the whole weight of thebody.

Some information is given by plot-ting down on diagrams the results of allthe experiments made on nearly levelground. This is done in Figs. 9 and 10,in which the points marked with a crossare those furnished by the experimentsmade in winter with the indicator appara-tus attached to the top of the lever. Thoserepresenting the experiments made in sum-mer, with the apparatus attached to thetreadle, are surrounded by a circle. Thescattered position of the points on thesediagrams is, of course, owing to the greatvariety of conditions under which the ob-servations were made,—the state of theroad, the wind, and the inclination (al-though always slight), having been verydifferent.

Nevertheless the curves drawn throughthe midst of these scattered points may betaken fairly to represent the average ex-penditure of energy in ordinary flat roadriding to attain speeds of from six to twelvemiles an hour; Fig. 9 furnishing theenergy which must be expended per mile,and Fig. 10 the energy per minute, or,in other words, the power which must be

exerted. Both of these rise rapidly withincreasing speeds, and show that the lowerspeeds are much the most economical.

It is of interest to inquire what is practi-cally the most economical speed to adopt.This is found in practice to be the speed atwhich the machine will travel when therider after lifting the rising leg does a littlemore than allow its weight to act on thedescending pedal. Sauntering in this wayis scarcely felt to be work at all, and isoften the ace which is best suited to re-lieve the fatigues of sedentary occupations.This, under the conditions of our experi-ments, has been found to furnish a speed ofnearly six miles an hour on an ordinaryroad without wind, and this experienceagrees well with Fig. 9; for, taking thestroke as ten inches, and the weight of theleg from the knee down, along with halfthe weight of the upper leg, to be seventeenpounds, we shall have fifteen foot-poundsof work done each stroke, or thirty eachrevolution of the wheel. This would as-sign 11,500 foot-pounds to the mile, which,if we venture to extend the curve in Fig.9 backwards a very little, will bring it to apoint which shows the corresponding speedto be five and three-quarter miles per hour.

This great efficiency of velocipedes whenridden slowly suggests that machines es-pecially adapted to be ridden with the leastpossible effort, at such low speeds as fromfour to six miles an hour, would be founduseful for many purposes. A step in thisdirection has already been taken by the in-troduction of the excellent little “Facile”bicycle, with driving-wheels sometimes assmall as thirty-eight inches. And morewould probably result from making ma-chines of the tricycle class with driving-wheels of from twenty-five to thirty inchesdiameter, for going to one’s office in allweather, for shopping, for carrying parcels,for gently sauntering in the open air, forcarrying invalids or children, and for manyother useful purposes, to which velocipedeshave as yet been little applied.

The machine with which the experi-ments in this paper were made was thatknown as the “Xtraordinary Challenge,”1880 pattern, roller bearings to a frontwheel of fifty-two inches, and cones to thehind wheel. The height of the rider isfive feet eleven and a half inches; lengthof leg, inside measure, thirty-six in-ches; length of stroke, nine three-quarterinches. The weight of the rider, ten and ahalf stones; weight of machine, sixtypounds. Hence the total weight of rider

ENERGY IN PROPELLING A BICYCLE.

275

and machine was 207 pounds. To adapt the machine without propelling it, till theour results to a rider whose weight along speed fell to about four miles an hour.with that of his machine is more or less Meanwhile the other manipulated the trig-than this, all the energies recorded in ger of the chronograph, and thus recordedTables I. and II. would, of course, have to the instants at which one treadle in succes-be altered in proportion to the change of sive revolutions reached its lowest position.weight. Thus, with a rider whose weightis thirteen and a half stones, the sauntering

From twelve to twenty such dots were pro-

pace above spoken of was found to beduced in each experiment.

nearer five than six miles.From the record so produced a curve was

plotted down on millimetric paper, givingthe relation between the times (in swings

addendum. of the chronograph pendulum) at whicheach revolution was completed, and the dis-

Since the foregoing pages were written tances (in circumferences of the wheel)we have constructed a chronograph, and traversed by the bicycle.have been able to resume the investigationby the kinetic method.

A straight ruler being placed to touch

Our chronograph consists of a heavy pen-this curve at any point enabled us to read

dulum, to the rod of which a pencil is at-off on the millimetric paper the tangent of

tached a few inches from the fulcrum. Be-its inclination, which was the velocity ofthe bicycle at the corresponding point of its

hind the pendulum a vertical board is journey. In this way the velocities at thelaced, mounted so that an assistant canby a winch make it travel upwards while

end of each five revolutions of the wheel

the pendulum is swinging. To this boardwere determined, and plotted down in a

strips of paper, about five feet in length, aresecond diagram, which gave the relation he-tween v, the velocity, and s, the distance trav-

fastened by drawing-pins, and on this paper ersed. This second diagram proved to bethe pencil attached to the pendulum tracesa wavy line in the form of a rough curve of

nearly a straight line, the deviations beingwithin the limits of errors of observation; and

sines. It only remained to have another the tangent of its inclination being read offpencil mounted on a trigger to produce dotsat the will of the observer, and the position

on the millimetric paper furnished the valuedv

of these dots in relation to the curve of of , which is the basis of the calculationsines gives with sufficient precision the

ds

times at which the dots are produced. Thewhich has next to be made. We made

observations were made as follows: Onetwenty-one experiments, each of which had

of us rode the bicycle, getting up a speedto be reduced in this way.

dvof from fourteen to sixteen miles an hour, The resulting values of are as fol-then took his feet off the treadles and ran lows:— d s

table iv.

ENERGY IN PROPELLING A BICYCLE.

276

We have to deduce from these the energyper mile which would maintain any of theseveral velocities which the bicycle passedthrough. This is effected by the formula

de dvmvd s

. . . . (1)d s

in which we must use some systematic setkinetic measures. The most convenient forsuch mechanical problems are the measuresbased on the second as unit of time, themetre as unit of length, and the kilogramas unit of mass. These give one metre persecond as the unit of velocity, and a Hyper-hectogrammetre as the unit of energy. Thehyper-hectogrammetre means the workdone in pushing against a force of onehyper-hectogram through a metre, and ahyper-hectogram, which is the unit of force,is the weight of a hectogram increased inthe proportion of 10: g (i.e., increasedabout 2 per cent.), g being gravity at theplace of observation.

The second column of Table IV. givesthe values of

de, using the swing of the pen-

to use one of the values furnished by the thirdcolumn of Table IV.)

dsdulum of the chronograph as unit of time,and the next column gives the equivalentvalues when a second is used as unit oftime, the swing of the pendulum havingbeen determined by independent experi-ments to be equal to 1.32 seconds. It isthese latter values that are to be used informula (1); m, in the same formula =207 pounds or 94 kilograms (see p. 275); vis the velocity in metres per second.

Hence de (in hyper-hectogrammetrerds per metre ) 94 x the energy being measured in foot-pounds,

and v, the velocity, in miles per hour.

( metresindv dv)x (where for we are To compare these results with those fur-v

per second ds d s nished by the indicator diagrams it will be

table vi.

ENERGY IN PROPELLING A BICYCLE.

table vi.

Results of the Kinetic Experiments for a Velocity of Nine Miles an Hour.

277

convenient to compute from Table VI. the These results are in substantia, agree-energy per mile, the energy per minute, ment with those of Tables I. and II.,and the coefficient of resistances at a veloc- though obtained by a wholly differentity of nine miles per hour, which was the method of observation. The problem hasaverage speed in the experiments recorded thus been worked out in three distinct waysin Tables I. and II. We thus obtain results which confirm each other.in the same form as in Tables I. and II.

diagram 1.

ENERGY IN PROPELLING A BICYCLE.

diagram ii.

2 7 0 ENERGY IN PROPELLING A BICYCLE.

diagram i i.i