Cursory remarks on the subject of wheel carriages ..

Part II. By

JOHN COOK,

OF LIQUORPOND STREET,

UouHon:

•AJUURD AND FABKBY,

Wkinntr Slrtnt, lanim*

Preface

Having made a promise in my " Cursory Remarks on Wheel Carriages," to furnish the public with a more ample illustration of wheels, together with correct drawings of, and explanations on, every principle of carriage in use, it becomes necessary for me to apologize for these drawings, and remarks, not appearing with this small publication, and to observe, that, from some peculiar circumstances involving my best interests and future welfare, that at no distant period will be made public, I am under the necessity of suspending for a time that part of my promised publication. I therefore beg leave for the present to claim this indulgence. But feeling that I might with propriety withdraw from it those remarks which bore more immediately upon the subject of wheels, and which was intended to be embodied with that work ; and that, while it would not injure my prospects, it would form a very appropriate second part to my " Cursory Remarks." I have therefore ventured to publish it as such, leaving the whole to the candid consideration of

a2

4 PREFACE.

those who choose to honour it by a perusal. I have also to observe, that my experiments have been more confined than I intended ; but as general principle, more than perfect accuracy, has been my aim, in order to give some sort of criterion founded upon scientific principles, for their general application, I trust they will be found to have answered my purpose. To many gentlemen and others who are partial to mechanical research, and to all concerned in the use of wheels, the following remarks, I am induced to think, will not be either uninteresting or useless ; and as I throw them on an enlightened and impartial public, I shall rest satisfied, by leaving them to their fate.

And am, with much respect,

The Public's obedient servant,

THE AUTHOR.

9, Fitzroy Place, Kentish Town.

REMARKS

ON

WHEEL CARRIAGES.

JLN treating of the subject of the comparative advantages of high and low wheels, on which so much contrariety of opinion has been expressed, it is, I consider, next to impossible, in order to come to any fair conclusions, to unconnect it with the roads on which they have to travel.

The excessive draught, and consequent fatigue to the horses from travelling on soft roads, is evident to the driver of every vehicle, and is at once a proof of the above assertion. In the dry summer season, those parts of the road which have been recently watered, are discovered by coachmen to add immediately to the draught the instant they drive the carriage upon it, and is sure to call down from them an opprobrious epithet upon the promoters of that act. As at least two-thirds of our seasons are wet, we ought to provide as much as possible a remedy for the inconvenience they occasion in this respect j for it does not require any ingenuity to discover that this difference of draught spoken of, must arise from the sinking of the wheel, thereby in effect lessening its circumference, and forming, as it were, a hill. Our forefathers were so sensible of this fact, that by a legislative enactment, they have allowed waggons to carry half a ton more in the summer than in winter ; and common sense will inform us, that a small wheel will sink deeper into soft ground than a large one; and will therefore, from this circumstance alone, suggest the exclusion of the former, and the adoption of the latter. Then when we consider how much friction is overcome by the increased size of the wheel, and the increase of power given to the inertia of the carriage, particularly on level roads by the lengthened lever, (which inertia, I shall shortly have occasion more particularly to explain) I think the mind must be induced to assent to their preference and adoption. Besides these considerations, there are others not less important, which involves both the comfort and expense of the proprietors of carriages ; viz. their contributing in an eminent degree to lessen that disagreeable noise which is generally heard inside, by their passing over uneven surfaces with a superiority of ease, that is manifest to almost every person, who but for a moment contemplates the subject.

The consequence of this circumstance must be equally obvious, viz. that they convey less jar to the carriage, and therefore it must of necessity, and I well know from experience, does wear considerably longer ; for there can be no doubt that it is this tremendous jar or tremor conveyed to carriages and their wheels, by their passing over these uneven surfaces, separating both the closeness of the frame-work, and the component parts of the timber itself, by destroying the natural cohesion between the particles, that wears them out in so short a time: As we always find that carriages used on London stones do not wear above l-3d so long as in the country. To this cause we may attribute the decaying and giving way of the beds of the axis, and those parts adjacent, which We generally find are the first to fail, and why the whole carriage decays sooner than the body, which is generally on springs.

There are some persons who assert that the small wheel is stronger than the large one, an idea which no doubt is derived from considering small arcs as capable of sustaining greater burden than large ones. This idea, abstractedly considered, is very just, but will not apply to the wheel of a carriage ; for wheels being made of materials which jar on percussion, materially deteriorates, and having constantly to pass over uneven surfaces, which engende'* that jar, or series of percussions, the more we reduce the wheel to the size of such uneven surfaces, the greater power of resistance will such surfaces have over the wheel. Experience fully establishes this fact, and falsifies the above assertion ; for the fore-wheels of carriages are always without exception worn out first, the joints more shaken, and the iron thinner than the hinder ones ; this being uniformly the case, I hope '?o one will contend that wheels lose their strength from being high, otherwise the hind wheels would uniformly be worn out first, which every coachmaker and hackneyman knows is contrary to experience. In fact, the higher wheels are, the more capable are they to withstand the shocks of their resisting medium, which are in effect thereby rendered weaker.

It appears evident, I trust, from the foregoing practical information, that wheels are not less strong from being high ; but in »rder to prove more decisively the relative utility and superiority of high wheels, I shall endeavour to dip somewhat deeper ittto the inquiry, and shall strive to rescue this subject from the uncertainty in which it seems to be involved. Indeed I cannot help observing, that I have considered it almost a disgrace to the enlightened state of mechanical knowledge, that the subject of carriage wheels is still the thetne of hypothesis, and that no fixed or certain principles have been laid down for their use. If, therefore, I fail in the attempt, it will only add one more to the unavailing endeavours which have been before the public ; but on the contrary, should it throw but a small degree of light upon the subject, it will not, I trust, be wholly useless, inasmuch as it may form at least a stimulus to the further exertions of others.

In prosecuting1 this short inquiry, it appears to me there are five points or considerations indefeasibly connected with it, and which must not be lost sight of during our progress: viz. 1st, the inclined plane. 2dly, the relative weight of wheels to their burden. 3dly, the vis inertia of the carriage. 4thly, the state of the roads ; and 5thly, friction between the axil and box.

The inclined plane is extremely important in this consideration, and I may say forms the test of our research ; and from which I trust I shall be enabled to deduce some important phenomena, that 1 believe has hitherto escaped observation.

The next point, viz. the relative weight of wheels to their burden, is not less important ; and I consider that they should not be treated of as apart from, but always as attached to, a carriage.

The vis inertia likewise is a constant companion of the whole, and must be brought in for its full share of the powerful effects produced.

The state of the roads, as being continually variable, at all times consequently affecting the progress of the vehicle, cannot be left out of the question, and the well known accompaniment. Friction must on no consideration be disregarded, being one of the greatest drawbacks to the progress of a carriage we have to contend against.

As we find hills add so excessively to the draught, and that in proportion to steepness of the ascent, arid as this situation is the worst that horses have to contend against, I consider that it is a most important thing to ascertain, in adapting wheels to carriages, their effect and relation, and what are the steepest hills horses have to encounter with them. For the steeper the hill the greater will be the power required to draw any burden up such hill j and the heavier the weight is, so in proportion must the power be increased.

A wheel, therefore, which is six feet high being as heavy again as one of three feet, that is, supposing them to be of equal strength, must of necessity require a greater power to purchase the weight. See fig. 1 and 2. pi. 1.

In examining these figures, it must naturally occur to us on the first inspection, that the power which holds fig. I in equilibro will not be sufficient to hold fig. 2 in equilibrio, the latter being as high again, and therefore of twice the weight.

In applying the observation on wheels descending inclined planes, in my " Cursory Remarks," page 12 and 13, to the opposite situation, we shall be led to conceive, without close examination, that as in that situation thie weight in the higher wheel, from being elevated, and consequently overhanging the fulcrum of the wheel further in proportion to its height, and thereby pressing with a corresponding force ; so in this opposite situation, the weight overhanging the fulcrum of the large wheel further than the small one, will therefore, from that circumstance, give an equal resistance. But this is not the case ; for in the first instance the effect stated has merely a reference to the wheel and its fulcrum on the ground, producing a greater degree of power as regarding the wheels' velocity. While in the latter instance it has reference only to the weight itself which acts upon the wheel ; for with respect to that weight, which is to be considered as the burden, situated upon an inclined plane, whether it be placed upon high or low props, its relative gravity is precisely the same, that is, with regard to the effect it may have in the line of traction. In the latter case the effect of the weight in the centre of the wheel becomes altered by being acted upon by a power in the direction of the line of draught A, while its natural tendency is pressing in the direction of the line B, so that it may be said to take a medium or diagonal course, like a ship acted on by the water and the wind, and therefore takes the direction of the line C.

We perceive also, the weight in going up hill must be taken by the horse in the direction of A, and therefore loses its power of acting with its whole force in the line B ; for until the effect of the weight be removed so far forward as to pass the line D, the whole carriage will remain motionless. But it will be useless to consider the subject of wheels as they may appear sketched upon paper, we must recollect their actual weight, and that any addition of height is attended with a proportional increase of weight, which I shall have occasion to consider more particularly, as being an essential feature in enabling me to ascertain where to limit their height, which, notwithstanding ^ich increase of weight, may be carried to considerable excess before any disadvantage will be experienced.

I propose to make a few observations on the five foregoing points, in a somewhat retrograde order. I shall begin with that of inertia, which, as I have observed, I consider to be indefeasibly connected with this whole subject, and which would therefore be greatly wanting and highly defective without it.

Inertia, or vis inertia, is described by Sir Isaac Newton to be " a power implanted in all matter whereby it resists any change endeavoured to be made in its state," or, " a principle by which bodies persist in a state of motion or rest." I may here observe, it is to this principle wre owe the regular motion of our own bodies in walking, that of birds in the air, and indeed of all animals as well as of machines, and which prevents us and them from being forced along by juts or throws, which, without this peculiar property of matter, must have been the case. For the purpose of explaining the effect of this principle on carriages, I shall consider inertia to be divided into two sorts, viz. active inertia and passive inertia; the first as regards the body being in motion, the latter as it regards its being at rest.

These two states, when considered with respect to carriages, have very different effects ; and in our experiments on this subject of draught-wheels, &c. unless we pay due regard to the effect this universal and inherent property of matter has upon them, our conclusions will be erroneous.

The carriage itself, when considered in reference to this principle, must also be treated of as divided into two parts, viz. the carriage and its wheels, which are effected somewhat differently, and which will require rather a distinct inquiry.

The active inertia peculiar to a carriage may be easily perceived when, being drawn along at a brisk pace, the horses are required suddenly to stop its progress. At this moment they are obliged to exert their utmost strength, in a contrary direction, to effect the object. When a carriage is going at the ordinary rate, if the horses could be released at the same instant, we should find the carriage go forward of its own accord several yards beyond the place where the horses were released.

The quantity of inertia in a carriage depends upon thi\ circumstances, viz. the quantity of power applied, the height of the wheel, the friction within the box of the wheel (the measure of which at all times depends upon the quantum of superincumbent weight), and the state of the roads. In proportion to the hardness and smoothness of the boxes and axles, the height of wheel, and the hardness of the road, so much will the inertia be facilitated, and their resistance overcome.

This principle of active inertia is of the highest importance in the draught of a carriage ; and the great secret of easy draught lies in constructing the carriage, so as this inertia of its whole weight may, with the application of springs, act upon the axles of the wheels as one condensed mass of matter.

The passive inertia of the carriage may be strongly evidenced by the following* circumstance, viz. when horses attempt to start with a carriage at rest, they are obliged to exert a considerable deal more power than is afterwards required to keep up the motion, As the weight in the first case endeavours to preserve its state of rest by its unwillingness to be moved, so in the latter case, when in motion, it endeavours to preserve or persevere in that state likewise.

The inertia of a carriage in motion is liable to be counteracted by several adventitious circumstances, such as the sinking of the wheels in soft roads, inequalities, as stones, gravel, a strong current of air, &c; and the friction in the boxes, which, in hoged roads*, as they are termed, is greatly augmented, matters to which I shall have occasion again to allude. Independently of this inertia of the carriage itself, the wheels have likewise an inertia of their own, which in point of velocity is generally as that of the carriage increasing or diminishing exactly in proportion as its velocity becomes more or less.

I shall now therefore inquire more particularly into the general effect of this inertia in regard to wheels, which are immediately opposed to, and effected by, the impediments of the road, and the excessive friction in their centres from the superincumbent weight. If we observe a boy trundling a hoop, we may notice what a regular motion it has, although the impulses are communicated by successive strokes, and if it were not of this peculiar property, would go forward by throws and starts, as before observed. So again in the balance of a watch, a pendulum, and numerous other instances. Now', if we contemplate the relative motion of a large and of a small wheel, we must consider both of them as attached to a carriage, and therefore put

* Roads elevated in the middle, the effects of which, oil the Hastings road, there fell most severely upon a passenger of the Swan coach, and also upon its proprietor, in a late trial at Guildford.

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CteAJ into action by the same power or weight, and that power constantly acting upon them in their progress over the same impediments or roads ; this will naturally lead us to the observations following : —

Suppose two wheels in motion, one of them as high again as the other (see plate II. fig. 1 and 2.) and having to pass over the same sized obstacle A.

Now, as both of these wheels are to be considered to be put in motion by the same force, and that force or weight (say fifty pounds) accompanies them during the whole time of the revolution, which is an important circumstance to be considered, they must each acquire the same velocity ; and from which we must infer, that both wheels would gradually acquire the precise velocity of their accompanying impulse (for I before remarked, a carriage wheel can have no acceleration beyond that of the carriage, as that at all times governs the wheels) ; as this is the case, we conclude, that notwithstanding the weight of the large wheel is double that of the small one, it must actually acquire the velocity of the latter. If so, then the first principle of mechanics will inform us, that if a body of a given weight has a velocity equal to another body of half that weight, it must overcome orstrike against a third body with double the force, because here a double weight is assimilated into the same velocity. Therefore the obstacle A (even if the wheels were of equal height) would be overcome with twice the ease ; and, multiplying the velocity into the weight of each gives us their power.

As suppose the high wheel to weigh 40 lbs. and the velocity 20 multiplied together, gives .... 800

And suppose the lower one to weigh 20 lbs. and its velocity the same or ... 20 multiplied, gives 400, half the

force of the former, — —•

But as this double weight arises from a double height, and as that height, we find by experiment, gives, even from a state of rest, nearly a proportionate advantage, I trust it must be acknowledged highly superior.

It is owing to this active inertia of matter, before referred to, that the increased weight of high wheels becomes of no material disadvantage ; and when, I say again, we consider that this increase of weight is the consequence of an increase of height, we shall become the more sensible of their superiority. Let us examine farther : —

Suppose the wheel (see fig. 1 and 2) to be as high again as the other, and impelled with an equal degree of force along the same road, and pressed by the same superincumbent weight, we shall find, that as the line of inertia, formed as in " Cursory Remarks/' p. 10, is thrown as forward again on the ground as that of the small one, so will it pass over the inequalities or obstacles with twice the ease; and therefore these obstacles cannot retard the velocity of the high wheel as they would the small one : and when we add the extra weight of the high wheel, which is assimilated into the velocity to the advantage of its lever-like principle from its height, its superiority in this light, and in every point of view on level road, I submit, must appear greatly in favour of its adoption. We may add to these considerations, that it is the softness of the roads that occasions a greater draught to the carriage than any other circumstance, from its allowing the superincumbent weight to press them into it, thereby weakening the force of the inertia of the wheels themselves, and therefore we may conclude, that the inertia or force of the carriage, which gives motion to the wheels, must likewise be lessened, and so retards the velocity of the whole machine, by weakening the momentum of the source of their motion, and hence the increase of draught. As, therefore, we find that high wheels to a burden require less power than small ones to pull them

Piatt or over the same sized obstacle, even from a state of rest, we must be blind to conviction not to acknowledge their great superiority, when acted on by the full impulse of the united active inertia of their burden and themselves.

There is, as before stated, a subject very closely connected with, and constantly affecting the subject of inertia last in part discussed, viz. friction, to lessen which in carriage wheels has been the object of research of hundreds of ingenious mechanics ; but the immense strength here required to meet the tremendous shocks a carriage has to undergo, has prevented the adoption of matiy ingenious contrivances, which otherwise might have been useful. Friction is a very excessive dravvback to the active inertia, and, consequently, draught of a carriage ; it is a natural result of weight, and always bears a certain proportion to it, and therefore the greater the weight the greater the friction. This friction tends most eminently to lessen the force of this inertia, and that in proportion to the roughness of the parts in contact, and likewise in proportion to the length of the space of that roughness.

That is, a body, say a sledge for instance, having to pass over a surface with a given force, must naturally be gradually retarded, until the friction becomes superior to the momentum of that body, and therefore induces it to a state of rest. Suppose a body, A (Plate 3, Fig. 1), has to pass or slide over a surface, B, by the impulse of a given force, say twenty pounds, that force must be uniformly Retarded until it gain a state of rest, which we will suppose to take place at C, when, if we wish it to pass on the same distance further, it will require the same impulse, or twenty pounds, as it had at A, to effect it. The shorter, therefore, this retarding surface is, say half, as Fig 2, at the end of which it is to receive a new impulse, the less exertion of power will be required to continue its motion. Now it must appear, that as the velocity of A, at its setting* out is 20, and coming to a state of rest at C, its medium force at B would be 10, and therefore if it is to receive a new impulse at half the distance, 10 only would be required to keep up its velocity.

The action of axletrees within their boxes is precisely on this principle, the box only forming the road to the sliding arm.

Now as friction increases in proportion to weight and roughness of surfaces, and inertia a constantly retarding force from this friction, and therefore the velocity greater in proportion as the space to run over is less: the more we can reduce the space forming the resistance, the less extrinsic power will the moving body require to continue its motion. I trust this is a theorem that will be admitted.

It is on this principle that high wheels may be traced to point out the most eminent advantages, inasmuch as they form the only remedy to excess of friction from excess of weight ; and indeed it is a peculiar property of the wheel by which we can keep lessening the friction, just in proportion as the weight engenders it.

The high wheel then, certainly forms the means of shortening our road of friction within the box, and therefore reduces the quantity of that friction in proportion to its height, by which the inertia is rendered effective, and less power required. I shall now endeavour to make this clear by the following diagram.

Pig. 3 represents two wheels, one as high again as the other, having the same sized box in each, which must be the case, as they are supposed to take an axletree of sufficient strength to carry a given weight. They have each eight intersections through the centre, which enables us to ascertain the proportion the circle of the box bears to the rim of each. We may thence perceive that the space in the rim of the larger wheel contained between 5 and 6 is just the same as that of the smaller one contained between 5 and 7, and tracing these sec* v^y e

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?VV?J tions to their boxes, we find that the space in the circle of the box of the large wheel (which is in fact the road to the arms of the axle) contained between O and X, is only half the distance of the length of the box in the small wheel that is contained between the corresponding marks, which' is the space in which the arm will have to trnvel in the box of the small one before its rim will have measured the same distance on the ground as the large one, and which space in the box is just double that which the arm will have to travel in the box of the large wheel before the rim will have measured the same distance on the ground as the large one.

We may illustrate this further, by supposing a carriage without wheels, and the arms of the axles to slide over a surface as smooth as a box, like a sledge, suppose the length of the space to be three feet, Plate 4, Fig. 1. If this carriage were drawn from 3 to 0, it would have three feet of friction ; but if it be placed on wheels of three feet diameter, as suppose Fig. 2. to be, it would go from 3 to 0 in one revolution of the wheels, because their circumference would just measure that distance.. Now supposing the arm and box to be two inches in. diameter, that would give six inches circumference for the box, which is now the road for the axle's arm ; and as this box makes the same revolution with the rim of the wheel, it therefore goes round only once, forming a space of only six inches for the arms to rub or slide over, while the carriage and wheels have passed through a space of three feet, so that suppose the outside circle of this wheel, Fig. 3, to be turned into a straight line, and the circumference of the box also, one would bear a proportion of six inches to three feet, as the lines A and B, Fig. 3. Now, an impulse given to the whole burden, sufficient to move it six inches only on the three feet surface, would, by the application of this wheel, be sufficient to cause the whole machine to

B pass through three feet ; while, without the wheel, the same strength would be required every six inches, and consequently take six times the labour to get through the said space of three feet, so that velocity is increased and friction lessened in proportion to the excess which the circumference of the wheel bears to that of its box ; and the effect of the lever in overcoming friction in the cohesion of substances may be thus explained : — Suppose the circle A, Plate 5, Fig. 1, to represent an axle-tree armf and the circle or ring round it to represent the box fastened so very tight as not to be moved upon the arm by the lever B ; but if an additional length, as C, be added, it must give double the power. From these observations it must follow, that the less resist- , ance there is to the momentum of a moving body, the greater will be its force, and therefore the less extrinsic power it will require to continue its motion, which in this case is the original source of that motion. But here, it will justly be remarked, a loss of time in this instance follows the gain of power; and therefore it will be asked, where is the advantage. But here we are supposing for a moment only that the centre is a stationary body, and the lever revolving round it ; and whenever this is the case, as in all mill and clock-work, this must invariably be the consequence. But with a carriage, as regarding the velocity of its passing motion, it is very different, and, what is most extraordinary, the contrary is the result, from the centre being not a revolving stationary body, but a passing unrevoking one ; not that the wheel itself makes more revolutions in the same space. On the contrary, as far as regards that alone, it obeys the above law of mechanics, and from hence the advantage is derived. But that, as far as regards its passing motion, together with the whole body, it is infinitely superior, because the great cause that retards our machine, viz. friction, is so much lessened, as before explained, leaving the active inertia to act with so much force j for we are assured, that if a body, once put