Although the motion of wheels and rollers over a smooth plane is attended with much less resistance or friction than the sliding of one flat surface over another, however smooth, yet practically it has been found impossible to get rid of resistance altogether. Coulomb made some experiments on the resistance which wooden rollers meet with when rolling on a wooden plane, from which experiments he deduced certain laws connecting this resistance with the size of the rollers and the force with which they are pressed on to the plane. These laws have been verified and extended to other materials by Navier and Morin, and are now set forth in many mechanical treatises as “
the laws of resistance to rolling
.” It does not appear, however, that any systematic investigation of this resistance has ever been undertaken or any attempts made to explain its nature. When hard surfaces are used it is very small, and it has doubtless been attributed to the inaccuracies of the surfaces and to a certain amount of crushing which takes place under the roller. On closer examination, however, it appears that these causes, although they doubtless explain a great part of the resistance which occurs in ordinary practice, are not sufficient to explain the resistance altogether; and that, if they could be removed, there would still be a definite resistance depending on the size and weight of the roller and on the nature of the material of which it and the plane are composed. If it were not so, a perfectly true roller when rolling on a perfectly true surface ought to experience no resistance, however soft the roller and the plane might be, provided both were made of perfectly elastic material so that the one did not crush the other; and we might expect, although these conditions are not absolutely fulfilled, that a roller of iron would roll as easily on a surface of india-rubber as on one of iron, or that an india-rubber roller would experience no more resistance than one of iron when rolling on a true plane. Such, however, is not the case. The resistance with india-rubber is very considerable; my experiments show it to be ten times as great as with iron. I am not aware that this fact has been previously recognized; and that it has often been overlooked is proved by the numerous attempts which have been made to use india-rubber tires for wheels, the invariable failure of which may, I think, in the absence of any other assigned cause, be fairly attributed to the excessive resistance which attends their use. Another fact which I do not think has been hitherto noticed, but of which I have had ample evidence, and which clearly shows the existence of some hitherto unexplained cause of resistance to rolling, is the tendency which a roller has to oscillate about any position in which it may be placed on a flat surface. However true and hard the roller and the surface may be, if the roller is but slightly disturbed it will not move continuously in one direction until it gradually comes to rest, but it will oscillate backwards and forwards through a greater or less angle, depending on the softness of the material. These oscillations are not due to the roller having settled into a hollow. This is strongly implied by the fact that the more care is taken to make the surfaces true and smooth the more regular and apparent do the oscillations become. But even if this is not a sufficient proof—if it is impossible to suppose that an iron roller on an iron plane can be made so true that when the one is resting on the other it will not be able to find some minute irregularities or hollows in which to settle—still we must be convinced when we find the same phenomenon existing when india-rubber is substituted for iron, and in such a marked degree that no irregularities there may be in the surface produce any effect upon it, much less serve to account for it.
On the kinematics of a concave sidecut line deformed on a flat surface