CHAPTER VII.

ON THE FRICTION, AND RESISTANCE OF CARRIAGES MOVED ON RAILROADS.

§ 1.-Different kinds of Friction.

In all carriages, moved on railways, or other roads, there is always a certain degree of obstruction, or resistance to their progressive motion, arising from the attrition of their rubbing parts, and the action of the wheels upon the rail; and this retardation is denominated the friction of the carriages, and is always greater or less in the proportion which the extent of rubbing action bears to the weight of the carriage. This resistance of wheel carriages is referable to two separate causes that arising from the pressure or attrition upon the axles ;-and the obstruction to the rolling of the wheels upon the rails or road. In the case of a common sledge, or a body dragged along the surface of a plane, the entire weight of the body is referable to the action of attrition, the parts subjected to attrition sliding over each other with the same velocity, as the progressive motion of the body on the plane. On the contrary, if the body be cylindrical, and rolled along the plane, no part of it is subjected to the action of attrition; the only resistance (which, when the surfaces are smooth and hard, is very trifling) being that produced by the rolling of the periphery upon the plane.

Suppose a cylinder composed of two concentric circles, one within another, let the interior cylinder be of

small diameter compared with that of the outer; if we now cause this cylinder to roll along a plane, upon the periphery of the outer circle, and place the body to be moved, or the carriage, upon the periphery of the inner cylinder; that portion of the resistance arising from attrition, will be represented by the weight of the body acting upon the periphery of the inner circle; and that portion arising from rolling, the resistance of the periphery of the outer circle upon the plane. And as the velocities of the peripheries of these circles will be in the ratio of their diameters, the velocity of the rubbing surface, compared with the velocity of the rolling action, will be as the radii of the respective circles. In this case the inner circle represents the axles, and the outer the wheels of a carriage; hence we have two distinct species of friction, viz., the friction of attrition, acting upon the axles; and that of rolling, acting on the periphery of the wheel: - the degree of resistance opposed to the promotion of the carriage, by the sliding of the axles upon the chairs or bearings which rest on them, is called the friction of attrition; and the retardation by the action of the periphery of the wheels rolling upon the rails, the rolling friction. In all wheel carriages, however, the two species of friction are in action at the same time, and, therefore, where it is not particularly expressed to the contrary, the term friction will be understood to comprehend both kinds of resistance combined. It will be afterwards necessary, when treating of locomotive carriages, to speak of that property of bodies in contact with each other, and subjected to pressure; the surfaces of which resist sliding, and which is employed for a mechanical purpose; the employment of such resistance, for that particular purpose, ceasing when the surfaces begin to slide over each other; whereas, in the case of the friction of attrition

above mentioned, the action only commences when the bodies slide over each other. We shall, therefore, denominate that force, which, acting upon two surfaces in contact with each other, and which is not sufficient to cause them to slide on each other, as the force of adhesion.

There are other species of obstructions presented to the motion of carriages, besides those already enumerated, such as the action of the wind, &c.; but as their effects in retarding motion at moderate velocities are trifling, we shall at present omit noticing their effect, but shall afterwards, when treating of rapid motion, recur to these obstructions.

Let f the resistance opposed to the free motion of a carriage upon a railroad, by the action of rolling, in parts of the weight w.

g that by attrition, upon the axles in parts of the weight

=

Then the power P, required to move the body over the plane will

In this case w represents the whole weight of the carriage, and w' that part resting upon the axles; and it follows from this, that the quantity of rubbing action, or that part of the friction of railway carriages, which arises from the attrition on the axles, will be in the inverse ratio of the wheels, or while the resistance arising from

D

W

the action of rolling will be always We have no decisive experi

f

ments to prove the value of f with different sized wheels; but as large wheels more easily surmount obstacles than wheels of small diameter, we may suppose the former will always present less resistance.