ON THE RESISTANCE OF ROAD VEHICLES TO TRACTION. 315 



The following are their conclusions : — 



That the resistance to rolling is composed of two elements : (i.) Fric- 

 tion of the wheel upon the I'oad ; (ii.) axle friction. 



(i.) That wheels of vehicles destroy the road in proportion to their 

 load, width of tyres, and speed. If the tyres be narrow the friction may 

 be simply treated as a rolling friction, but if the tyre be wide then a 

 pivoting action is introduced. 



The effect which a wheel produces upon the road depends upon the 

 load upon the wheel, the resistance of the material of which the road is 

 made, and on the nature of the surface. If the load be great and the 

 tyres narrow, the wheel will form a rut in the road, but if the tyre be 

 wide, the load becomes distributed and does not damage the roadway. 

 A wheel ti-avelling along a road badly kept or badly constructed meets 

 with obstacles against which it strikes and surmounts with difficulty, and 

 from which it falls to the ground again with a force proportional to its 

 weight and the height of the obstacle, This action being continually 

 carried on is very destructive to the roads. 



In cases where roads are uneven, springs should carry the load, as 

 they convert the series of shocks into a simple increase of pressure and 

 preserve the horizontal component of the force, which otherwise would 

 be lost. 



The destructive effect of a wheel upon the road increases with the 

 load, the speed remaining constant, but the rate of increase of damage 

 to the road is far greater than the inci'ease of the load. 



The influence of speed is such that, with equal loads, on a well-kepfe 

 road, the destructive effect of the wheel decreases with an increase of 

 speed, but on a badly kept road the reverse takes place. 



MM. Corr^ze and Manes proved, by direct experiment, that the ratio- 

 between the tractive effort and the load increases with the speed. 



Carriages with four wheels in unequal pairs require less tractive effort 

 than those with two wheels or two equal pairs of wheels. 



(ii.) yla;^e/rtc<ion.— By the contact of a spindle with its bearings a, 

 sliding friction is produced. 



Suppose the coefficient of friction = jVj ^^^ lo3,d = P, 



Then total resistance due to axle friction = jL p ^ 



If ratio of radius of wheel to that of axle = ^V > 



n^, resistance at axle of wheel , 



Then — — -—. -, = ^V 



resistance at circumterence 



Thei'efore resistance at circumference =■ -ttI^ P. 



But on a good road resistance to traction = -}-, P. 



So the axle friction only = ^ that of total resistance. 



Edgeworth experimented and found, in 1808, that on a rough road a 

 vehicle with springs had only one-third the resistance of one without, at 

 8 '8 kilometres per hour. 



III. The Work of Coriolis (1835). 



Coriolis, a civil engineer, applied the theorem of work to the traction 

 of vehicles and investigated the work of resistance. He proceeded as 

 follows : — 



Let F equal the tractive effort and s the distance run. Then the 

 integral of the quantity F ds will equal the total "vv^ork due tO the reaction 

 gf the ground. 



