ON THE RESISTANCE OF ROAD VEHICLES TO TRACTION. 325 



Dupuit found that the moan force required to draw a vehicle loaded 

 up to 1,000 kilos was 



On macadam roads = 30 kilos 

 On paved roads = 20 kilos 



That on flagstones perfectly dressed the tractive force required equals 

 6 kilos per ton, and that on asphalte equals about 10 kilos per ton. i'roin 

 the above he obtained the following ratio : — 



The resistance on railroads : the resistance on pavements : the resist- 

 ance on macadam : : 1:4:6; but these resistances are not in proportion 

 to the respective roughnesses, which are as 1 : 15 : 30. 



M. Dupuit performed experiments on the efiect of tlie width of tyres, 

 and carefully noticed the manner in which they wore. He found that the 

 edges became furrowed into deep grooves, and that some particles of the 

 stretched iron became detached ; also that the wood having at first a 

 rectilinear section was found after being considerably used to be elliptical. 



Experiments were made with wide tyres, and it was found that for a 

 tyre 17 cm. in width only 9 cm. were in actual contact, and 6 cm. of a 

 11 cm. tyre ; from this he concluded that the length of contact is of more 

 importance than the width, this being at least 14 cm. for a tyre 2 m. in 

 diameter ; that wide tyres are only useful when they bear on the road 

 throughout their whole width, and in cases when the road is soft, uneven, 

 and in a bad condition. 



Dupuit states that from actual experiments he found that a tyre of 

 17 cm. after a few weeks' wear was reduced to 14 cm. and after a few 

 months' to 11 cm., and that after a 17 cm. tyre had been run 4,000 miles 

 it was worn out and showed a loss of 1 kilo for every 20 miles and per 

 ton of useful load carried. 



And, moreover, since the tyre is rounded, it is necessary to admit that 

 the pressure is unequal throughout its whole width, and that not only 

 does it diminish on both sides of the centre but to the right and left, that 

 the surface in contact is not square or rectilinear in section but elliptical, 

 forming an ellipse the major axis of which increases far more rapidly 

 with the diameter of the tyre than the minor axis increases with the 

 widtli of tyre. 



From another series of experiments Dupuit proved that under a 

 pressure of 2,000 kilos, scarcely jV of the material of the road was 

 subjected to any strain. From this he concluded that 4,000 kilos might 

 be taken as a standard load for a two-wheel vehicle, and the weighting 

 distributed as follows : — 



Wheels (one pair) . . . 600 kilos 

 Axle and frame . . . 520 „ 

 Useful load .... 2.880 „ 



4,000 kilos = Total load 



Dtqmit on the Ejfect of Hollows and Sises in Soads. 

 Dupuit obtained the following formulse : — 



e'=e\/ ' R and e"=eV TTR" 



