THE ANIMAL AS A MOTOR. 



6l 



20. The Draught of Vehicles is a case of rolling 

 friction.* Morin, who made very extended experi- 

 ments, states its laws as follows : 



(1) On hard surfaces, as paved and macadamized 

 roads, the resistance is directly proportional to the 

 weight of vehicle and load, inversely proportional to 

 the diameter of wheel, and independent of the breadth 

 of wheel-tire. It increases with velocity. 



(2) On soft ground the resistance increases inversely 

 as the breadth of tire. It does not sensibly vary with 

 velocity. Morin concludes, also, that the line of draught 

 should be horizontal. 



Dupuit, on macadamized roads, found the resistance 

 to vary nearly inversely as the square root of the di- 

 ameter of wheel and directly as the load. He found 

 the resistance on pavements to be increased at high 

 speeds by the concussions incident to rapid movem&nt. 

 Clark obtains a somewhat less simple law, which he ex- 

 presses thus : 



R^a^bv^ yfcv. . . . . (i) 



The work of hauling is then 



U — Rs — {a-\-bv-{- ^/~cl^vt. ... (2) 



This formula is deduced from the experiments of 

 Macneil on metalled " roads.f The values of the 

 constants are, in British measures, ^=30 ; b — \ c — \o 

 pounds per ton, v being given in miles per hour, / in 

 hours.;}: 



* Friction and Lost work; Thurston, p. 84. 

 f Clark's Manual, p. 964. 

 X Parnell on Roads, p. 464. 



