326 REPORT— 1902. 



in which 



=tractive force on the level | R = Radius of the wheel. 



6' = „ „ in a hollow ' E i = Radius on surface of the 



e"= „ ,, on a rise i road, either concave or 



I convex. 



By giving different values to R] in reference to R, Dupuit found that 

 the hollows have the effect of increasing the pull to a large extent, and 

 their influence has a greater effect as the diameter of the wheel increases, 

 and that the rises had the effect of decreasing the pull ; but that the 

 increase was always greater than the decrease. 



From experiments Dujauit concluded that, providing the road was 

 undulating and had no very sudden rises or depressions, the effect of the 

 undulations was practically nil. 



VI. Theoretical Investigations of Edmund Leahy, C.E. (1847). 



In an exhaustive treatise on ' The Making and Repairing of Roads ' 

 Mr. Leahy states that the power required to move a car upon a level 

 road depends upon the friction of the axles and the resistance to rolling. 

 The friction of the axles is the same in nearly all cases, as long as the 

 load and the car are the same ; but the resistance to rolling, having its 

 immediate I action at the tyre, must be variable according to the descrip- 

 tion of road upon which the wheels move. 



He proves that the friction at the axle can be represented by the 

 following formula : — 



P=W f tan A .... (1) 



where P is that force applied at the tyre which is just sufficient to rotate 

 the wheel when supported on its axle, whei-e W is the load on the axle, 

 d the diameter of the axle, 2r the diameter of the wheel, and where A is 

 the limiting angle of resistance for the surfaces in contact. 



He then goes on to consider the resistance to rolling, which may be 

 due to either or both of two causes — namely, irregularity of surface, or 

 yielding of surface over which the vehicle passes. 



Dealing with irregularity of surface first, he obtains a formula for 

 the initial effort required to surmount an obstacle. 



The formula is 



P=W^-''Y^' (2) 



j — h 



where P is the tractive effort required, r is the radius of the wheel, 

 W is the load on the wheel, and h is the height of the obstacle. He 

 further proves that when the tractor, be it horse or motor, is unable to 

 exert this initial effort, the minimum velocity which the vehicle must 

 have to surmount the obstacle is given by 



r r, P /length of arc described by centre of \ 1 ,„k 



^ ^^■'^ -^9 ^ZZJi \ W \ wheel in passing over the obstacle ) ] ' ^ ' 



V is the least velocity which, together with the draught P, will enable 

 the vehicle to mount the obstacle. 



