40 TRANSPORTATION ON LAND BY VEHICLES:- THE ROADS 



Steep roads are always rough roads, since they are more severely injured by erosion and traffic. 

 The lowest gaps of a mountain system are the "strategic points" of a road system. 



III. The tractive force of a team or of a locomotive lifts a certain load or weight G, to which the 

 weight (g) of the animals or of the locomotive must be added, by D . sin A feet, where D represents the 

 length of an incline and A the angle of the grade. 



The work accomplished by the horses or by the locomotive for every foot of distance traveled amounts, 



in foot pounds, to /^ \ • . 



(G - g) sm A 



Theoretically, the horse-power required to haul a certain load up to a certain point is independent 

 of the grade. If the horses, e. g., are allowed the same total time for haulage at a proportionally decreased 

 average speed on a steep grade, their task of lifting is no more severe, either in toto or per minute, than 

 it would be on a reduced grade. On steep roads, however, horses and machines are apt to be overworked. 



Gravity resistance increases in exact proportion to steepness of grade expressed in per cent. Thus 

 it is always 20 pounds per ton of load for each per cent. 



Work of lifting equals weight lifted times height of lifting. Height of lifting equals velocity of lifting 

 (number of feet per second) times number of seconds required for lifting. 



A heavy horse puts up per second a force of 154 lbs. at a speed of 4 ft. (over 1 horse-power) during 

 eight hours of working time. An average horse yields only - ., horse -power. If the work time is decreased, 

 the tractive force can be proportionally increased when speed remains the same. 



After Mascheck, the ratio between standard force, speed, and time (F, S, T) and actual force, speed, 

 and time (f, s, t) is shown by the following appro.ximation : - 



f -^"^ s t^ 

 Steep grades reduce the cost of road building but increase the cost of maintenance of traffic. 



IV. The motive power P hauling a load up hill must overcome :- 



(a) The frictional resistance R, which is equal to the coefficient of friction f multiplied by the pressure 



of the weight G on the road „ t 



R = fg cos A ; 



(b) The gravity of the object to be moved (weight of load G and weight of tractive force 

 [locomotives, horses] g) amounting to (G -*- g) sin A; 



(c) Hence P = (G — g) sin A + fg cos A; 



and, since cos A approximates 1, r^ , 



• » P - fg 

 sm A = „ , 



G + g 



(E) CURVES. Curves in roads take the place of angles. Curves inside the angle decrease the 

 length and increase the grade. Curves outside the angle increase the length and decrease the grade. 



I. The minimum radius permissible on road curves depends on the flexibility of the vehicles using it. 



(a) Four wheel waggons. This flexibility is governed by the distance (e) between the axles (equal 

 to the length of the reach or coupling pole) and the maximum of the angle (A), which the tongue and 

 the prolonged coupling pole may form. According to the construction of the waggon, this angle varies 

 from 30 to 45 degrees unless the front wheels are made to cut under the bed (as in high bolstered log 



waggons). The radius of the curve measured from the middle of the front axle is . , or measured from 



g sm A 



the middle of the rear axle — r 



tg A 



Obviously, the shorter the distance between the axles, the smaller is the permissible radius. 



As tg A differs slightly from sin A for angles of 30 to 45 degrees, the hind wheels cannot follow in 

 the same rut behind the front wheels, and the width of the road in a curve must be correspondingly 

 increased by the difference of the radii running to the front and the hind wheels. 



