44 TRANSPORTATION ON LAND BY VEHICLES: -THE ROADS 



1. Find the radius R of the curve. 



2. Find the angle of the curve. 



3. Design the curve of 25". 



Start from A, deflect from AC by 12'^ 30 and run a chord of 100 feet, reaching G; then move the compass 

 from A to 0, deflect from A Q by 25", run a chord of 100 feet, &c. 



REMARKS: — In developing a road system showing a great many curves, it is wisest to make a 

 plane table map of all of them to begin with, and to stake the curves out from the map, with the help 

 of the map. In S-curves on a railroad, a tangent 100 feet long should form the stem of the S. 



(F) WIDTH OF ROADS: -The cross section of a road shows a "lower side slope," an "actual travelling 

 bed" (the crown) and an "upper side slope," frequently with a side ditch. 



The width of a road depends on:- 



(a) track of vehicle (locomotive, car, waggon, sled) used; 



(b) width of bolsters ; 



(c) meanderings of road and radius of curves; 



(d) configuration and composition of the ground; 



(e) length of pieces loaded. 



The wheels of the vehicle or the edges of the ties should not come within a distance closer than 

 one foot of the edges of the road. The minimum width of the road must, therefore, equal track (ties) 

 plus two feet. 



In order to avoid ruts in waggon roads, add ',,, of track width, so as to allow the teams to change the 

 ruts. Where loaded waggons meet one another, the width of the road should be doubled. 



Theoretically, a steep slope of a mountain side requires, for various reasons, a wide road. Practically, 

 however, the road is narrowed under such circumstances. 



Wide roads are maintained at a smaller expense than narrow roads. 



The expense of road building E bears the following proportion to the width of the road w and to 

 the grade of the slope A, f being a factor depending on toughness of soil to work, on price of labor, &c. 



W" 



E=f > 2 tgA 



Per foot of road measured lengthwise, every additional foot added to the width of the road requires 

 the removal of (tgA) cubic feet more dirt than were required in the case of the preceding foot. The 

 expense of dirt moving incurred for the 1st, 2nd, 3rd, 4th, &c. foot forms an arithmetical progression in 

 which the constant factor equals tgA >' expense per cubic foot of dirt. 



Building a road on "half solid base" (one half of the road on solid ground, the other half on filled 

 ground), the expense of dirt work is reduced by 75 per cent. In this case, the cost of breastworks (if 

 any) must be added. 



Every additional foot of width of road costs more than the last preceding foot, however, not merely 

 because it requires the moving of more dirt, but also because it necessitates the moving of material harder 

 than that which was encountered with the preceding foot. 



