HIGHWAY CONSTRUCTION 



The 

 is equal to 



resistance clue to gravity on any incline in pounds per ton 



2000 



rate of grade 



The following table shows the resistance due to gravity on dif- 

 ferent grades. 



TABLE 2. 

 Resistance Due to Gravity on Different Inclinations. 



Grade 1 in 20 30 40 50 00 70 SO 90 100 200 300 400 



Rise in feet per mile . . .264 176 132 105 88 75 66 58 52 26 17 13 

 Resistance in Ib. per ton .112 74 -J 56 45 38 32 28 25 22 1 1 j 7 J 5-i 

 The additional resistance caused by inclines may be investigated 

 in the following manner: Suppose the whole weight to be borne on 

 one pair of wheels, and that the tractive force is applied in a direction 

 parallel to the surface of the road. 



Let AB in Fig. 3 represent a portion of the inclined road, C 

 being a vehicle just sustained in its position by a force acting in the 

 direction CD. It is evident that the vehicle is kept in its position 

 by three forces; namely, by its own weight W acting in the vertical 

 direction C F, by the force F applied in the direction C D parallel 

 to the surface of the road, and by the pressure P which the vehicle 

 exerts against the surface of the road acting in the direction C E 



perpendicular to same. To 

 determine the relative magni- 

 tude of these three forces, 

 draw a horizontal line A G 

 and the vertical one B G; 

 then, since the two lines C F 

 and B G are parallel and 

 are both cut by the line A B, 

 they must make the two 

 angles . C F E and A B G 



equal; also the two angles C E F and A G B are equal; therefore, the 

 remaining angles F C E and BAG are equal, and the two triangles 

 C F E and A B G are similar. And as the three sides of the former 

 are proportional to the three forces by which' the vehicle is sustained, 

 so also are the three sides of the latter; namely, AB or the length 

 of the road is proportional to W, or the weight of the vehicle; B G, 



Pig. 3. 



