TRANSPORTATION ON LAND BY VEH1CLES:-THE ROADS 



39 



The coefficient of friction on roads is generally given (in per cent of the pressure of the load moved) for 



Loose sand 



Fresh earth 



Common dirl 



Gravel 



Macadam ... 



Pavement ... 



Iron shod sleds on hard snow 



Railroad 



25 " approximately 

 12"5"o approximately 

 10 7o approximately 

 5 7n approximately 

 3'3"'i, approximately 

 r4"/„ approximately 

 3'3 " approximately 



or 500 lbs. per ton 



or 250 lbs. per ton 



or 200 lbs. per ton 



or 100 lbs. per ton 



or 66 lbs. per ton 



or 28 lbs. per ton 



or 66 lbs. per ton 



or 6 lbs. per ton 



0"3"o approximately; 



The coefficient of friction within the hub is inversely proportioned to the square root of the diameter 

 of the wheel. Within reasonable limits, the size of the wheel may be disregarded. 



In railroads, there must be considered the combined friction of the journals and of the wheel flanges 

 against the rails, which depends, aside from curvatures, on quality of the track and of rolling stock. It is 

 at least 5 pounds per ton; it amounts to 6' > pounds for first class equipment; to 20-40 pounds for bad 

 equipment; and in extreme cases it rises to 100 pounds per ton. 



In addition, the frictional resistance depends on the speed, to a certain extent. This additional resistance 



equals, in pounds per ton, approximately 3 + ^ , wherein S represents the speed. At a speed of 



36 miles, for example, the frictional resistance is increased by 9 pounds per ton. The geared locomotive, 

 being slow of speed, encounters little speed resistance. 



(D) GRAVITY RESISTANCE ON ROADS. 



I. The interdependence between degrees, sin and tg of grade is the following: — 



grade 



1/ 



'2 

 1 



IV2 



2 



2V2 

 3 



3V2 

 4 



47. 



sin 

 0-87 

 1-75 

 2-62 

 3-49 

 4-36 

 5-23 

 6-11 

 6-98 

 7-85 



Within reasonable limits (up to 8") sin and tg are almost equal. 



Grade is expressed either in degrees or in per cent. The percentage is equal to the tangent of the 

 angle forming the grade. The ratio between percentage P and angle A is, for grades not exceeding 

 15 degrees, surprisingly constant, amounting to 0,0175. 



P 

 100 



A X 0-0175 



II. The mileage of the shortest route joining two points of different elevation is inversely proportioned 



to the percentage of the grade. If distance and difference in elevation are approximately known from a 



map, then the average percentage on an airline road amounts to 100 times the difference in elevation 



divided by distance. 



,^„ difference in elevation 



p = 100 



distance ^ 



If the percentage thus obtained is too heavy for the purpose, counter curves (zigzags, switchbacks) 

 are required, with a view to increasing the distance. 



