MOTIVE POWER AND ROLLING STOCK 347 
of single-expansion rod locomotives with a piston speed not 
exceeding 200 feet per minute is as follows: 
^ d'X L X .85 p, 
D 
when T represents the tractive force, 
d represents the diameter of the cylinder in inches, 
L represents the length of piston stroke in inches, 
.85 p represents 85 per cent of the boiler pressure,^ 
D represents the diameter of the driving wheel in inches. 
As the speed increases the tractive force decreases because the 
mean effective pressure in the cylinders falls and friction also 
increases. 
Resistance to Gravity. — The resistance to gravity increases in 
exact proportion to the grade and is 20 pounds per ton of 2000 
pounds for each 1 per cent rise in grade; e.g., for a 0.5 per cent 
grade it is 10 pounds per ton and for a 4 per cent grade it is 80 
pounds per ton. 
Resistance due to Friction. — The resistance due to friction 
varies with the character and condition of the roadbed and the 
rolling stock. 
The resistance of the flange friction of wooden rails is about 
twice that of steel rails. Poorly laid or crooked rails and over- 
loading increase the rolling friction, which is also greater in cold 
weather than in warm and greater for empty cars than for loaded 
ones. 
Logging cars of good construction, and with well-oiled bearings 
should have a frictional resistance of from 20 to 25 pounds per 
ton of weight handled. 
The frictional resistance on curves s extremely variable be- 
cause it is governed by numerous factors, among which are the 
degree of curvature, length of the wheel base of locomotives and 
cars, elevation of the outer rail, speed, condition of rolling stock 
and track, length of train, and length of the curved section. 
Frictional resistance is partially overcome by increasing the 
width of track on curves -^V inch for each 2\ degrees of curvature, 
and also by coning the face of the car wheels so that the greatest 
diameter is next the flange. When crowded against the rail the 
' This has been found by practical test to be the average effective pressure 
in the cylinder. 
