Experiments to determine the tractive resistance due to the surface vary considerably, for it is impossible to secure like conditions of surface smoothness and cleanliness, to say nothing of hardness. The tractive resistance will with some materials vary with the temperature. That of sheet asphalt, for example, may be twice as much in summer as in winter. The tractive resistance may not be directly proportional to the load although it is customary to express it in pounds per ton. It is conceivable that a heavy load because it sinks into the road crust may require a greater number of pounds to move it than a light load that does not greatly sink in. This also leads to the effect of width of tire and diameter of wheel. Many experiments have shown the tractive force to be less with wide than narrow tires, due, no doubt, to the unequal sinking into the road crust. Likewise wheels ought, for the same reason, to show less resistance for large diameters; in fact some engineers give it as varying inversely as the diameter of the wheel. The results of tests, while varying much, show in a general way, the direct pull necessary to draw a load at slow speed on the level in well-lubricated wagons to be approximately as follows: ----------------------------------------+------------+--------------- | |μ = coefficient |Lbs. per Ton|of Resistance ----------------------------------------+------------+--------------- Upon Steel rails | 10 | ¹⁄₂₀₀ Sheet asphalt, good condition | 20 | ¹⁄₁₀₀ Asphaltic macadam or concrete, good| | condition | 20 | ¹⁄₁₀₀ Concrete, good condition | 20 | ¹⁄₁₀₀ Brick, good condition | 20 | ¹⁄₁₀₀ Broken stone water-bound macadam, | | good condition | 30 | ³⁄₂₀₀ Gravel, good condition | 30 | ³⁄₂₀₀ Sand clay, good condition | 60 | ³⁄₁₀₀ Earth, best condition | 67 | ¹⁄₃₀ Earth, medium condition | 100 | ¹⁄₂₀ Earth, poor condition | 300 | ³⁄₂₀ ----------------------------------------+------------+--------------- =Resistance Due to Grade.=--The resistance due to grade is just as marked as that due to surface. The work necessary to draw a load up an inclined plane is the same as that of drawing on a level along the base of the plane and lifting it directly up to the height of the plane. A mathematical analysis[182] based upon this fact leads to the formulas: For a horse-drawn load, _t_ - _g_ _L_ = ---------_H_. (1) μ + _g_ For a tractor, _P_ _L_ = ------- - _T_. (2) μ + _g_ For an automobile or truck,