Grade Resistances. — Tractive resistance due to grade is independent of the nature of the road surface or of the size of the wheels. It is equal to the load multiplied by the sine of the angle made by the grade with the hor izontal. Thus in Fig. 2 the tractive force P, due to the grade, is the force necessary to pre vent the wheel from rolling down the slope under the action of the weight W, or it is the component of W parallel to the slope ac.
Grades are ordinarily expressed in terms of rise or fall in feet per hundred, or as percentage of horizontal distance.
For all ordinary cases of small inclinations ab is approximately equal to ac, and we may take or the tractive force necessary to overcome any grade equals the load multiplied by the percentage of grade.
The total tractive force necessary to haul a load up an inclined road equals the sum of the force necessary to haul the load upon the same surface when level and the force necessary to overcome the grade resistance. Thus, if we wish to find the tractive effort necessary to haul a load of 2 tons up a grade of 3 ft. in too over a
good macadam road. Taking the resistance of the road surface when level at 6o lbs. per ton, we have for the total resistance In going down the grade, the force due to grade becomes a propelling force, and the tractive effort required is the difference between the surface resist ance and grade force. In case the grade force be the greater, the resulting tractive force becomes negative, or it will be necessary to apply the force as a resistance to prevent acceleration of the velocity in the descent.
The angle for which the tractive force required for a given surface equals the grade resistance is called the Angle of Repose for that surface. In the case given above, 2 X 6o — 4000 X o = o, or the angle of repose for a surface whose level resistance is 6o lbs. per ton is a 3 per cent grade. If a vehicle were left standing upon that inclination, it should remain standing with the forces just balanced. If it were started down the grade, it should continue to move at a uniform rate, without the application of any other force.