Equation (3) indicates that the load, including its own weight, that a truck or an automobile can draw varies directly as the horse-power exerted effectively, and inversely as the velocity. Also it decreases as the coefficient of road resistance, μ, and the gradient g increases.
The resistance coefficient, μ may include axle or internal resistance of the vehicle plus road surface resistance plus air resistance. The axle resistance is nearly a constant, the road resistance likewise, but the air resistance depends upon the speed v, varying approximately as the square of the velocity. W. S. James, in the Journal of the Society of Automotive Engineers, June, 1921, uses the formula
F = CAV2
| where | F | = | the wind force in pounds; |
| C | = | a constant, varies from .003 to .004; | |
| A | = | frontal area of automobile in square feet approximately 26; | |
| V | = | velocity in miles per hour. |
His researches show that the available engine effort P of equation (3) or horse power h is not quite constant but varies with the speed. His table follows:
| Car Speed m.p.h. | Available Engine Effort Per 1000 lb. of Car Weight, Lbs. | Air Resistance Per 1000 lb. of Car Weight, Lbs. |
|---|---|---|
| 15 | 107.3 | 4.9 |
| 16 | 105.2 | 6.8 |
| 20 | 107.6 | 8.8 |
| 25 | 106.0 | 13.4 |
| 30 | 103.9 | 19.2 |
| 35 | 101.2 | 26.0 |
| 40 | 98.0 | 34.1 |
| 45 | 94.1 | 43.4 |
| 50 | 86.8 | 53.8 |
Returning to Equation (3) which has been plotted in two different ways on [page 260], it may be seen that the load that can be hauled up a grade decreases with the per cent of grade very rapidly for the roads having a small coefficient of resistance and very much less rapidly for larger resistances. For example, on steel rails, resistance 10 pounds per ton, μ = 1⁄200, a 1 per cent grade reduces the load to one-third the load that may be hauled on the level, and a 5 per cent grade reduces it to less than one-tenth of the same load. With a good asphalt, brick or concrete road, resistance 20 pounds per ton, μ = 1⁄100, a 1 per cent grade reduces the load to one-half, while a 5 per cent grade reduces it to about one-sixth the load that can be drawn on a level road. While for an earth road in bad condition or a dry sand road, 300 pounds per ton resistance, μ = 3⁄20, a five per cent grade only reduces the level grade load by one-fourth. This shows clearly that the better the road surface the less the grade must be in order to benefit by it. The plots on page 260 show the same thing in different ways, and also that the maximum load that can be hauled with a given force at a constant speed is greater, no matter what the grade, on the better types of roads than on the poorer, but that the very great advantages due to hard roads come with the better type of roads. Incidentally this plot shows that the load that may be hauled, other things being equal, on steel tracks, is very much greater than that that can be hauled on the best hard surfaced road with same power, therefore it will never be possible to haul loads on highways as cheaply as on railways unless the operating expenses on the highways can be made materially less than on railways.
Graphical representation of the effect of grade on the load that can be drawn.
