American Rural Highways

by T. R. Agg

where

f_r = rolling resistance of road surface.
f_i = resistance due to internal friction in the vehicle.
f_p = resistance due to impact of the road surface.
f_a = resistance due to air.
f_g = resistance due to grade, which is positive when ascending and negative when descending.

All of the above in pounds per ton of 2000 lbs.

Let T = the tractive effort applied to the vehicle by any means.

T >= must be greater than F in order to move the vehicle.

By an inspection of (1), it will be seen that for a given vehicle and any type of road surface, all terms are constant except f_a and f_g. f_a varies as the speed of the vehicle and the driver can materially decrease f_a by reducing speed. f_g varies with the rate of grade. For any vehicle loaded for satisfactory operation on a level road with the power available, the limiting condition is the factor f_g. If the load is such as barely to permit motion on a level road, any hill will stall the vehicle. Therefore, in practice the load is always so adjusted that there is an excess of power on a level road. If draft animals are employed the load is usually about one fourth of that which the animals could actually move by their maximum effort for a short period. With motor vehicles, the excess power is provided for by gearing.

If it be assured a load of convenient size is being moved on a level road by draft animals, there is a limit to the rate of grade up which the load can be drawn by the maximum effort of the animals.

Tests indicate that the horse can pull at a speed of 2½ miles per hour, an amount equal to 1/8 to 1/10 of its weight, and for short intervals can pull ¾ of its weight. The maximum effort possible is therefore six times the average pull, but this is possible for only short intervals. A very short steep hill would afford a condition where such effort would be utilized. But for hills of any length, that is, one hundred feet or more but not to exceed five hundred feet, it is safe to count on the draft animal pulling three times his normal pulling power for sustained effort.

The limiting grade for the horse drawn vehicle is therefore one requiring, to overcome the effect of grade, or f_g, a pull in excess of three times that exerted on the level.

A team of draft animals weighing 1800 lbs. each could exert a continuous pull of about 1/10 of their weight or 360 lbs. If it be assumed that the character of the vehicle and the road surface is such that f_r + f_i + f_p + f_a = 100 lbs. per gross ton on a level section of road, then the gross load for the team would be 3.6 tons. The same team could for a short time exert an additional pull of three times 360 lbs. or 1080 lbs. For each 1 per cent of grade a pull of 20 lbs. per ton would be required or f_g for the 3.6 tons load would be 72 lbs. for each per cent of grade. At that rate, the limiting grade for the team would be fifteen per cent.