To find the force requisite to sustain a vehicle upon an inclined road (the effects of friction being neglected), divide the weight of the vehicle and its load by the inclined length of the road, the vertical rise of which is one foot, and the quotient is the force required.
To find the pressure of a vehicle against the surface of an inclined road, multiply the weight of the loaded vehicle by the horizontal length of the road; and divide the product by the inclined length of the same; the quotient is the pressure required.
The force with which a vehicle presses upon an inclined road is always less than its actual weight; the difference is so small that, unless the inclination is very steep, it may be taken equal to the weight of the loaded vehicle.
To find the resistance to traction in passing up or down an incline, ascertain the resistance on a. level road having the same surface as the incline, to which add, if the vehicle ascends, or subtract, if it descends, the force requisite to sustain it on the incline; the sum or difference, as the case may be, will express the resistance. .
Tractive Power and Gradients. The necessity for easy grades-is dependent upon the power of the horse to overcome the resistance to motion composed of the four forces, friction, collision, gravity, and the resistance of the air.
All estimates on the tractive power of horses must to a certain extent be vague, owing to the different strengths and speeds of animals of the same kind, as well as to the extent of their training to any • particular kind of work.
The draught or pull which a good average horse, weighing 1,200 pounds, can exert on a level, smooth road at a speed of 21 miles per hour is 100 pounds, equivalent to 22,000 foot-pounds per minute, or 13,200,000 foot-pounds per day of 10 hours.
The tractive power diminishes as the speed increases and, per haps, within certain limits, say from 4 to 4 miles per hour, nearly in inverse proportion to it. Thus the average tractive force of a horse, on a level, and actually pulling for 10 hours, may be assumed approximately as follows: Tractive Power of Horses at Different Velocities.
The work done by a horse is greatest when the velocity with which he moves is of the greatest velocity with which he can move when unloaded; and the force thus exerted is 0.45 of the utmost
force that he can exert at a dead pull.
The- traction power of a horse may be increased in about the same proportion as the time is diminished, so that when working from 5 to 10 hours, on a level, it will be about as shown in the following • table: Hours per day Traction (pounds) Hours per day Traction (pounds) 10 100 7 1461 9 1111 6 166 8 125 5 200 The tractive power of teams is about as follows 1 horse = 1 2 horses 0.95 X 2 = 1.90 3 0.85X 3 = 2.55 4 " 1 0.80X 4 = 3.20 Loss of Tractive Power. on Inclines. In ascending in clines a horse's power diminishes rapidly; a large portion of his strength is expended in overcoming the resistance of gravity due to his own weight and that of the load. Table 5 shows that as the steepness of the grade increases the efficiency of both the horse and the road surface diminishes; that the more of the horse's energy is expended in overcoming gravity the less remains to overcome the surface resistance.
Effects of Grades Upon the Load a Horse can Draw on Different Pavements.
Table 6 shows the gross load which an average horse, weighing 1,200 pounds, can draw on different kinds of road surfaces, on a level and on grades rising five and ten feet per one hundred feet.
The decrease in the load which a horse can draw upon an incline is not .due alone to gravity; it varies with the amount of foothold afforded by the road surface. The tangent of the angle of inclination should not be greater than the coefficient of tractional resistance; therefore it is evident that the smoother the road surface, the easier should be the grade. The smoother the surface the less the foothold, and consequently the load.
The loss of tractive power on inclines is greater than any inves tigation will show; for, besides the increase of draught caused by gravity, the power of the horse is much diminished by fatigue upon a long ascent, and even in greater ratio than man, owing to its anatom ical formation and great weight. Though a horse on a level is as strong as five men, on a grade of 15 per cent, it is less strong than three; for three men carrying each 100 pounds will ascend such a grade faster and with less fatigue than a horse with 300 pounds.