Class B. Rise and fall on grades so steep as to require either the holding back of the load by the team or the application of brakes.
Class C. Rise and fall on the maximum grade.
An example of the first class of rise and fall is shown in The team is relieved on the down grade an amount exactly equal to the extra tax upon the up grade, and the only effect upon the team is that the effort is concentrated on the up grade instead of being uniformly distributed over the road; but as the slope is assumed to be equal to or less than the angle of repose, the maximum effort is equal to or less than twice the normal. If the grade line rises above the level instead of dipping below it, the case is not changed except that the rise is a little more unfavor ble, since the team has no relief before the increase in effort is required. Therefore this class of rise and fall costs little or nothing.
In the preceding examples, a change of velocity would alter the power required at any particular instant; but in wagon-road traffic the speed is always small and consequently the effect of variations of speed are quite small, and may be entirely neglected. On rail roads a variation of the velocity materially affects the cost of rise and fall.
If the grade is greater than the angle of repose, the team in de scending must hold back the load, which is lost energy, or brakes must be applied, which tend to destroy the road; and in ascending, the demand upon the team is greater than twice the normal. There fore in either case this class of rise and fall adds to the cost of oper ating the road.
If the grade is the maximum, it may be sufficient to limit the amount of the load a team may draw over the more level portions of the road, and therefore greatly add to the cost of transportation. As a chain is no stronger than its weakest link, so a road is no better than its steepest grade.
Cost of Rise and Fall. What does it cost to develop the power required to haul a load up a grade less than the grade of repose? In other words, what is the cost of Class A rise and fall? The cost of transportation consists chiefly of the cost of driving, of feed, and of the wear and tear on the team. Usually the cost of driving will be approximately half of the total cost of transportation ; and as a team can draw a load up the grade of repose at practically the same speed, at least for short stretches, as upon the level, there will usually be no material increase in the cost of driving. Even
though the team may travel slower because of the grade, the cost of the increased time can scarcely be computed because of the im possibility of determining the value of fractions of time for other purposes. The cost of feed and of wear and tear on the team must vary approximately as the total power developed. Therefore the conclusion may be drawn that rise and fall belonging to Class A will not add appreciably to the cost of transportation. This conclusion is corroborated by the popular belief that a gently undulating road is less fatiguing to horses than one which is perfectly level. The argument in support of this belief is that alternations of ascents, descents, and levels call into play different muscles, allowing some to rest while others are exerted, and thus relieving each in turn. The argument is false, and probably originated in the prejudices of man in his quest for variety, rather than in the anatomy of the horse; but the above theory would not have gained its wide popularity if a gently undulating road were appreciably more fatiguing to a horse than a perfectly level one. A perfectly level road is the best for ease of transportation.
If the grade is steeper or longer than that up which the team can draw the normal load by exerting twice the tractive power re quired on the level, i. e., if the rise and fall belongs to Class C, then the grade has the effect of limiting the load that can be drawn over the level portion of the road, and consequently increases the cost of transportation. The load which a team can draw up any grade can be approximately computed as in § 65. If the load that can be drawn up any particular grade is, for example, three fourths of normal load on the level; then it will cost as much to haul three fourths of a load with this grade as a full load without the grade. If the cost with a grade less than the maximum is 10 cents per ton- .