Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

1
a = R
W;

and to find the number by which to equate, we have only to place the values of R and W in the formula. For example, let the speed be twenty miles per hour, the corresponding resistance is 10.3 lbs. per ton. W being one ton, or 2240 lbs., we have

1
a = R
W = 10.3
2240 = 1
218 of 5280, (the number of feet in one mile,)

1
218 of 5280 = 24 feet.

In the same manner we have

Speed, in miles, per hour.	Equating number.
15	22
20	24
30	32
40	41
50	53
60	67
100	155

Thus when we take the speed as thirty miles per hour, for each thirty-two feet rise we shall consume an amount of power sufficient to move the train one mile on a level. In descending, the grade instead of being an obstacle, becomes an aid; indeed the incline may be such as to move the trains independently of the steam power. Thus if on account of ascending grades we increase the equated length, so also in descending we must reduce the length. The amount of reduction is not, however, the reverse of the increase in ascending, as after thirty or forty feet any additional fall per mile instead of being an advantage is an evil; as too much gravity obliges us to run down grades with brakes on. Twenty-five feet per mile is sufficient to allow the train to roll down, and any more than this is of very little use. Therefore for every mile of grade descending at the rate of twenty-five feet per mile we may deduct one mile in equating, and for every mile of grade descending twelve and one half feet per mile deduct a proportional amount; but for any more fall per mile than twenty-five feet, no allowance should be made; i. e., if we descend at the rate of forty feet per mile, we may deduct one mile in equating for the twenty-five feet of fall, and throw aside the remaining fifteen feet.

55. This is a common method of equating for grades, and represents a length which is proportional to the power expended, but not proportional to the cost of working, as the ratios of power expended and cost of working under different conditions are very different, double power requiring only twenty per cent. more working capital. The above rules, therefore, require a correction.

The cost of working a power represented by unity being expressed by	100;
That of working a power 2 is expressed by	125;
That of working a power 3 is expressed by	150;
That of working a power 4 is expressed by	175;
That of working a power 5 is expressed by	200.
(See Appendix F.)

Now the resistance on a level being at a velocity of twenty miles per hour, 10.3 lbs. per ton by the formula