are very few localities where the rails on any line of railway can be laid perfectly level or horizontal for more than comparatively short distances. By far the greater portion have to be laid on inclined planes of varying rates of inclination to suit the general formation of the district traversed, and the circumstances of the line to be constructed.
The degree, or rate of inclination, of these inclined planes, or gradients, may be expressed in various ways. A very general method is to state the number of feet, metres, etc., which can be measured along the gradient before an increased rise or fall of one foot or metre, etc., is obtained. Thus a gradient of 1 in 200 signifies a rise or fall of 1 foot in 200 feet, or 1 metre in 200 metres.
Sometimes the rate of inclination is expressed by stating the number of feet of rise or fall in a mile. In this way a gradient would be described as falling at the rate of 30 feet in a mile, rising at the rate of 20 feet in a mile, etc. Twenty feet to a mile is equal to 1 in 264.
Another method is to give the percentage of rise or fall. In this way the inclination would be expressed as a 1 per cent. gradient, 2 per cent. gradient, ½ per cent. gradient, etc., which for comparison would signify 1 in 100, 1 in 50, and 1 in 200 respectively.
The gradients of a railway most materially influence its facility and cost of working, and every effort should be used to make them as easy as possible consistent with the prospect of the line.
Steep gradients signify heavy locomotives, increased cost of motive-power, reduced speed, and light loads.
The following tabulated memoranda show the approximate loads, exclusive of engine and tender, which can be hauled on the level and on certain inclines at various speeds by engines of the quoted capacities and steam admissions. A medium-sized, ordinary type of passenger and goods engine has been selected for each of the examples. The working of the passenger engine and train is assumed to be under favourable circumstances, with fine weather, fairly straight line, first-class permanent way, modern rolling-stock with oil axle-boxes and perfect lubrication, and all the conditions most suitable to ensure the least resistance to the moving load. For the goods engine and train a greater resistance per ton of load is assumed, as the goods trucks are never so perfect or easy in the running as the passenger carriages. A certain amount of side wind is taken into consideration, and also an allowance for moderately sharp curves, the object being to indicate what may be looked upon as fair, average, workable loads.
The loads for engines of larger or smaller dimensions, or higher or lower pressures, may be obtained by working out the proportion between the tractive force put down in any of the columns of the tabulated memoranda and the ascertained tractive force of any other engine under the same conditions of cut-off and speed.
| Passenger Engine. Six wheels, driving and trailing wheels coupled, 6 ft. 6 ins. diameter. Cylinders, 17 ft. × 24 ft. Locked-down pressure on safety-valves, 140 lbs. per square inch. Assumed pressure at cylinders, 120 lbs. per square inch. Weight of engine 39 tons. ” tender 24 tons. 000000000000 63 tons. | Goods Engine. Six wheels, all coupled, 4 ft. 6 ins. diameter. Cylinders, 17 ft. × 24 ft. Locked-down pressure on safety-valves, 140 lbs. per square inch. Assumed pressure at cylinders, 120 lbs. per square inch. Weight of engine 34 tons. ” tender 24 tons. 000000000000 58 tons. | |||||||
| Assumed cut-off | ¼ | ⅓ | ½ | ¾ | ¼ | ⅓ | ½ | ¾ |
| ” mean effective pressure, lbs. | 45 | 56 | 76 | 100 | 45 | 56 | 76 | 100 |
| ” tractive force, lbs. | 4000 | 4979 | 6758 | 8892 | 5780 | 7192 | 9760 | 12844 |
| Speed in miles per hour | 60 | 40 | 30 | 15 | 40 | 30 | 20 | 15 |
| Tons. | Tons. | Tons. | Tons. | Tons. | Tons. | Tons. | Tons. | |
| Level | 97 | 230 | 447 | 892 | 213 | 358 | 623 | 907 |
| 1 in 1000 | 84 | 196 | 373 | 707 | 187 | 310 | 532 | 768 |
| ” 800 | 81 | 188 | 358 | 671 | 181 | 299 | 512 | 739 |
| ” 600 | 76 | 177 | 335 | 618 | 172 | 285 | 482 | 695 |
| ” 400 | 68 | 157 | 296 | 533 | 157 | 257 | 432 | 621 |
| ” 300 | 60 | 141 | 263 | 467 | 143 | 233 | 390 | 560 |
| ” 250 | 55 | 129 | 241 | 424 | 133 | 216 | 361 | 519 |
| ” 200 | 47 | 114 | 213 | 372 | 120 | 195 | 324 | 467 |
| ” 150 | 37 | 93 | 177 | 304 | 101 | 165 | 276 | 397 |
| ” 100 | 21 | 63 | 126 | 217 | ||||