1568
THE Oil Y AND PRACTICE OF ENGINEERING.
Book II
railway, demand from the civil engineer very considerable attention. In the Treatise onLocomotive Engines by Chevalier F. M. G. De Pambour, the author, after stating thatinclined planes are a great obstacle to the motion on railways, supposes if a train of 100tons be drawn by an engine on a level, the friction of the carriages will produce a resistanceof 8 lbs. per ton, and consequently the power required of the engine will be 800 lbs. Hethen supposes the same train ascending an inclined plane at ^; on that plane, besides theresistance owing to the friction of the waggons, a fresh resistance occurs, which is the gravityof the total mass in motion on the plane : that gravity is the force by virtue of which thetrain would roll back if it were not retained, and is equal to the weight of the mass, dividedby the number indicating the inclination of the plane. If therefore, in this case, the load of100 tons be drawn by an engine weighing ten tons, the total mass placed on the inclined
plane will be 110 tons, or 246*400 pounds ; thus its gravity on the inclined plane at will
be lbs. =2*464 lbs. The surplus of traction required of the engine on account of
that circumstance is therefore 2*464 lbs.; and as on a level one ton load is represented byeight pounds traction, 2*464 lbs. represents the resistance that would be offered by a loadof 308 tons on a level. The engine which before drew 100 tons must now draw 408 tons,or must exert the same effort as if it drew 408 tons on a level: upon this data the authorabove quoted has calculated the resistance on inclined planes; some writers have given theangle of repose as 1 in 280; and the Irish Railway Commissioners have stated that at theangle of 1 in 140 a velocity is acquired which has a useful practical effect.
On the London and Birmingham line of railway, where the plane for a considerablelength was 1 in 75, the trains attained a velocity of thirty miles an hour. A gradient of1 foot per mile is equal to a rise of 1 in 5280 ; of 10 feet, to 1 in 528: of 20 feet, to 1 in264, and tables are calculated showing the inclination up to 60 feet, or 1 in 88 ; and othertables have been drawn up, to show the lengths of equivalent horizontal lines to gradients,from 1 in 90 to 1 in 1500
Ascending.
Descending.
Mean.
Gradient.
Ascending.
Descending.
Mean.
1 in 90
2-66
1-00
1 *83
1 in 200
1-75
•83
1-29
— 95
2-58
1*00
1*79
— 2S0
1-60
•83
1-21
— 100
2-50
1*00
1-75
— 300
1*50
•83
1*16
— 110
2-36
100
1*68
— 350
1 *43
•83
1*13
— 120
2-25
1*00
1*62
— 400
1-37
•83
1*10
—. 130
2-15
1*00
1-57
— 500
1*30
•83
1*06
— 140
2 07
1-00
1-53
— 750
1*20
■83
1-01
__ 160
1.94
•83
1*43
— 1000
1-15
•85
1 -00
— 180
1*83
•83
1-33
— 1500
1*10
*90
1*00
To calculate the resistance of the trains on an inclined plane, we have in the work beforealluded to a very useful table for engines weighing from 8 to 12 tons, with the load theydraw. Where the engine weighs 8 tons, the following table may apply.
Equivalent Load on a Level, the inclination of the Plane being —■
Load in Tons.
333
*03
303
533
T35
T03
25
44
48
56
71
87
117
50
83
91
105
131
158
212
75
122
133
153
191
230
307
100
161
176
201
251
302
402
125
200
218-
249
311
373
497
150
239
261
298
371
445
592
By such a table we can observe the resistance of the trains on inclined planes.
Width between the Rails _On the first establishment of railways, the clear width between
the rails was fixed by parliament at 4 feet 8^ inches, which is that of the Liverpool andManchester line; but since the year 1836 this has been optional with the engineer, andthe Great Western is 7 feet between the rails. The width between the two lines of railwayis ordinarily the same as that between the rails ; but upon the London and Birmingham line it is 6 feet, though, for all practical purposes, 4 feet 8J inches has been found sufficient.A proper width outside the rails is, however, exceedingly important, in order to obtain therequisite stability or firmness in the embankments for fixing the blocks and rails.
Whether the broad or narrow gauge will eventually prevail, it is difficult to decide; butcertainly the latter is the most economical in construction, and, if equally answering the