The curvature on any road cannot be adjusted to trains moving at different speeds.
66. The tractive power acts always tangent to the curve at the point where the engine is, and thus tends to pull the cars against the inner rail. The tangential force, generated by the motion of the cars, tends to keep the flanges of the wheels against the outer rail; and only when a just balance is made between the tractive and tangential forces, the wheel will run without impinging on either rail, (the wheel being properly coned). For these forces to balance, there must be a fixed ratio between the weight of a car and the speed, (not the weight of a train, as the shackling allows the cars to act nearly independently, some indeed rubbing hard for a moment against the rail, while the next car is working at ease). Whenever the right proportion is departed from, as it nearly always is, (and perhaps necessarily in some cases,) upon railroads, the wheels will rub against one rail or the other. Thus on any road where the speed on the same curve, or the radii of curvature under the same speed, differ, there must be loss of power, and dragging or pushing against the rails.
67. We are obliged to elevate the outer rail (see chapter XIII.), for the fastest trains, and the slower trains on such roads will therefore always drag against the inner rails. Thus in practice we generally find the inside of the outer rail most worn on passenger roads, and the inside of the inner rail upon chiefly freight roads.
68. It has been the practice of some engineers in equating for curvature, to add one fourth of a mile to the measured length for each 360° of curvature, disregarding the radius, as the length of circumference increases inversely as the degree of curvature.
69. Now in equating for grades, in doubling the power we do not double the expense of working. We however increase it more by curvature than we do by grades, because besides requiring double power, the wear and tear of cars and rails and all machinery is increased upon curves, which is not the case upon grades.
70. The analysis of expense (in Appendix F.) upon the New York system of roads, gives the following:—
| Locomotives, | 40 | per cent. |
| Cars, | 20 | per cent. |
| Way and works, | 15 | per cent. |
| or in all, | 75 | per cent. |
Now each 360° will be equal to 75
100 of one quarter of a mile, or 75
400 of a mile; whence the number of degrees which shall cause an expense equal to one straight and level mile, will be 1920°.
71. The number of degrees by Mr. McCallum’s estimate would be thus:—
The resistance upon a level being ten lbs. per ton, and that due to curves one half pound per ton, per degree per one hundred feet; the length of a 2° curve to equal one mile will be