4,000-ton trains around the curve, the grade throughout the length of the curve must be decreased. The amount to
reduce it is a problem of engineering beyond the scope of this text. Curves located on grades that have been
reduced in this way are said to be compensated.
3.5.
COMPUTING CURVATURE
The sharpness of a curve depends directly on the length of its
radius.
Long radii result in light curvature; short radii, in sharp. Compare the
sharpness of the curves in the accompanying sketch. Each of the three
has
the same number of degrees; that is, each represents the same
portion of an entire circle. However, the curve with the short,
broken line radii is much sharper than the other two. At the same
time, the curve with the dot-dash radii is sharper than the one with
the long, solid-line radii. Most railroads, subways, and elevated lines
in
countries other than the United States and Great Britain designate the
sharpness of a curve by specifying the radius. In those two countries, it
is given
in degree of curvature.
The method of computing the degree of curvature of track is shown
in the two
drawings in figure 3.2. A chord, 100 feet long, is placed so that the two ends
touch
the
curved track, on the inner side of the outside rail, at points A. A central angle is
formed by the
two radii running to the center, C. The degree of curvature in the drawing at the
left in figure 3.2 is
9 degrees, a much sharper curve than would be found on a main line. The degree of
curvature in
the
drawing at the right is 20 degrees, a much sharper curve than the 9-degree one. The dotted lines at d represent
the same portion of a circle as does the arc representing the track between points A. Since there are 360 degrees
in a circle, the 9-degree curvature illustrated represents 1/40th of a circle (360) and the 20-degree curvature
illustrated
9
represents 1/18 of a circle (360).
20
64
Previous Page
