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

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