notebook. But if you measure only 1/2 inch, it means that the rail curves inward there. The midpoint of the
string is 1 inch minus 1/2 inch, or 1/2 inch, or 4/8 inch nearer the rail than are the ends of the string. Therefore,
you would enter -4 in your notebook, indicating a reverse bend of 1/2 inch.
Now that you have measured and recorded the ordinate at each station, you have finished the first phase
of your fieldwork. Next, you must take your notebook home or to the office and calculate how much you need to
move the track at each station to achieve a smooth curve. Columns 1 and 2 of figure 3.5 show the station
numbers and measured ordinates of a short curve.
For instructional purposes, the curve described in figure 3.5 has been purposely shortened and simplified;
in practice, you would rarely see one like it. A railway curve usually contains dozens if not hundreds of stations.
Remember, the longest in the United States is over 9 miles! A curve may be compound, that is, consisting of two
or more joined circular curves of different degree; or it may be reverse, curving first in one direction and then in
another. But the principles discussed apply to them all. With this method, you can line any curve if you work
carefully, check your figures at every opportunity, and adjust your results as often as necessary. The following
subparagraphs and annex A explain generally the use and evaluation of figures.
a. Annex A. The curve calculated in figure 3.5 is diagramed in annex A, sheet 1. Study that sheet as
you read the explanation of it. The solid line represents the track itself, while the broken lines are the 62-foot
string stretched from station to station. The curvature in the diagram is greatly increased, so that you can easily
see and compare the ordinates at each station, and so that the distortion of the curve is obvious. The actual curve
is so gentle that the largest measured ordinate is only 9/8 inch. However, a 200-ton locomotive at 60 mph (96
kmph) would slam into such a stretch with a great deal of force. Even such minor deviations in high-speed track
would cause an uncomfortable ride and high maintenance costs; therefore, the curve should be relined.
b. Analysis. You can see from the diagram that the curve should make a continuous turn to the right.
However, at Sta. 1 there is a slight bend to the left. In column 2 of figure 3.5, you see a negative ordinate listed
for that station, while all the others are positive. A negative ordinate always indicates such a wrong or