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.

3.21.

EVALUATING FIGURES

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