reverse bend. When it is not designed into a curve, it is called a dogleg. At Sta. 8, the diagram shows another
dogleg. In column 2, the measured ordinates decrease from Sta. 5 through Sta. 7, increase at Sta. 8, and then
continue to decrease. If these faults were corrected, it would be a fairly smooth curve. The stringline calculation
shows you how to correct them.
c. Selecting new ordinates. Next, you must select an ordinate for each station of the new curve. Since
the ordinates are smaller near each tangent, it should be a spiraled curve. This means that the new ordinates
should increase by regular amounts to a maximum, remain constant for several stations on the circular part of the
curve, and then decrease to zero at about the same rate they increased. One thing limits you at this point: the sum
of the proposed ordinates must always equal the sum of the measured ordinates. Note that columns 2 and 3 of
figure 3.5 each total 36. This principle gives you a chance to check your work; if they are not equal, the proposed
ordinates must be revised. By looking at the measured ordinates, you can see that there are 10 stations on the
curve, but that stations 0 and 9 are on the tangents and can have no ordinates, while stations 1 and 8 are at the
ends of the tangents and will have very small ordinates. If the curve is spiraled, the ordinates at stations 2 and 7
will be less than those on the circular part of the curve. Therefore, most of the curvature will be at stations 3
through 6 where the curve is circular.
You may have a track chart, similar to the one in annex C, which shows what the curvature should be. If
you do, you can simply change degrees to inches--1 degree equals 1 inch, convert the inches to eighths, and enter
the result at each of those stations. If you don't, you usually take the average ordinate on the circular part of the
curve. Here, for stations 3 through 6, the ordinates are 7, 7, 9, and 6, a total of 29 and an average of more than 7.
But if you use an ordinate of 7 at each of the four stations, they total 28, while the sum of proposed ordinates can
be only 36. This leaves only 8, or 4 for each of the two spirals located on either end of the curve. So perhaps 7 is
too large; try 6 for each of the ordinates on the curve. Then the total is 24, and the spirals have 6 each. Since
there are two stations on each spiral, values of 2 and 4 provide a regularly increasing curve to full curvature of 6.
Therefore, in column 3 of figure 3.5, you enter these figures--2, 4, 6, 6, 6, 6, 4, 2. Sometimes, on long curves, it
is necessary to try three or four different spirals before you get one that fits, but here it was easy.
d. Calculating errors. The difference between the measured and the proposed ordinate is the error at a
station. If the
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