Simple Curve Layout
To lay out the simple curve (arc definition) justcomputed above, you should usually use the procedure that follows.
1. With the instrument placed at thePI, the instrumentman sights on the preceding PI or at a distant station and keeps the chainman on the line while the tangent distance is measured to locate the PC. After the PC has been staked out, the instrumentman then trains the instrument on the forward PI to locate the PT.
2. The instrumentman then sets up at thePC and measures the angle from the PI to the PT. This angle should be equal to one half of the I angle; if it is not, either the PC or the PT has been located in the wrong position.
3. With the first deflection angle (3°10’) set on theplates, the instrumentman keeps the chainman on line as the first subchord distance (42.18 feet) is measured from the PC.
4. Without touching the lower motion screw, the instrumentman sets the second deflection angle (6°55’) on the plates. The chainman measures the chord from the previous station while the instrumentman keeps the head chainman on line.
5. The crew stakes out the succeeding stations in the same manner. If the work is done correctly, the last deflection angle will point on thePT. That distance will be the subchord length (7.79 feet) from the last station before the PT.
When it is impossible to stake out the entire curve from thePC, a modified method of the procedure described above is used. Stake out the curve as far as possible from the PC. If a station cannot be seen from the PC for some reason, move the transit forward and set up over a station along the curve. Pick a station for a backsight and set the deflection angle for that station on the plates. Sight on this station with the telescope in the reverse position. Plunge the telescope and set
Figure 11-11.—Inaccessible PI.
the remainder of the stations in the same way as you would if the transit was set over thePC. If the setup in the curve has been made but the next stake cannot be set because of obstructions, the curve can be backed in. To back in a curve, occupy the PT. Sight on the PI and set one half of the I angle of the plates. The transit is now oriented so that, if the PC is observed, the plates will read zero, which is the deflection angle shown in the notes for that station. The curve stakes can then be set in the same order shown in the notes or in the reverse order. Remember to use the deflection angles and chords from the top of the column or from the bottom of the column. Although the back-in method has been set up as a way to avoid obstructions, it is also very widely used as a method for laying out curves. The method is to proceed to the approximate midpoint of the curve by laying out the deflection angles and chords from the PC and then laying out the remainder of the curve from the PT. If this method is used, any error in the curve is in the center where it is less noticeable.
So far in our discussions, we have begun staking out curves by setting up the transit at thePI. But whatPI is inaccessible? This condition is illustrated in figure 11-11. In this situation, you locate the curve elements using the following steps:
1. As shown in figure 11-11, mark two intervisiblepoints A and B on the tangents so that line AB clears the obstacle.
2. Measure anglesa and b by setting up at both A and B.
3. Measure the distanceAB.
4. Compute inaccessible distanceAV and BV using the formulas given in figure 11-11.
5. Determine the tangent distance from thePI to the PC on the basis of the degree of curve or other given limiting factor.
6. Locate thePC at a distance T minus AV from the point A and the PT at a distance T minus BV from point B.
Figure 11-12 shows field notes for the curve wesolved and staked out above. By now you should be
Figure 11-12.—Field notes for laying out a simple curve.
familiar enough with field notes to preclude a completediscussion of everything shown in these notes. You should notice, however, that the stations are entered in reverse order (bottom to top). In this manner the data is presented as it appears in the field when you are sighting ahead on the line. This same practice applies to the sketch shown on the right-hand page of the field notes.
For information about other situations involving inaccessible points or the uses of external and middle ordinate distance, spiral transitions, and other types of horizontal curves, study books such as those mentioned at the beginning of this chapter.