Terrain Restrictions

To solve a simple curve, the surveyor must know three parts. Normally, these will be the PI, I angle, and degree of curve. Sometimes, however, the terrain features limit the size of various elements of the curve. If this happens, the surveyor must determine the degree of curve from the limiting factor.

Inaccessible PI
Under certain conditions, it may be impossible or impractical to occupy the PI. In this case, the surveyor locates the curve elements by using the following steps (figure 6).

1. Mark two intervisible points A and B, one on each of the tangents, so that line AB (a random line connecting the tangents) will clear the obstruction.
2. Measure angles a and b by setting up at both A and B.
3. Measure the distance AB.
4. Compute inaccessible distances AV and BV as follows:
5. Determine the tangent distance from the PI to the PC on the basis of the degree of curve or other given limiting factor.
6. Locate the PC at a distance T minus AV from the point A and the PT at distance T minus BV from point B.
7. Proceed with the curve computation and layout.

Inaccessible PC
When the PC is inaccessible, as illustrated in figure 7, and both the PI and PT are set and readily accessible, the surveyor must establish the location of an offset station at the PC.

1. Place the instrument on the PT and back the curve in as far as possible.
2. Select one of the stations (for example, “P”) on the curve, so that a line PQ, parallel to the tangent line AV, will clear the obstacle at the PC.
3. Compute and record the length of line PW so that point W is on the tangent line AV and line PW is perpendicular to the tangent. The length of line PW = R (l – Cos dp), where dp is that portion of the central angle subtended by AP and equal to two times the deflection angle of P.
4. Establish point W on the tangent line by setting the instrument at the PI and laying off angle V (V = 180° – I). This sights the instrument along the tangent AV. Swing a tape using the computed length of line PW and the line of sight to set point W.
5. Measure and record the length of line VW along the tangent.
6. Place the instrument at point P. Backsight point W and lay off a 90-degree angle to sight along line PQ, parallel to AV.
7. Measure along this line of sight to a point Q beyond the obstacle. Set point Q, and record the distance PQ.
8. Place the instrument at point Q, backsight P, and lay off a 90-degree angle to sight along line QS. Measure, along this line of sight, a distance QS equals PW, and set point S. Note that the station number of point S = PI – (line VW + line PQ).
9. Set an offset PC at point Y by measuring from point Q toward point P a distance equal to the station of the PC minus station S. To set the PC after the obstacle has been removed, place the instrument at point Y, backsight point Q, lay off a 90-degree angle and a distance from Y to the PC equal to line PW and QS. Carefully set reference points for points Q, S, Y, and W to insure points are available to set the PC after clearing and construction have begun.

Inaccessible PT
When the PT is inaccessible, as illustrated in figure 8, and both the PI and PC are readily accessible, the surveyor must establish an offset station at the PT using the method for inaccessible PC with the following exceptions.

1. Letter the curve so that point A is at the PT instead of the PC (see figure 8).
2. Lay the curve in as far as possible from the PC instead of the PT.
3. Angle dp is the angle at the center of the curve between point P and the PT, which is equal to two times the difference between the deflection at P and one half of I. Follow the steps for inaccessible PC to set lines PQ and QS. Note that the station at point S equals the computed station value of PT plus YQ.
4. Use station S to number the stations of the alignment ahead.

Obstacle on Curve
Some curves have obstacles large enough to interfere with the line of sight and taping. Normally, only a few stations are affected. The surveyor should not waste too much time on preliminary work. Figure 9 illustrates a method of bypassing an obstacle on a curve.

1. Set the instrument over the PC with the horizontal circle at 0˚ 00’, and sight on the PI. Check I/2 from the PI to the PT, if possible.
2. Set as many stations on the curve as possible before the obstacle, point b.
3. Set the instrument over the PT with the plates at the value of I/2. Sight on the PI.
4. Back in as many stations as possible beyond the obstacle, point e.
5. After the obstacle is removed, the obstructed stations c and d can be set.