Curve Layout

The following is the procedure to lay out a curve using a one-minute instrument with a horizontal circle that reads to the right. The values are the same as those used to demonstrate the solution of a simple curve.

Setting PC and PT
With the instrument at the PI, the instrumentman sights on the preceding PI and keeps the head tapeman on line while the tangent distance is measured. A stake is set on line and marked to show the PC and its station value.

The instrumentman now points the instrument on the forward PI, and the tangent distance is measured to set and mark a stake for the PT.

Laying Out Curve from PC
The procedure for laying out a curve from the PC is described as follows. Note that the procedure varies depending on whether the road curves to the left or to the right.

Road Curves to Right. The instrument is set up at the PC with the horizontal circle at 0°00’ on the PI.

1. The angle to the PT is measured if the PT can be seen. This angle will equal one half of the I angle if the PC and PT are located properly.
2. Without touching the lower motion, the first deflection angle, d1 (0° 39’), is set on the horizontal circle. The instrumentman keeps the head tapeman on line while the first subchord distance, C1 (8.67 feet), is measured from the PC to set and mark station 16+50.
3. The instrumentman now sets the second deflection angle, d1 + dstd (2° 32’), on the horizontal circle. The tapemen measure the standard chord (25 feet) from the previously set station (16+50) while the instrument man keeps the head tapeman on line to set station 16+75.
4. The succeeding stations are staked out in the same manner. If the work is done correctly, the last deflection angle will point on the PT, and the last distance will be the subchord length, C2 (16.33 feet), to the PT.

Road Curves to Left. As in the procedures noted, the instrument occupies the PC and is set at 0°00’ pointing on the PI.

1. The angle is measured to the PT, if possible, and subtracted from 360 degrees. The result will equal one half the I angle if the PC and PT are positioned properly.
2. The first deflection, dl (0° 39’), is subtracted from 360 degrees, and the remainder is set on the horizontal circle. The first subchord, Cl (8.67 feet), is measured from the PC, and a stake is set on line and marked for station 16+50.
3. The remaining stations are set by continuing to subtract their deflection angles from 360 degrees and setting the results on the horizontal circles. The chord distances are measured from the previously set station.
4. The last station set before the PT should be C2 (16.33 feet from the PT), and its deflection should equal the angle measured in (1) above plus the last deflection, d2 (1° 14’).

Laying Out Curve from Intermediate Setup
When it is impossible to stake the entire curve from the PC, the surveyor must use an adaptation of the above procedure.

1. Stake out as many stations from the PC as possible.
2. Move the instrument forward to any station on the curve.
3. Pick another station already in place, and set the deflection angle for that station on the horizontal circle. Sight that station with the instruments telescope in the reverse position.
4. Plunge the telescope, and set the remaining stations as if the instrument was set over the PC.

Laying Out Curve from PT
If a setup on the curve has been made and it is still impossible to set all the remaining stations due to some obstruction, the surveyor can “back in” the remainder of the curve from the PT. Although this procedure has been set up as a method to avoid obstructions, it is widely used for laying out curves. When using the “backing in method,” the surveyor sets approximately one half the curve stations from the PC and the remainder from the PT. With this method, any error in the curve is in its center where it is less noticeable.

Road Curves to Right. Occupy the PT, and sight the PI with one half of the I angle on the horizontal circle. The instrument is now oriented so that if the PC is sighted, the instrument will read 0°00’.

The remaining stations can be set by using their deflections and chord distances from the PC or in their reverse order from the PT.

Road Curves to Left. Occupy the PT and sight the PI with 360 degrees minus one half of the I angle on the horizontal circle. The instrument should read 0° 00’ if the PC is sighted.

Set the remaining stations by using their deflections and chord distances as if computed from the PC or by computing the deflections in reverse order from the PT.