Spiral Curve Layout

The following is the procedure to lay out a spiral curve, using a one-minute instrument with a horizontal circle that reads to the right. Figure 17 illustrates this procedure.

Setting TS and ST
With the instrument at the PI, the instrumentman sights along the back tangent and keeps the head tapeman on line while the tangent distance (Ts) is measured. A stake is set on line and marked to show the TS and its station value.

The instrumentman now sights along the forward tangent to measure and set the ST.

Laying Out First Spiral from TS to SC
Set up the instrument at the TS, pointing on the PI, with 0°00’ on the horizontal circle.

1. Check the angle to the ST, if possible. The angle should equal one half of the I angle if the TS and ST are located properly.
2. The first deflection (a1/ 0˚ 01’) is subtracted from 360 degrees, and the remainder is set on the horizontal circle. Measure the standard spiral chord length (25 feet) from the TS, and set the first spiral station (38 + 54.66) on line.
3. The remaining spiral stations are set by subtracting their deflection angles from 360 degrees and measuring 25 feet from the previously set station.

Laying Out Circular Arc from SC to CS
Set up the instrument at the SC with a value of A minus A (5° 00’- 1°40’ = 3° 20’) on the horizontal circle. Sight the TS with the instrument telescope in the reverse position.

1. Plunge the telescope. Rotate the telescope until 0° 00’ is read on the horizontal circle. The instrument is now sighted along the tangent to the circular arc at the SC.
2. The first deflection (dl /0° 24’) is subtracted from 360 degrees, and the remainder is set on the horizontal circle. The first subchord (c1 / 20.34 feet) is measured from the SC, and a stake is set on line
   and marked for station 41+00.
3. The remaining circular arc stations are set by subtracting their deflection angles from 360 degrees and measuring the corresponding chord distance from the previously set station.

Laying Out Second Spiral from ST to CS
Set up the instrument at the ST, pointing on the PI, with 0° 00’ on the horizontal circle.

1. Check the angle to the CS. The angle should equal 1° 40’ if the CS is located properly.
2. Set the spiral stations using their deflection angles in reverse order and the standard spiral chord length (25 feet).

Correct any error encountered by adjusting the circular arc chords from the SC to the CS.

Intermediate Setup
When the instrument must be moved to an intermediate point on the spiral, the deflection angles computed from the TS cannot be used for the remainder of the spiral. In this respect, a spiral differs from a circular curve.

Calculating Deflection Angles Following are the procedures for calculating the deflection angles and staking the spiral.

Example:
D = 4°
Ls = 250 ft (for highways)
V =60 mph
I = 24° 10’
Point 5 = intermediate point

1. Calculate the deflection angles for the first five points. These angles are: a₁ = 0° 01’, a₂ = 0˚ 04’, a₃ = 0˚ 09’, a₄ = 0° 16’, and a₅ = 0° 25’.
2. The deflection angles for points 6, 7, 8, 9, and 10, with the instrument at point 5, are calculated with the use of table 2. Table 2 is read as follows: with the instrument at any point, coefficients are obtained which, when multiplied by a1, give the deflection angles to the other points of the spiral. Therefore, with the instrument at point 5, the coefficients for points 6, 7, 8, 9, and 10 are 16, 34, 54, 76, and 100, respectively.
   Multiply these coefficients by a₁ to obtain the deflection angles. These angles are a₆ = 16a1 = 0° 16’, a₇ = 34a₁ = 0˚ 34’, a₈ = 54a₁ = 0° 54’, a₉ = 76a₁ = 1°16’, and a₁₀ = 100a₁= 1˚ 40’.
3. Table 2 is also used to orient the instrument over point 5 with a backsight on the TS. The angular value from point 5 to point zero (TS) equals the coefficient from table 2 times a₁. This angle equals 50a₁= 0° 50’.
   Staking. Stake the first five points according to the procedure. Check point 5 by repetition to insure accuracy.
   Set up the instrument over point 5. Set the horizontal circle at the angular value determined above. With the telescope inverted, sight on the TS (point zero).
   Plunge the telescope, and stake the remainder of the curve (points 6, 7, 8, 9, and 10) by subtracting the deflection angles from 360 degrees.

Field Notes for Spirals. Figure 18 shows a typical page of data recorded for the layout of a spiral.