Setting out right hand side composite curve

A composite curve has a circular arc between two transition (spiral) curves. A right-hand curve turns to the right of the direction of travel, so the deflection angles are measured clockwise. It is set out with a theodolite and tape by the deflection angle method.

            V (IP)
           /  \
          /    \
    TS o/        \o ST
        \ SC  CS /
         '--___--'

Preliminary computations

1. Length of spiral $L_s = v^3/(CR)$, shift $s = L_s^2/(24R)$, spiral angle $\theta_s = L_s/(2R)$.
2. Tangent length $T_s = (R+s)\tan(\Delta/2) + L_s/2$; $L_c = R(\Delta - 2\theta_s)$.
3. Chainages: TS = IP − $T_s$, SC = TS + $L_s$, CS = SC + $L_c$, ST = CS + $L_s$.
4. Deflection angles of the transition: $\alpha = 573\,l^2/(RL_s)$ minutes; of the circular arc: $\delta = 1718.87\,c/R$ minutes.

Field procedure

1. Locate TS and ST by measuring $T_s$ from the IP along both tangents.
2. First transition (instrument at TS): set zero and sight the IP. Turn the telescope clockwise by $\alpha_1$, measure $l_1$ (sub-chord) from TS to fix point 1. Then set $\alpha_2$, swing the tape from point 1 and fix point 2, and so on to SC. The last angle is $\alpha_s = \theta_s/3$.
3. Circular arc (instrument at SC): sight TS with the plates set at $360^\circ - \tfrac{2}{3}\theta_s$, plunge the telescope and turn clockwise until the circle reads $0^\circ00'00''$; this line is the tangent at SC. Set clockwise deflection angles $\delta_1,\ \delta_1+\delta_2,\dots$ and fix the arc points with the chords. The last angle should be $(\Delta-2\theta_s)/2$ at CS.
4. Second transition (instrument at ST): set zero and sight the IP. Because this transition is set from the far end, the points are located by angles measured anticlockwise (reading $360^\circ - \alpha$ for a right-hand curve), with $l$ measured from ST back to CS.
5. Check: the arc and the two transitions must join exactly at SC and CS; any small misclosure is distributed over the last few pegs.

If the full curve is not visible from the SC (obstruction), the instrument is shifted to an intermediate station and re-oriented by backsighting.