Transition curve 6°, Ls=90 m, chainage 13+700

Deflection angle between the tangents

Bearing of T₁V (travelling towards V) $= 80^\circ30'$. Bearing of T₂V is observed from T₂ towards V, $300^\circ30'$, so the forward direction of travel from V to T₂ is $300^\circ30' - 180^\circ = 120^\circ30'$.

$$\Delta = 120^\circ30' - 80^\circ30' = 40^\circ\ \text{(deflection to the right)}$$

Radius and transition elements

6° curve with a 30 m arc: $R = 1718.87/6 = 286.48$ m. $L_s = 90$ m.

$$\begin{aligned} s &= \frac{L_s^2}{24R} = \frac{90^2}{24\times 286.48} = 1.178\ \text{m}\\ \theta_s &= \frac{L_s}{2R} = 9.000^\circ\\ T_s &= (R+s)\tan 20^\circ + \frac{L_s}{2} = 149.70\ \text{m}\\ L_c &= R(\Delta-2\theta_s) = 110.00\ \text{m} \end{aligned}$$

Chainage of V $= 13700$ m (13+700 km).

First two deflection angles

Transition curve (theodolite at TS), $\alpha = 573\,l^2/(RL_s)$ minutes, points at multiples of 10 m:

Circular curve (theodolite at SC), $\delta = 1718.87\,c/R$ minutes, points at multiples of 30 m:

Answer: transition: 0°02′05″ and 0°08′37″; circular: 0°58′11″ and 3°58′11″.