Transition curve from spiral angle 8.35

Reading of the data

The angle of intersection 137.23° is the interior angle between the two straights, so the deflection angle is $\Delta=180^\circ-137.23^\circ=42.77^\circ$. Radius $R=325$ m, spiral angle $\theta_s=8.35^\circ$.

Length of transition curve

For a spiral, $\theta_s=\dfrac{L_s}{2R}$ (radians), so

$$L_s=2R\theta_s=2(325)(0.14573)=94.73\ \text{m}$$

Combined length of curve

• Shift: $s=\dfrac{L_s^2}{24R}=\dfrac{94.73^2}{24(325)}=1.150$ m
• Central angle of the circular arc: $\Delta_c=\Delta-2\theta_s=42.77-2(8.35)=26.07^\circ$
• Circular arc length: $L_c=R\Delta_c=325(0.45501)=147.88$ m

$$L=L_c+2L_s=147.88+2(94.73)=337.33\ \text{m}$$

Length of tangent (from PI to the start of the transition)

$$T_s=(R+s)\tan\frac{\Delta}{2}+\frac{L_s}{2}=(326.150)\tan(21.39^\circ)+47.36=175.08\ \text{m}$$

Answer: $L_s=94.7$ m; combined curve length = 337.3 m; tangent length $T_s=175.1$ m.

(If the given angle were instead the deflection angle, $\Delta=137.23^\circ$, the same $L_s$ results with $\Delta_c=120.53^\circ$, total length 873.1 m and $T_s=880.2$ m.)