Transition curve length from spiral angle 10.32

Reading of the data

The angle of intersection 145.37° is the interior angle between the two straights, so the deflection angle is $\Delta=180^\circ-145.37^\circ=34.63^\circ$. Radius $R=350$ m, spiral angle $\theta_s=10.32^\circ$.

Length of transition curve

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

$$L_s=2R\theta_s=2(350)(0.18012)=126.08\ \text{m}$$

Combined length of curve

• Shift: $s=\dfrac{L_s^2}{24R}=\dfrac{126.08^2}{24(350)}=1.892$ m
• Central angle of the circular arc: $\Delta_c=\Delta-2\theta_s=34.63-2(10.32)=13.99^\circ$
• Circular arc length: $L_c=R\Delta_c=350(0.24417)=85.46$ m

$$L=L_c+2L_s=85.46+2(126.08)=337.63\ \text{m}$$

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

$$T_s=(R+s)\tan\frac{\Delta}{2}+\frac{L_s}{2}=(351.892)\tan(17.32^\circ)+63.04=172.74\ \text{m}$$

Answer: $L_s=126.1$ m; combined curve length = 337.6 m; tangent length $T_s=172.7$ m.

(If the given angle were instead the deflection angle, $\Delta=145.37^\circ$, the same $L_s$ results with $\Delta_c=124.73^\circ$, total length 1014.1 m and $T_s=1191.8$ m.)