Composite curve with 48 degree deflection

(1) Radius of circular curve

The centrifugal ratio (= $e+f$) is $\dfrac{V^2}{127R}=\dfrac{1}{6}$:

$$R=\frac{6V^2}{127}=\frac{6(60)^2}{127}=170.08\ \text{m}$$

(2) Length of transition curve

$V=60/3.6=16.67$ m/s, $C=0.45$ m/s³:

$$L_s=\frac{V^3}{CR}=\frac{16.67^3}{0.45(170.08)}=60.49\ \text{m}$$

(3) Total length of composite curve

• Spiral angle: $\theta_s=\dfrac{L_s}{2R}=0.1778$ rad $=10.189^\circ$
• Central angle of circular arc: $\Delta_c=48^\circ-2(10.189^\circ)=27.622^\circ$
• Circular arc: $L_c=R\Delta_c=170.08(0.4821)=81.99$ m

$$L=L_c+2L_s=81.99+2(60.49)=202.97\ \text{m}$$

Answer: $R\approx170.1$ m; $L_s\approx60.5$ m; total length of composite curve $\approx203.0$ m.