Skip to main content

Transition curve 200 m radius, 60 kmph

Short answer

Horizontal curve radius 200 m, speed 60 km/h, deflection 54.5°, PI chainage 1063 m. Transition length 40 m by comfort criterion. Combined curve length 230.2 m. Curve starts at chainage 939.8 m and ends at 1170.1 m.

A horizontal curve of 200 m radius is to be set out connecting two straights. The maximum speed of the vehicle on the curve is restricted to 60 kmph. Transition curves are to be introduced at each end of the circular curve. If the angle of intersection and chainage at the point of intersection is 125°30' and 1063 m calculate: (a) Length of transition curve for comfort condition (b) Length of combined curve (c) Chainage of beginning and end of curve.

Reading of the data

The angle of intersection 125°30′ is taken as the interior angle between the straights, so the deflection angle is Δ=180∘−125∘30′=54.5∘\Delta=180^\circ-125^\circ30'=54.5^\circ. R=200R=200 m, V=60V=60 km/h, PI at chainage 1063 m.

(a) Length of transition curve (comfort condition)

C=8075+V=80135=0.593C=\dfrac{80}{75+V}=\dfrac{80}{135}=0.593 m/s³, V=16.67V=16.67 m/s:

Ls=V3CR=16.6730.593(200)=39.06 mL_s=\frac{V^3}{CR}=\frac{16.67^3}{0.593(200)}=39.06\ \text{m}

Adopt Ls=40L_s=40 m.

(b) Length of combined curve

  • Shift: s=Ls224R=40224(200)=0.333s=\dfrac{L_s^2}{24R}=\dfrac{40^2}{24(200)}=0.333 m
  • Spiral angle: θs=Ls2R=0.1000\theta_s=\dfrac{L_s}{2R}=0.1000 rad =5.730∘=5.730^\circ
  • Arc angle: Δc=54.5∘−2(5.730∘)=43.041∘\Delta_c=54.5^\circ-2(5.730^\circ)=43.041^\circ
  • Arc length: Lc=RΔc=150.24L_c=R\Delta_c=150.24 m
L=Lc+2Ls=150.24+2(40)=230.24 mL=L_c+2L_s=150.24+2(40)=230.24\ \text{m}

(c) Chainages

Ts=(R+s)tan⁡Δ2+Ls2=(200.333)tan⁡(27.25∘)+20=123.18 mT_s=(R+s)\tan\frac{\Delta}{2}+\frac{L_s}{2}=(200.333)\tan(27.25^\circ)+20=123.18\ \text{m}
  • Beginning of curve = 1063 − 123.18 = 939.82 m
  • End of curve = 939.82 + 230.24 = 1170.06 m

Answer: Ls=40L_s=40 m; combined curve length = 230.2 m; curve starts at 939.8 m and ends at 1170.1 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Transportation Engineering I chapter 3 questions →