---
title: "Transition curve in hilly region, 60 m radius"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-65c-tc-hilly"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-65c-tc-hilly
site: BCT Engineering
---

# Transition curve in hilly region, 60 m radius

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2065 Chaitra (old course), 4+2+2 marks
- Video: [Length of Transition curve l Numerical l Transportation Engineering l CE](https://www.youtube.com/watch?v=eE5IFBSdOIQ) — ONLINETYARI CLASSES
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-65c-tc-hilly
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A two lane pavement 7 m in width in hilly region has a curve of radius 60 m, the design speed is 40 kmph. Determine the length of transition curve, total curve length and total tangent length if the deflection angle of the curve is 60°. Take superelevation = 0.07, extra width = 1.2 m, 1:N = 1:60. Assume that the rotation of pavement is about centre line.

## Short answer

Transition length is governed by comfort, 32.9 m, and IRC hilly formula, 26.7 m; adopt Ls=35 m. Total curve length is 97.83 m and tangent length on each side is 52.63 m.

## Answer

#### Given
$V=40$ km/h, $R=60$ m, $e=0.07$, $W=7.0$ m, extra widening $W_e=1.2$ m, rate $1$ in $N=60$, rotation about the centre line, deflection angle $\Delta=60^\circ$.

#### (a) Length of transition curve (greatest of three)
1. **Comfort:** $C=\dfrac{80}{75+40}=0.696$ m/s³, $V=11.11$ m/s

$$
L_s=\frac{V^3}{CR}=\frac{11.11^3}{0.696(60)}=32.9\ \text{m}
$$

2. **Superelevation (rotation about centre line):**

$$
L_s=\frac{N\,e\,(W+W_e)}{2}=\frac{60(0.07)(8.2)}{2}=17.2\ \text{m}
$$

3. **IRC empirical (mountainous/steep terrain):** $L_s=\dfrac{V^2}{R}=\dfrac{40^2}{60}=26.7$ m.

Adopt **L_s = 35 m**.

#### (b) Total curve length
- Shift: $s=\dfrac{L_s^2}{24R}=\dfrac{35^2}{24(60)}=0.851$ m
- Spiral angle: $\theta_s=\dfrac{L_s}{2R}=0.2917$ rad $=16.71^\circ$
- Arc angle: $\Delta_c=60^\circ-2(16.71^\circ)=26.58^\circ$
- Arc length: $L_c=R\Delta_c=27.83$ m

$$
L=L_c+2L_s=27.83+2(35)=97.83\ \text{m}
$$

#### (c) Total tangent length

$$
T_s=(R+s)\tan\frac{\Delta}{2}+\frac{L_s}{2}=(60.851)\tan30^\circ+17.5=52.63\ \text{m}
$$

This is the tangent length from the PI to each end of the curve ($2T_s=105.26$ m for both sides).

**Answer:** $L_s=35$ m; total curve length = 97.8 m; tangent length $T_s=52.6$ m on each side.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Comfort gives 32.9 m, superelevation 17.2 m, empirical 26.7 m. Which governs?
   A. The greatest, 32.9 m, adopt 35 m
   B. 17.2 m, the least
   C. 26.7 m, the IRC value
   D. The sum of all three
   Answer: A. The longest satisfies all criteria. (Key point: Governing length)

2. With Ls = 35 m and R = 60 m, what is the circular arc angle?
   A. 60° - 16.71° = 43.29°
   B. 60° - 2(16.71°) = 26.58°
   C. 60° + 33.4° = 93.4°
   D. 16.71°
   Answer: B. Both spirals consume theta_s each of the deflection angle. (Key point: Arc angle)

3. Which formula gives Ts?
   A. R tan Delta
   B. (R + s) tan Delta + Ls
   C. (R + s) tan(Delta/2) + Ls/2
   D. (R - s) tan(Delta/2) - Ls/2
   Answer: C. The shifted circle's tangent plus half the spiral length. (Key point: Tangent)

## Related in Transportation Engineering I

- [Transition curve 200 m radius, 60 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-70m-tc-200) — Transportation Engineering I, chapter 3
- [Transition curve for 300 m radius, 7 m pavement](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-64p-tc-300) — Transportation Engineering I, chapter 3
- [Transition curve length and shift, 7.2 m pavement](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-62j-tc-shift) — Transportation Engineering I, chapter 3
- [Transition curve 220 m radius, 65 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-68bh-tc-65) — Transportation Engineering I, chapter 3
- [Transition curve and edge elevations, hilly terrain](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-79a-tc-super-elevations) — Transportation Engineering I, chapter 3
- [Transition curve 400 m radius, 85 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-tc-400-85) — Transportation Engineering I, chapter 3, asked 2×

## Related in other subjects

- [Transition curve R=300 m, deflection 40°](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-curve-80kmph-radius-300) — Surveying II, chapter 6
- [Transition curve, road 8 m, R=300 m, 60°](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-road-8m-300m-60-70kmph) — Surveying II, chapter 6, asked 2×
- [Function of transition curve, deflection angle](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-curve-function-deflection-angle) — Surveying II, chapter 6
- [Transition curve road 8 m, R=330 m, 60°](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-road-8m-330m-deflection-60) — Surveying II, chapter 6, asked 2×