---
title: "Transition curve for NH, 200 m radius"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-66m-tc-200"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-66m-tc-200
site: BCT Engineering
---

# Transition curve for NH, 200 m radius

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2066 Magh (old course), 6 marks
- Video: [#highways, #curve, #transition, Design of Transition curve on a highway, Transition on curves.](https://www.youtube.com/watch?v=0Mp2UzTLOss) — Transportation Engg Talks | Satish IITR
- 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-66m-tc-200
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A National Highway passing through a rolling terrain has a horizontal curve of radius of 200 m. Find out the length of a transition curve assuming suitable data.

## Short answer

Assume V=65 km/h, e=0.07, widening 0.7 m. Transition lengths are 51.5 m for comfort, 40.4 m for superelevation, and 57.0 m by IRC formula. Adopt 60 m.

## Answer

Design speed is not given. A radius of 200 m cannot be used at the 80 km/h ruling speed ($R_{min}\approx229$ m), so the minimum design speed for a National Highway in rolling terrain, 65 km/h, is adopted.

#### Assumptions
- Design speed $V=65$ km/h; carriageway width $W=7.0$ m (two lanes, IRC/NRS 2070); National Highway in rolling terrain; pavement rotated about the **centre line**; rate of introduction of superelevation 1 in $N=150$ (IRC: 1 in 150 for plain and rolling terrain).

#### Superelevation and extra widening
- $e=\dfrac{V^2}{225R}=\dfrac{65^2}{225(200)}=0.0939>0.07$, so **e = 0.07**. Friction needed $=\dfrac{V^2}{127R}-e=0.096<0.15$ (safe).
- Mechanical widening $W_m=\dfrac{nl^2}{2R}=\dfrac{2(6.1)^2}{2(200)}=0.186$ m; psychological widening $W_{ps}=\dfrac{V}{9.5\sqrt R}=0.484$ m; total $W_e=0.67\approx0.7$ m.

#### Length of transition curve (greatest of three)
1. **Rate of change of centrifugal acceleration:** $C=\dfrac{80}{75+65}=0.571$ m/s³

$$
L_s=\frac{(65/3.6)^3}{CR}=\frac{18.06^3}{0.571(200)}=51.5\ \text{m}
$$

2. **Rate of introduction of superelevation:**

$$
L_s=\frac{N\,e\,(W+W_e)}{2}=\frac{150(0.07)(7.0+0.7)}{2}=40.4\ \text{m}
$$

3. **IRC empirical formula** (plain/rolling terrain):

$$
L_s=\frac{2.7V^2}{R}=\frac{2.7(65)^2}{200}=57.0\ \text{m}
$$


The greatest value governs. **Answer: adopt L_s = 60 m** (calculated 57.0 m). The shift is $s=\dfrac{L_s^2}{24R}=0.75$ m.

## Check yourself

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

1. Why is 65 km/h adopted when speed is not given?
   A. R = 200 m is below the minimum for 80 km/h, so the minimum NH rolling-terrain speed is used
   B. 200 m is the radius for 65 km/h exactly
   C. All National Highways use 65 km/h
   D. The speed is irrelevant to the transition
   Answer: A. At 80 km/h R_min is about 229 m, so a lower design speed suits R = 200 m. (Key point: Design speed choice)

2. V^2/225R = 0.0939. What e is used?
   A. 0.0939
   B. 0.07 (maximum)
   C. 0.15
   D. 0.03
   Answer: B. e is capped at 0.07 for plain/rolling terrain. (Key point: Superelevation)

3. Which of 51.5, 40.4 and 57.0 m governs?
   A. 40.4 m, the least
   B. 51.5 m, the comfort value
   C. 57.0 m, the greatest, adopt 60 m
   D. The sum of the three
   Answer: C. The greatest of the three criteria governs. (Key point: Governing Ls)

## Related in Transportation Engineering I

- [Transition curve and shift for 250 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-79c-tc-250) — 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 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 310 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-80c-tc-310) — Transportation Engineering I, chapter 3
- [Transition curve 625 m radius, 90 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-75b-tc-625) — Transportation Engineering I, chapter 3
- [Transition curve for 230 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81c-tc-230) — Transportation Engineering I, chapter 3

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