---
title: "Transition curve about centre line, 65 kmph"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-67m-tc-65"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-67m-tc-65
site: BCT Engineering
---

# Transition curve about centre line, 65 kmph

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2067 Mangsir (old course), 8 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-67m-tc-65
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Calculate the length of a transition curve required for a road with carriageway width of 7.0 m on a straight portion, if the design speed is 65 kmph. Assume that the road is passing through a rolling terrain. The radius of the horizontal curve is 200 m and pavement is rotated about the centre line. Assume suitable data if necessary.

## Answer

#### Assumptions
- Design speed $V=65$ km/h; carriageway width $W=7.0$ m (two lanes, IRC/NRS 2070); 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. e = V^2/225R = 0.0939 is calculated. What is used?
   A. 0.0939
   B. 0.07, the maximum for rolling terrain
   C. 0.15
   D. 0.05
   Answer: B. It is limited to 0.07; friction needed is then 0.096 < 0.15, so safe. (Key point: Superelevation)

2. With widening, which formula gives Ls for introducing superelevation (centre-line rotation)?
   A. Ls = N e (W + We) / 2 = 40.4 m
   B. Ls = N e W = 73.5 m
   C. Ls = e (W + We) / N
   D. Ls = N e We
   Answer: A. Width W + We = 7.7 m is rotated; each edge moves e(W+We)/2 at 1 in N. (Key point: Superelevation run-off)

3. Which value governs among 51.5, 40.4 and 57.0 m?
   A. 40.4 m, the smallest
   B. 51.5 m, the middle
   C. 57.0 m (IRC), the greatest, rounded to 60 m
   D. The average, 49.6 m
   Answer: C. The greatest satisfies all three criteria. (Key point: Governing value)

## Related in Transportation Engineering I

- [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 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 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 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 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×

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