---
title: "Transition curve 220 m radius, 65 kmph"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-68bh-tc-65"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-68bh-tc-65
site: BCT Engineering
---

# Transition curve 220 m radius, 65 kmph

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2068 Bhadra (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-68bh-tc-65
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Calculate the length of transition curve using the following data: i) Design speed = 65 kmph ii) Radius of circular curve = 220 m iii) Allowable rate of introduction of super elevation (Pavement rotated about centre line) = 1 in 150 iv) Pavement width including extra widening = 7.5 m

## Short answer

Superelevation restricted to 0.07. Length by rate of centrifugal acceleration = 46.8 m, by superelevation introduction = 39.4 m, IRC formula = 51.9 m. Greatest value adopted as transition length = 55 m.

## Answer

#### Superelevation
$e=\dfrac{V^2}{225R}=\dfrac{65^2}{225(220)}=0.0854$. This exceeds 0.07, the maximum for plain/rolling terrain (IRC/NRS), so **e = 0.07**. Friction required $=\dfrac{V^2}{127R}-e=0.081<0.15$, so it is safe.

#### Length of transition curve (the greatest of three)
1. **Rate of change of centrifugal acceleration:** $C=\dfrac{80}{75+65}=0.571$ m/s³, $V=18.06$ m/s

$$
L_s=\frac{V^3}{CR}=\frac{18.06^3}{0.571(220)}=46.8\ \text{m}
$$

2. **Rate of introduction of superelevation** (1 in 150, rotation about centre line, so each edge moves $eW/2$ from the centre line):

$$
L_s=\frac{N\,e\,W}{2}=\frac{150(0.07)(7.5)}{2}=39.4\ \text{m}
$$

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

$$
L_s=\frac{2.7V^2}{R}=\frac{2.7(65)^2}{220}=51.9\ \text{m}
$$


**Answer:** the greatest value governs, so adopt **L_s = 55 m** (calculated 51.9 m). Shift $s=\dfrac{L_s^2}{24R}=0.57$ m.

## Check yourself

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

1. Calculated e = V^2/225R = 0.0854 exceeds the maximum. What is adopted?
   A. e = 0.0854
   B. e = 0.07, the maximum for plain/rolling terrain
   C. e = 0.10
   D. e = 0.04
   Answer: B. Superelevation is capped at 0.07, with the rest taken by friction (needed f = 0.081 < 0.15). (Key point: Superelevation limit)

2. How is the final transition length chosen from the three criteria?
   A. The smallest of the three values
   B. The average of the three values
   C. The greatest of the three values
   D. The one from the IRC formula only
   Answer: C. The longest satisfies all criteria, so the greatest governs (51.9 m, adopt 55 m). (Key point: Governing criterion)

3. For rotation about the centre line, what is the length for introducing superelevation?
   A. Ls = N e W / 2 = 39.4 m
   B. Ls = N e W = 78.8 m
   C. Ls = e W / N
   D. Ls = N W / 2e
   Answer: A. Each edge moves eW/2 from the centre line, and at 1 in N this takes N x eW/2 of length. (Key point: Rate of introduction)

## Related in Transportation Engineering I

- [Transition curve about centre line, 65 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-67m-tc-65) — 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, pavement 7 m](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-77c-tc-220) — 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 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×
- [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

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