---
title: "Transition curve for 300 m radius, 7 m pavement"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-64p-tc-300"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-64p-tc-300
site: BCT Engineering
---

# Transition curve for 300 m radius, 7 m pavement

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2064 Poush (old course), 8 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-64p-tc-300
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A transition curve needed to connect a circular section with a straight section of a highway. If the design speed of highway is 90[?] kmph and radius of the circular section is 300 m. Determine the length of transition curve for comfort and for introducing super elevation at your suitably selected desirable rate. The width of pavement at straight section is 7 m and length of the wheel base of the design vehicle is 6.1 m.

## Short answer

Comfort length = V³/(CR) = 104.2 m; superelevation length = N e (W+We)/2 = 40.4 m. Adopt greater value: Ls = 105 m.

## Answer

**Reading:** the design speed is read as **90 km/h** (the digit in the scan is doubtful).

#### Data and assumptions
$R=300$ m, $W=7$ m, wheel base $l=6.1$ m. Rotation of the pavement about the centre line, desirable rate of introduction of superelevation 1 in $N=150$ (IRC, plain and rolling terrain).

#### Superelevation and widening
- $e=\dfrac{V^2}{225R}=\dfrac{90^2}{225(300)}=0.120>0.07$, so adopt **e = 0.07**. Friction needed $=\dfrac{V^2}{127R}-e=0.143<0.15$ (safe).
- Mechanical widening $W_m=\dfrac{nl^2}{2R}=\dfrac{2(6.1)^2}{2(300)}=0.124$ m; psychological $W_{ps}=\dfrac{V}{9.5\sqrt R}=0.547$ m. $W_e=0.67\approx0.7$ m.

#### (a) Length for comfort
$C=\dfrac{80}{75+90}=0.485$ m/s³, below the lower limit 0.5, so take $C=0.5$ m/s³. $V=25$ m/s:

$$
L_s=\frac{V^3}{CR}=\frac{25^3}{0.5(300)}=104.2\ \text{m}
$$

#### (b) Length for introducing superelevation

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

(The IRC empirical value $2.7V^2/R=72.9$ m is also smaller than the comfort value.)

#### Design length
The greater value, comfort, governs: **L_s = 105 m** (calculated 104.2 m). The shift would be $s=\dfrac{105^2}{24(300)}=1.53$ m.

## Check yourself

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

1. C = 80/(75+V) = 0.485 for 90 km/h. What C is used?
   A. 0.485
   B. 0.5 m/s^3, since C is limited to 0.5 to 0.8
   C. 0.8
   D. 1.0
   Answer: B. The formula value is below the lower limit, so 0.5 is taken. (Key point: Comfort C)

2. Which formula gives the comfort length?
   A. Ls = V^3 / (C R) = 104.2 m
   B. Ls = V^2 / (C R)
   C. Ls = N e W / 2
   D. Ls = 2.7 V^2 / R
   Answer: A. Ls = V^3/(CR) with V in m/s limits the rate of change of centrifugal acceleration. (Key point: Comfort length)

3. Comfort gives 104.2 m, superelevation 40.4 m, IRC 72.9 m. What is adopted?
   A. 40 m
   B. 73 m
   C. 105 m, the comfort value (greatest)
   D. The average of the three
   Answer: C. The greatest governs. (Key point: Governing)

## Related in Transportation Engineering I

- [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 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 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 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
- [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

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- [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, IP 3605](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-road-8m-300m-3605-50kmh) — Surveying II, chapter 6, asked 3×
- [Transition curve R=180 m, speed 13.2 m/s](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-curve-180m-radius-132) — Surveying II, chapter 6