---
title: "Composite curve with 48 degree deflection"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-72m-composite-60"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-72m-composite-60
site: BCT Engineering
---

# Composite curve with 48 degree deflection

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2072 Magh, 8 marks
- 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-72m-composite-60
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

The curve consists of circular arc combined with transition curve at both ends. Calculate the radius of the circular curve, the length of transition curve and total length of composite curve with the following data: a) Design speed = 60 kmph, b) Maximum centrifugal ratio = 1/6, c) Maximum rate of change of centrifugal acceleration = 0.45 m/s³, d) Deflection angle = 48°

## Short answer

Radius from centrifugal ratio 1/6: R = 6×60²/127 ≈ 170.1 m. Transition length from rate of change of centrifugal acceleration 0.45 m/s³: Ls ≈ 60.5 m. Total composite length including circular arc is 203.0 m.

## Answer

#### (1) Radius of circular curve
The centrifugal ratio (= $e+f$) is $\dfrac{V^2}{127R}=\dfrac{1}{6}$:

$$
R=\frac{6V^2}{127}=\frac{6(60)^2}{127}=170.08\ \text{m}
$$

#### (2) Length of transition curve
$V=60/3.6=16.67$ m/s, $C=0.45$ m/s³:

$$
L_s=\frac{V^3}{CR}=\frac{16.67^3}{0.45(170.08)}=60.49\ \text{m}
$$

#### (3) Total length of composite curve
- Spiral angle: $\theta_s=\dfrac{L_s}{2R}=0.1778$ rad $=10.189^\circ$
- Central angle of circular arc: $\Delta_c=48^\circ-2(10.189^\circ)=27.622^\circ$
- Circular arc: $L_c=R\Delta_c=170.08(0.4821)=81.99$ m

$$
L=L_c+2L_s=81.99+2(60.49)=202.97\ \text{m}
$$

**Answer:** $R\approx170.1$ m; $L_s\approx60.5$ m; total length of composite curve $\approx203.0$ m.

## Check yourself

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

1. What does the centrifugal ratio equal?
   A. e + f = V^2/(127R)
   B. V^2/(254R)
   C. e - f
   D. V/(127R)
   Answer: A. Setting it to 1/6 gives R = 6V^2/127 = 170.1 m. (Key point: Centrifugal ratio)

2. How is Ls found from C = 0.45 m/s^3?
   A. Ls = V^2/(CR)
   B. Ls = V^3/(CR) with V in m/s = 60.5 m
   C. Ls = CR/V^3
   D. Ls = 2.7V^2/R
   Answer: B. 16.67^3/(0.45 x 170.08) = 60.49 m. (Key point: Transition length)

3. What is the spiral angle?
   A. θs = Ls/R = 20.4°
   B. θs = Ls^2/24R
   C. θs = Ls/(2R) rad = 10.19°
   D. θs = Δ/2
   Answer: C. 0.1778 rad. (Key point: Spiral angle)

4. How is the total composite curve length determined?
   A. L = RΔ only
   B. L = RΔ + 2Ls
   C. L = 2R(Δ - θs)
   D. L = R(Δ - 2θs) + 2Ls = 203 m
   Answer: D. Circular arc is 81.99 m plus two spirals of 60.49 m. (Key point: Total length)

## Related in Transportation Engineering I

- [Composite curve, 65 kmph, centrifugal ratio 1/5](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-71bh-composite-65) — 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×
- [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 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 in hilly region, 60 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-65c-tc-hilly) — Transportation Engineering I, chapter 3

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