---
title: "Composite curve, 65 kmph, centrifugal ratio 1/5"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-71bh-composite-65"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-71bh-composite-65
site: BCT Engineering
---

# Composite curve, 65 kmph, centrifugal ratio 1/5

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2071 Bhadra, 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-71bh-composite-65
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A vehicle moving in a horizontal curve at a design speed of 65 kmph, develops a centrifugal ratio of 1/5. The deflection angle at curve is 48°. Calculate:
a) radius of circular curve
b) length of transition curve by rate of change of centrifugal acceleration criteria
c) total length of composite curve

## Short answer

For design speed 65 km/h and centrifugal ratio 1/5, circular curve radius is 166.3 m. Transition curve length by rate of change of centrifugal acceleration is 61.9 m. Total composite curve length with 48° deflection is 201.3 m.

## Answer

#### (a) Radius of circular curve
Centrifugal ratio $=\dfrac{V^2}{127R}=\dfrac{1}{5}$:

$$
R=\frac{5V^2}{127}=\frac{5(65)^2}{127}=166.34\ \text{m}
$$

#### (b) Length of transition curve (rate of change of centrifugal acceleration)
IRC: $C=\dfrac{80}{75+V}=\dfrac{80}{140}=0.571$ m/s³ (within the permitted range 0.5 to 0.8). $V=65/3.6=18.06$ m/s.

$$
L_s=\frac{V^3}{CR}=\frac{18.06^3}{0.571(166.34)}=61.93\ \text{m}
$$

#### (c) Total length of composite curve
- Spiral angle $\theta_s=\dfrac{L_s}{2R}=0.1861$ rad $=10.665^\circ$
- Circular arc angle $\Delta_c=48^\circ-2\theta_s=26.669^\circ$
- Circular arc length $L_c=R\Delta_c=166.34(0.4655)=77.42$ m

$$
L=L_c+2L_s=77.42+2(61.93)=201.28\ \text{m}
$$

**Answer:** $R=166.3$ m; $L_s=61.9$ m; total composite curve length $=201.3$ m.

## Check yourself

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

1. How is R found from the centrifugal ratio 1/5?
   A. R = 5V^2/127 = 166.3 m
   B. R = V^2/(127 x 5)
   C. R = 127/(5V^2)
   D. R = 5V/127
   Answer: A. V^2/(127R) = 1/5. (Key point: Radius)

2. What formula gives C used here?
   A. C = 80/V
   B. C = 80/(75 + V) = 0.571 m/s^3
   C. C = 0.5 always
   D. C = V^2/R
   Answer: B. IRC empirical expression; within 0.5 to 0.8. (Key point: Rate of change)

3. How is Ls computed?
   A. Ls = V^2/(CR)
   B. Ls = 2.7V^2/R only
   C. Ls = V^3/(CR) with V = 18.06 m/s = 61.9 m
   D. Ls = CR/V
   Answer: C. 18.06^3 / (0.571 x 166.34). (Key point: Ls)

4. How is total length computed?
   A. L = RΔ
   B. L = RΔ + Ls
   C. L = Ls + R
   D. L = R(Δ - 2θs) + 2Ls = 201.3 m
   Answer: D. Arc 77.42 m plus two spirals. (Key point: Total length)

## Related in Transportation Engineering I

- [Composite curve with 48 degree deflection](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-72m-composite-60) — 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 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 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 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 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

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- [Composite curve design, IP 1150 m, Rankine](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acomposite-curve-rankine-ip-1150) — Surveying II, chapter 6, asked 2×
- [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
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