---
title: "Transition curve: definition and need"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:tc-objectives"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/tc-objectives
site: BCT Engineering
---

# Transition curve: definition and need

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2078 Poush, 3 marks; 2073 Magh; 2072 Ashwin; 2071 Magh; 2070 Bhadra; 2063 Kartik (old course), 1+2 marks (asked 6 times)
- Video: [Define Transition Curve | Requirements and types of Transition Curve | Prashant YT | Surveying 2nd |](https://www.youtube.com/watch?v=Puxs9_BXgbQ) — Prashant YT
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/tc-objectives
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Define transition curve. What are its objectives/functions and necessity in horizontal alignment? List the types of transition curve.

## Short answer

A transition curve gradually changes radius from infinity at a tangent to R at a circular curve. Objectives: introduce centrifugal force and superelevation gradually, provide extra widening, improve appearance, reduce skidding/overturning, and keep vehicles in lane. Types: spiral (clothoid) recommended by IRC, cubic parabola used on railways, and Bernoulli's lemniscate for large deflection angles.

## Answer

A **transition curve** is a curve of gradually changing radius, provided between a straight and a circular curve (or between two circular curves), so that the radius changes from infinity at the tangent to $R$ at the circular curve.

#### Objectives and need
1. To introduce the **centrifugal force gradually** from zero to its full value, avoiding a sudden jerk to the passengers and the load.
2. To allow gradual introduction of the **superelevation** over the length of the curve.
3. To allow gradual **introduction of the extra widening.**
4. To **improve the appearance** of the road by avoiding a visible kink at the junction of the straight and the curve.
5. To reduce the chance of **skidding, overturning** and lateral shift of the vehicle, so that the speed is more uniform.
6. To keep the vehicle within its lane (a vehicle naturally follows a transition path while entering a curve).

#### Types of transition curve
1. **Spiral (clothoid / Euler spiral)** - the radius varies inversely with the length; recommended by IRC.
2. **Cubic parabola** - $y = x^3 /(6RL_s)$; practically the same as the spiral for small deflection angles, and widely used on railways.
3. **Bernoulli's lemniscate** - used on roads where the deflection angle is large (e.g. loops); its radius decreases more slowly than that of the spiral.

## Check yourself

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

1. A transition curve has radius that:
   A. Is constant
   B. Changes gradually from infinity at the tangent to R at the circular curve
   C. Is zero at start
   D. Is always larger than R
   Answer: B. It provides a gradual change of radius between straight and circular curve. (Key point: Definition)

2. Which is an objective of the transition curve?
   A. To increase speed
   B. To reduce land
   C. To introduce centrifugal force and superelevation gradually
   D. To remove camber
   Answer: C. Gradual introduction avoids jerk and permits gradual superelevation and widening. (Key point: Function)

3. Which is a type of transition curve?
   A. Parabola with vertical axis
   B. Spiral (clothoid), cubic parabola, Bernoulli's lemniscate
   C. Simple circle
   D. Straight line
   Answer: B. Standard types are spiral, cubic parabola and lemniscate. (Key point: Types)

## Related in Transportation Engineering I

- [Definition of highway alignment](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Adefine-alignment) — Transportation Engineering I, chapter 2, asked 4×
- [Length of transition curve (criteria)](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Atc-length-methods) — Transportation Engineering I, chapter 3, asked 8×
- [Transition curve for 230 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81c-tc-230) — 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 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

## Related in other subjects

- [Derive deflection angle of transition curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-deflection-angle-derivation) — Surveying II, chapter 6, asked 3×
- [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 road 8 m, R=330 m, 60°](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-road-8m-330m-deflection-60) — Surveying II, chapter 6, asked 2×
- [Transition curve, road 8 m, R=300 m, 60°](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-road-8m-300m-60-70kmph) — Surveying II, chapter 6, asked 2×