---
title: "Superelevation and equilibrium superelevation"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:super-define-equilibrium"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/super-define-equilibrium
site: BCT Engineering
---

# Superelevation and equilibrium superelevation

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2080 Chaitra, 2 marks
- Video: [Superelevation | Superelevation in highway engineering](https://www.youtube.com/watch?v=9B7QslOHeN8) — Engineer's Coach
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/super-define-equilibrium
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Define superelevation and equilibrium superelevation. State the assumptions made.

## Short answer

Superelevation is the inward transverse slope on curves raising the outer edge. Equilibrium superelevation (e = V²/127R) balances centrifugal force entirely by weight component, requiring zero lateral friction. Assumptions: point mass at uniform speed, constant radius, plane pavement, zero friction, small angle approximation, and no overturning considered.

## Answer

**Superelevation (cant)** is the transverse slope provided at a horizontal curve by raising the outer edge of the pavement above the inner edge, so that a component of the vehicle's weight acts against the centrifugal force.

**Equilibrium superelevation** is the value of superelevation at which the centrifugal force is completely balanced by the weight component, so that **no lateral friction** is needed:

$$
e = \tan\theta = \frac{v^2}{gR}
\qquad\left(= \frac{V^2}{127R}\ \text{with } V \text{ in km/h}\right)
$$

#### Assumptions
1. The vehicle is treated as a **point mass** moving at a **uniform speed** $v$.
2. The curve has a **constant radius** $R$, and the pavement is a plane surface with a uniform slope.
3. **Lateral friction is zero** (neglected) in the equilibrium condition.
4. The vehicle neither skids nor overturns, and the height of its centre of gravity is not considered in the basic derivation.
5. The superelevation is small, so $\sin\theta \approx \tan\theta$ and $\cos\theta \approx 1$.

## Check yourself

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

1. Superelevation is
   A. raising the inner edge above the outer edge
   B. raising the outer edge above the inner edge at a horizontal curve
   C. a crown on straights
   D. widening the carriageway
   Answer: B. The outer edge is raised so a weight component acts against centrifugal force. (Key point: Superelevation meaning)

2. At equilibrium superelevation, lateral friction needed is
   A. maximum
   B. equal to e
   C. zero
   D. equal to 0.15
   Answer: C. The weight component fully balances centrifugal force, so no friction is needed: e = v^2/(gR). (Key point: Equilibrium superelevation)

3. Which is an assumption in the derivation?
   A. Friction is large
   B. The vehicle is a point mass at uniform speed on a constant radius curve
   C. The radius varies
   D. The superelevation is large
   Answer: B. The vehicle is a point mass at uniform speed, radius constant, friction neglected, and e small. (Key point: Assumption)

## Related in Transportation Engineering I

- [Superelevation design for 150 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-79j-super-150) — 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

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