---
title: "Effect of centrifugal force on horizontal curve"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:centrifugal-effect"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/centrifugal-effect
site: BCT Engineering
---

# Effect of centrifugal force on horizontal curve

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2081 Chaitra, 5 marks; 2075 Bhadra (asked 2 times)
- Video: [Overturning and Skidding effect on horizontal curve](https://www.youtube.com/watch?v=V1vhal6GD3s) — Civil Engineering & Stuff
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/centrifugal-effect
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Discuss the effect of centrifugal force on a horizontal curve (the effects of a horizontal curve on which vehicle stability depends).

## Short answer

Centrifugal force P=Wv^2/(gR) acts outward on a curve, causing overturning when v^2/(gR) >= b/(2h), skidding when v^2/(gR) >= f, passenger discomfort, reduced steering control, uneven tyre wear and accident risk. Remedies are superelevation, adequate radius, transition curve and speed limits.

## Answer

When a vehicle moves along a horizontal curve of radius $R$ at speed $v$, a **centrifugal force** $P = \dfrac{Wv^2}{gR}$ acts outwards (horizontally, through the centre of gravity). The ratio $P/W = v^2/(gR)$ is called the centrifugal ratio. It has the following effects:

1. **Tendency to overturn** the vehicle about the outer wheels, because $P$ acts at the height $h$ of the centre of gravity, while the weight $W$ resists with a lever arm of $b/2$ ($b$ = wheel track). Overturning begins when
   $$
   \frac{v^2}{gR} \ge \frac{b}{2h}
   $$
2. **Tendency to skid sideways** (lateral skidding) outwards when $P$ is more than the lateral friction $fW$:
   $$
   \frac{v^2}{gR} \ge f
   $$
3. **Discomfort and strain** to passengers and the load; the load may shift in goods vehicles.
4. **Reduced steering control:** the driver drifts to the outer edge and may encroach on the opposite lane.
5. **Uneven tyre wear and higher fuel use** due to lateral slip.
6. **Higher chance of accidents,** especially for vehicles with a high centre of gravity (trucks, buses) or on wet roads.

**Remedies:** superelevation, an adequate radius, a transition curve, speed restriction, and warning signs. Normally $f < b/2h$, so a vehicle skids before it overturns.

## Check yourself

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

1. What is the centrifugal force on a vehicle of weight W at speed v on radius R?
   A. Wv/(gR)
   B. W v^2/(gR)
   C. W g R/v^2
   D. W v^2/R^2
   Answer: B. P = W v^2/(gR) acts outward through the centre of gravity. (Key point: Centrifugal force)

2. Overturning about the outer wheels begins when v^2/(gR) is at least
   A. f
   B. e + f
   C. b/(2h)
   D. 2h/b
   Answer: C. Moment of P about the outer wheel (P h) exceeds the restoring moment W b/2, so v^2/(gR) >= b/(2h). (Key point: Overturning condition)

3. In a well-designed curve, which usually occurs first?
   A. Overturning, because f is greater than b/2h
   B. Skidding, because f is less than b/2h
   C. Both at the same time
   D. Neither can ever occur
   Answer: B. Normally f is smaller than b/2h, so a vehicle skids before it overturns. (Key point: Skid before overturn)

4. Which of these is a remedy for centrifugal effects on a curve?
   A. Reducing the curve radius
   B. Removing the transition curve
   C. Providing superelevation
   D. Increasing the speed limit
   Answer: C. Superelevation, adequate radius, transition curves and speed restriction reduce the effects. (Key point: Remedies)

## 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
- [Vertical curve with horizontal curve, 45 degrees](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-77c-vc-horizontal) — Transportation Engineering I, chapter 3
- [Highway curves and effects without superelevation](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Acurve-effects-without-super) — 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
- [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 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

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