---
title: "Superelevation on 100 m radius curve"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-62j-super-100"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-62j-super-100
site: BCT Engineering
---

# Superelevation on 100 m radius curve

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2062 Jestha (old course), 10 marks
- Video: [Super Elevation calculation](https://www.youtube.com/watch?v=HS4EP8JSliY) — Engr Suliman Khan
- 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-62j-super-100
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

The radius of horizontal circular curve is 100 m. The design speed is 60 kmph. The coefficient of lateral friction is 0.17.
i) Calculate the super elevation if full lateral friction is called into play.
ii) Calculate the coefficient of friction needed if no super elevation is provided.

## Short answer

For R=100 m and V=60 km/h, e+f=0.2835. With f=0.17, superelevation e=0.113 (11.3%). With e=0, required friction f=0.283, exceeding the permissible 0.17, so skidding occurs.

## Answer

For a vehicle on a banked curve, the full balance of forces gives

$$
e+f=\frac{V^2}{127R}
$$

with $V$ in km/h and $R$ in m. Here $\dfrac{V^2}{127R}=\dfrac{60^2}{127(100)}=0.2835$.

#### (i) Superelevation if full lateral friction is called into play

$$
e=\frac{V^2}{127R}-f=0.2835-0.17=0.1135
$$

**e = 0.113 (about 11.3%)**. This is above the usual maximum of 7% (plain and rolling terrain, IRC/NRS) and 10% (hill roads, IRC), so it cannot be fully provided in practice. It means 60 km/h is too high for $R=100$ m with $f=0.17$ unless the maximum superelevation is accepted and speed or radius is changed.

#### (ii) Friction needed if no superelevation is provided ($e=0$)

$$
f=\frac{V^2}{127R}=0.2835
$$

**f = 0.283**. This is more than the permissible 0.15 to 0.17, so the vehicle would skid sideways. Hence superelevation is necessary.

**Answer:** (i) $e=0.113$; (ii) $f=0.283$.

## Check yourself

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

1. Which equation relates e, f, V (km/h) and R?
   A. e + f = V^2 / (127 R)
   B. e + f = V^2 / (225 R)
   C. e - f = V^2 / (127 R)
   D. e f = V^2 / R
   Answer: A. The force balance on a banked curve gives e + f = V^2/127R = 0.2835. (Key point: Balance equation)

2. What e is needed when f = 0.17 is fully used?
   A. 0.2835 + 0.17 = 0.4535
   B. e = 0.2835 - 0.17 = 0.1135
   C. 0.17
   D. 0.2835 x 0.17
   Answer: B. e = V^2/127R - f. (Key point: Full friction)

3. What friction is needed when e = 0?
   A. f = 0.1135
   B. f = 0.17 exactly
   C. f = 0.2835, above the permissible limit, so the vehicle would skid
   D. f = 0.0
   Answer: C. With e = 0, f must supply all of V^2/127R, which exceeds 0.15 to 0.17. (Key point: No superelevation)

## 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 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 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
- [Valley curve design, 100 kmph, 1 in 40](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-valley-100-312) — Transportation Engineering I, chapter 3, asked 2×
- [Vertical curve +2% and +5.5%, 60 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-79c-vc-2-55) — 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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