---
title: "Transition curve and edge elevations, hilly terrain"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-79a-tc-super-elevations"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-79a-tc-super-elevations
site: BCT Engineering
---

# Transition curve and edge elevations, hilly terrain

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2079 Ashwin, 8 marks
- Video: [Calculate Transition Curve Length and Curve Shift for a 70 km/h Highway || Transportation Curve](https://www.youtube.com/watch?v=Ujq1XpkrFKM) — OPengineer
- 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-79a-tc-super-elevations
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A transition curve is to be provided to connect a straight and circular curve of radius 325 m of a two lane road in a hilly terrain with heavy rainfall. Design the length of transition curve assuming suitable data. The design speed of the highway is 60 kmph and rate of introduction of super elevation is to be 1 in 60. Determine the elevations of outer edges at two typical straight and circular curved sections of the road with centre line at elevations of 312.23 m and 312.9 m respectively considering a parabolic camber of 2.5% to be provided.

## Short answer

Superelevation e=5%. Transition length from centrifugal acceleration, superelevation introduction rate, and empirical formula is 25 m. Outer edge RL on straight is 312.14 m; on circular curve it is 313.08 m.

## Answer

**Given:** $R = 325$ m, $V = 60$ km/h, two-lane road in hilly terrain with heavy rainfall, rate of introduction of superelevation 1 in 60, centre-line levels 312.23 m (straight) and 312.9 m (circular curve), parabolic camber 2.5%.

**Assumptions:** carriageway $W = 7.0$ m; extra widening is neglected for edge levels; the pavement is rotated about the centre line.

#### Step 1: Superelevation
$$
e = \frac{V^2}{225R} = \frac{60^2}{225\times325} = 0.0492 \approx 5\%
$$
Check: $f = \dfrac{60^2}{127\times325} - 0.05 = 0.037 < 0.15$, OK. ($e_{max}=10\%$ in hills, and not more than 7% in snowy areas.)

#### Step 2: Length of transition curve ($v = 16.67$ m/s)
- **Centrifugal acceleration:** $C = \dfrac{80}{75+60} = 0.593$ m/s³, $L_s = \dfrac{v^3}{CR} = \dfrac{16.67^3}{0.593\times325} = 24.0$ m
- **Superelevation rate 1 in 60:** the outer edge rises from $-nW/2 = -0.0875$ m (below the crown) to $+eW/2 = +0.175$ m, a rise of 0.2625 m:
  $L_s = 60\times0.2625 = 15.75$ m
- **IRC empirical (mountainous/steep terrain):** $L_s = \dfrac{V^2}{R} = \dfrac{60^2}{325} = 11.1$ m (the formula $2.7V^2/R$ applies only to plain and rolling terrain)

Adopt the largest, rounded up: **$L_s = 25$ m**.

#### Step 3: Outer edge elevations
**Straight section (centre line 312.23 m):** with a parabolic camber of 2.5% on a 7.0 m carriageway, the drop from crown to edge $= n\,W/2 = 0.025\times3.5 = 0.0875$ m.
$$
RL_{outer} = 312.23 - 0.0875 = \mathbf{312.14\ m}
$$

**Circular curve section (centre line 312.9 m):** full superelevation of 5%, with the pavement rotated about the centre line, so the outer edge is raised $eW/2 = 0.05\times3.5 = 0.175$ m.
$$
RL_{outer} = 312.90 + 0.175 = \mathbf{313.08\ m}
$$
(The inner edge is at $312.90 - 0.175 = 312.73$ m.)

**Answer:** $e = 5\%$, $L_s = 25$ m; outer edge levels: 312.14 m on the straight and 313.08 m on the circular curve.

## Check yourself

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

1. For V = 60 km/h and R = 325 m, the superelevation e = V^2/(225R) is about
   A. 0.049, adopt 5%
   B. 0.113
   C. 0.15
   D. 0.025
   Answer: A. 3600/(225 x 325) = 0.0492, adopted as 5%. (Key point: Superelevation)

2. The outer edge rises from -0.0875 m to +0.175 m. What is Ls for 1 in 60?
   A. 60 x 0.175 = 10.5 m
   B. 60 x 0.2625 = 15.75 m
   C. 60 x 0.0875 = 5.25 m
   D. 30 m
   Answer: B. The total rise is 0.2625 m, so Ls = 60 x 0.2625 = 15.75 m. (Key point: Transition length criterion with 1 in 60)

3. Criteria gave 24.0 m, 15.75 m and 29.9 m. The adopted Ls is
   A. 15.75 m
   B. 24.0 m
   C. 30 m, the greatest rounded
   D. The average, 23 m
   Answer: C. The greatest governs: Ls = 30 m. (Key point: Adopted transition length)

4. On the straight, with centre line 312.23 m and 2.5% camber on 7 m, the outer edge level is
   A. 312.32 m
   B. 312.14 m
   C. 312.23 m
   D. 311.98 m
   Answer: B. Drop = 0.025 x 3.5 = 0.0875 m; 312.23 - 0.0875 = 312.14 m. (Key point: Outer edge on the straight)

5. On the circular curve with centre line 312.9 m, e = 5%, rotation about the centre line, the outer edge is
   A. 312.73 m
   B. 312.81 m
   C. 313.08 m
   D. 313.25 m
   Answer: C. Outer edge is raised eW/2 = 0.05 x 3.5 = 0.175 m, giving 313.075, about 313.08 m. (Key point: Outer edge on circular curve)

## Related in Transportation Engineering I

- [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
- [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 for 310 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-80c-tc-310) — 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 for 300 m radius, 7 m pavement](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-64p-tc-300) — 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

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