---
title: "Converting two-way slope to one-way slope"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:super-attainment-drainage"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/super-attainment-drainage
site: BCT Engineering
---

# Converting two-way slope to one-way slope

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2065 Kartik (old course), 8 marks; 2064 Poush (old course), 8 marks (asked 2 times)
- Video: [How to Calculate Slope / Level of Camber & Superelevation in Highway / Road || By Civil Guruji](https://www.youtube.com/watch?v=bHCpaskWlec) — The Institute of Construction Managment 
- 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-attainment-drainage
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Due to drainage problem, the inner edge cannot be lowered and a superelevation of 'e' is to be introduced. Explain with the help of a neat sketch how you obtain the one way slope, e, from the two way slope, n, where e > n. Given the road width is W m and the transition curve length is L m.

## Short answer

When the inner edge is fixed, rotate the pavement about the inner edge over transition length L. The outer half levels at distance nL/(2e), reaches one-way slope n at nL/e, and full slope e at L; the outer edge finally is eW above the inner edge and the centre rises (e-n)W/2.

## Answer

When the inner edge cannot be lowered (because of a drainage problem), the pavement is rotated about the **inner edge** and the outer edge is raised. The two-way (cambered) section with slope $n$ on each side is changed to a one-way section of slope $e$ over the transition length $L$ in three stages.

#### Notation
$W$ = pavement width, $n$ = camber, $e$ = full superelevation ($e>n$), $L$ = length of transition. The inner edge level is held fixed. The outer edge must rise by $eW$ relative to the inner edge over $L$ (at a uniform rate $eW/L$).

#### Stages (cross-sections)
```text
 A (normal)      B (outer flat)  C (one-way n)   D (one-way e)
   /\            ____/            ___.-'          ___.---'
  /  \          /                ./              ./   
 inner fixed at all sections --> ^ (same level)
```
- **Section A (start):** normal crown, both halves slope at $n$.
- **Stage 1 (A to B):** the outer half is rotated about the crown until it is level (slope $0$). The outer edge rises $nW/2$, so B is at a distance
  $$
  x_B = \frac{nW/2}{eW/L} = \frac{nL}{2e}
  $$
- **Stage 2 (B to C):** the outer half is rotated further until the whole pavement has a uniform one-way slope $n$. The outer edge has now risen $nW$ in all:
  $$
  x_C = \frac{nW}{eW/L} = \frac{nL}{e}
  $$
- **Stage 3 (C to D):** the whole pavement is rotated about the inner edge, increasing the one-way slope from $n$ to $e$ at the end of the transition, $x_D = L$. The outer edge has risen $eW$.

#### Level of the outer edge
At a distance $x$ from the start, the outer edge is $\dfrac{eW}{L}x$ above its original level (relative to the inner edge). At D, the outer edge is $eW$ above the inner edge, and the centre line has risen by $\dfrac{(e-n)W}{2}$ above its original level.

Any extra widening is provided over the same length $L$.

## Check yourself

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

1. When the inner edge cannot be lowered due to drainage, about which line is the pavement rotated?
   A. The crown
   B. The centre line
   C. The outer edge
   D. The inner edge
   Answer: D. The inner edge level is held fixed and the outer edge is raised. (Key point: Axis of rotation)

2. In stage 1 (A to B), what is done to the outer half of the pavement?
   A. It is rotated about the crown until it is level (slope 0)
   B. It is lowered below the inner edge
   C. It is given the full slope e
   D. It is widened by L
   Answer: A. The outer half is first rotated about the crown to flat, raising the outer edge by nW/2. (Key point: Stage 1)

3. At what distance from the start does the whole pavement get a uniform one-way slope n?
   A. nL/2e
   B. eL/n
   C. nL/e
   D. L
   Answer: C. The outer edge has to rise nW at the rate eW/L, giving x = nL/e. (Key point: Distance to section C)

4. What happens in stage 3 (C to D)?
   A. The crown is reintroduced
   B. The whole pavement is rotated about the inner edge, increasing the one-way slope from n to e at distance L
   C. The inner edge is lowered by eW
   D. Only the inner half is rotated
   Answer: B. From C to D the full pavement rotates about the inner edge until slope e is reached at the end of transition L. (Key point: Stage 3)

## Related in Transportation Engineering I

- [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 and edge elevations, hilly terrain](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-79a-tc-super-elevations) — Transportation Engineering I, chapter 3
- [Raising outer edge for superelevation](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-63k-super-raise) — Transportation Engineering I, chapter 3
- [Transition curve 220 m, pavement 7 m](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-77c-tc-220) — Transportation Engineering I, chapter 3
- [Transition curve length and shift, 7.2 m pavement](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-62j-tc-shift) — Transportation Engineering I, chapter 3
- [Transition curve length from spiral angle 10.32](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-73bh-tc-spiral) — Transportation Engineering I, chapter 3, asked 2×

## Related in other subjects

- [Isochrones, one and two way drainage](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aisochrones-one-two-way-drainage) — Soil Mechanics, chapter 9
- [One-way vs two-way drainage time](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aone-way-two-way-drainage-time) — Soil Mechanics, chapter 9
- [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×