---
title: "Vertical curve at PVI 243.154 m"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-64s-vc-243"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-64s-vc-243
site: BCT Engineering
---

# Vertical curve at PVI 243.154 m

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2064 Shrawan (old course), 8 marks
- Video: [Vertical Curve Fundamentals | Highway Alignment and Design](https://www.youtube.com/watch?v=qZVZyf_9r2k) — Daniel Findley
- 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-64s-vc-243
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A descending section of a road with 3% grade meets an ascending section with 4% grade. Design the vertical curve. The stopping sight distance requirement is 120 m. Calculate the formation levels of main points on curve and at a distance of 30 m both sides from the point of vertical intersection (PVI). The reduce level of PVI is 243.154 m. Assume other data suitably.

## Short answer

L = 180 m; BVC = 245.85 m, EVC = 246.75 m; 30 m before PVI = 244.75 m, after = 245.05 m; lowest point at 77.1 m from BVC, RL = 244.70 m.

## Answer

A −3% grade meeting +4% is a **valley curve**; $N=0.03+0.04=0.07$. PVI RL = 243.154 m.

#### Assumptions
SSD $S=120$ m (given) corresponds to a design speed of about 77 km/h for $t=2.5$ s and $f=0.35$, so $V=75$ km/h is taken for the comfort check. Headlight height 0.75 m, beam angle 1°, $C=0.6$ m/s³.

#### Length of curve
- Headlight criterion ($L>S$): $L=\dfrac{NS^2}{1.5+0.035S}=\dfrac{0.07(120)^2}{1.5+0.035(120)}=176.8$ m
- Comfort criterion: $L=2\sqrt{\dfrac{NV^3}{C}}=2\sqrt{\dfrac{0.07(20.83)^3}{0.6}}=65.0$ m

Adopt **L = 180 m**; half = 90 m.

#### Formation levels

$$
RL_{BVC}=243.154+0.03(90)=245.854\ \text{m},\qquad RL_{EVC}=243.154+0.04(90)=246.754\ \text{m}
$$

With $x$ from BVC: $y=RL_{BVC}-0.03x+\dfrac{0.07x^2}{2(180)}$.
- 30 m before PVI ($x=60$ m): $y=\mathbf{244.754}$ m
- 30 m after PVI ($x=120$ m): $y=\mathbf{245.054}$ m
- Lowest point: $x=\dfrac{0.03(180)}{0.07}=77.14$ m from BVC, $y=\mathbf{244.697}$ m

**Answer:** L = 180 m; BVC = 245.85 m; EVC = 246.75 m; 30 m before PVI = 244.75 m; 30 m after PVI = 245.05 m; lowest point = 244.70 m.

## Check yourself

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

1. A -3% grade meets +4%. Type and N?
   A. Valley curve, N = 0.07
   B. Summit curve, N = 0.07
   C. Valley curve, N = 0.01
   D. Summit curve, N = 0.01
   Answer: A. Descending then ascending is a valley curve; N = 0.03 + 0.04. (Key point: Curve type)

2. Headlight gives 176.8 m and comfort 65.0 m. What is adopted?
   A. 65 m, the comfort length
   B. 180 m, as the headlight (larger) criterion governs
   C. 120 m, equal to S
   D. 115 m, the average
   Answer: B. The larger of the two lengths is used. (Key point: Governing criterion)

3. How is RL_BVC found?
   A. RL_PVI + g1 x L/2 = 243.154 + 0.03(90)
   B. RL_PVI - 0.03(90)
   C. RL_PVI + 0.04(90)
   D. RL_PVI + NL/8
   Answer: A. BVC is on the descending tangent, above the PVI. (Key point: BVC level)

4. Which equation gives levels on the valley curve?
   A. y = RL_BVC - g1 x - N x^2/(2L)
   B. y = RL_BVC + g1 x + N x^2/(2L)
   C. y = RL_BVC - g1 x + N x^2 / (2L)
   D. y = RL_BVC - g1 x
   Answer: C. Valley curve lies above the tangent, so the offset is added. (Key point: Level on curve)

## Related in Transportation Engineering I

- [Vertical curve with 300 m grade sections](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-65k-vc-300) — Transportation Engineering I, chapter 3
- [Vertical curve for overtaking sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81c-vc-overtaking) — Transportation Engineering I, chapter 3
- [Vertical curve elevations at 185 m from PVI](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-72m-vc-185) — Transportation Engineering I, chapter 3
- [Vertical curve with intermediate sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81a-vc-intermediate) — Transportation Engineering I, chapter 3
- [Vertical curve 35 m headlight and momentum grade](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-80c-vc-headlight-35m) — Transportation Engineering I, chapter 3
- [Stopping sight distance at 50 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-66m-ssd-50) — Transportation Engineering I, chapter 3

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