# Vertical Alignment of Highways - IES Previous Year Questions

1.â€ƒA summit curve is formed at the intersection of a 3% up gradient and 5% down gradient. To provide a stopping distance of 128 m, the length of the summit curve needed will be _____ .

**[IES 1995, IES 2005]**

- 298 m
- 322 m
- 340 m
- 271 m

**Answer:**Option A

**Explanation:**

N

_{1}= 0.03, N

_{2}= - 0.05

Deviation angle, N = | N

_{1}- N

_{2}| = | 0.03 - (-0.05) | = 0.08

For Stopping Sight Distance,

Height of driverâ€™s eye, H = 1.2 m

Height of obstacle, h = 0.15 m

Assuming L > SSD, L =

^{2}/ (√ 2H + √ 2h )

^{2}

⇒ L =

^{2}/ (√ 2 x 1.2 + √ 2 x 0.15 )

^{2}

Hence, Length of summit curve = 297.89 m

2.â€ƒWhich of the following are the criteria associated with the design of sag vertical curve ?

- Provision of minimum stopping sight distance.
- Adequate drainage.
- Comfortable operation.Â
- Pleasant appearance.

Select the correct answer using the codes given below:

**[IES 1996]**

- 2 and 3
- 2, 3 and 4
- 1 and 3
- 1, 2 and 4

**Answer:**Option B

**Explanation:**

The design of the valley (sag) curve depends on

- Rider's comfort
- Headlight Sight Distance
- Drainage at lowest point
- Aesthetic appearance

3. â€ƒWhich of the criteria given below are used for the design of valley vertical curves on roads ?

- Rider comfort
- Headlight sight distance
- Drainage

Select the correct answer using the codes given below:

**[IES 1998]**

- 1 and 3
- 2 and 3
- 1 and 2
- 1, 2 and 3

**Answer:**Option D

**Explanation:**

The design of the valley curve depends on

- Rider's comfort
- Headlight Sight Distance
- Drainage at lowest point
- Aesthetic appearance

4. â€ƒIf a descending gradient of 1 in 25 meets an ascending gradient of 1 in 40, then the length of valley curve required for a headlight sight distance of 100 m will be _____ .

**[IES 1999]**

- 130 m
- 310 m
- 630 m
- 30 m

**Answer:**Option A

**Explanation:**

N

_{1}= - 1/25, N

_{2}= 1/40

Deviation angle, N = | N

_{1}- N

_{2}| = | (-1/25) - (1/40) | = 0.065

For Headlight Sight Distance,

Height of headlight, h

_{1}= 0.75 m

Angle of Headlight, α = 1°, tan 1° = 0.0175

Assuming L > HSD, L =

^{2}/ 2h

_{1}+ 2S tan α

⇒ L =

^{2}/ (2 x 0.75) + (2 x 100 x 0.0175)

Hence, Length of valley curve = 130 m

5. â€ƒAn ascending gradient of 1 in 100 meets a descending gradient of 1 in 50. The length of the summit curve required to provide an overtaking sight distance of 500 m will be _____ .

**[IES 1999]**

- 781 m
- 470 m
- 170 m
- 938 m

**Answer:**Option A

**Explanation:**

N

_{1}= 1/100, N

_{2}= - 1/50

Deviation angle, N = | N

_{1}- N

_{2}| = | (1/100) - (-1/50) | = 0.03

For Overtaking Sight Distance,

Height of driverâ€™s eye, H = 1.2 m

Height of obstacle, h = 1.2 m

Assuming L > OSD, L =

^{2}/ (√ 2H + √ 2h )

^{2}

⇒ L =

^{2}/ (√ 2 x 1.2 + √ 2 x 1.2 )

^{2}

Hence, Length of summit curve = 781.25 m

6. â€ƒThe camber provided on a sloping road is 1 in 48. Which one of the following is the ruling gradient ?

**[IES 2003]**

- 1 in 20
- 1 in 24
- 1 in 30
- 1 in 15

**Answer:**Option C

**Explanation:**

As per IRC, the ruling gradient for plain and rolling (sloping) terrain is 1 in 30.

7. â€ƒWhich one of the following are the accepted criteria for design of valley curve for highways ?

- Headlight sight distance
- Passing and non-passing sight distance
- Aesthetic consideration
- Motorist comfort
- Drainage control

Select the correct answer using the codes given below:

**[IES 2003]**

- 1, 3, 4 and 5
- 2, 3, 4 and 5
- 1 and 5
- 1, 2, 3 and 4

**Answer:**Option A

**Explanation:**

The design of the valley curve depends on

- Rider's comfort
- Headlight Sight Distance
- Drainage at lowest point
- Aesthetic appearance

8. â€ƒA rising gradient of 1 in 50 meets a falling gradient of 1 in 30. Which one of the following is the length of the vertical curve if the stopping sight distance is 120 m?

**[IES 2006]**

- 158 m
- 140 m
- 120 m
- 174 m

**Answer:**Option D

**Explanation:**

N

_{1}= 1/50, N

_{2}= - 1/30

Deviation angle, N = | N

_{1}- N

_{2}| = | (1/50) - (- 1/30) | = 0.053

For Stopping Sight Distance,

Height of driverâ€™s eye, H = 1.2 m

Height of obstacle, h = 0.15 m

Assuming L > SSD, L =

^{2}/ (√ 2H + √ 2h )

^{2}

⇒ L =

^{2}/ (√ 2 x 1.2 + √ 2 x 0.15 )

^{2}

Hence, Length of vertical curve = 174.5 m

9. â€ƒA 3% downgrade curve is followed by a 1% upgrade curve and rate of change of grade adopted is 0.1% per 20 m length. The length of the respective vertical curve is _____ .

**[IES 2011]**

- 200 m
- 100 m
- 400 m
- 800 m

**Answer:**Option D

**Explanation:**

N

_{1}= - 0.03, N

_{2}= 0.01

Thus, total deviation angle N = | N

_{1}- N

_{2}| = |-0.03 - 0.01 | = 0.04 = 4%

Rate of change of gradient = 0.1% per 20 m

For 0.1% change in gradient, length = 20 m.

Hence, for 4% change in gradient, length =

10. â€ƒWhile aligning a hill road with a ruling gradient of 6%, a horizontal curve of 75 m radius is encountered. The compensated gradient at the curve will be _____ .

**[IES 2014]**

- 2%
- 3%
- 5%
- 1%

**Answer:**Option C

**Explanation:**

Grade Compensation =

Thus, grade compensation = 1.0%

Compensated gradient = Ruling gradient - grade compensation

⇒ Compensated gradient = 6 - 1 = 5%