1. SURVEYING VADODARA INSTITUTE OF ENGINEERING
NAME: Ashish1 Bhargav2 Bhargav3
1-Patel Ashish B, Civil Engineering dept.[ ]
2-Patel Bhargav N, Civil Engineering dept.[ ]
3-Patel Bhargav P, Civil Engineering dept.[ ]
VADODARA INSTITUTE OF ENGINEERING
Guided By
Prof. A. S. Mandot

2. Contents Introduction to Curve Types of Curves Combined Curve
Vertical Curve
Advantages of vertical curve
Types of vertical curve
Summit curve or convex curve
Valley curve or concave curve
Length of vertical curve

3. INTRODUCTION TO CURVES
Curves are provided whenever there is a turning or an inclination in the road or a railway.

4. CURVES Horizontal Curve Vertical Curve
Types of curves
CURVES Horizontal Curve Vertical Curve
Circular Curve
1. Simple Curve
2. Compound Curve
3. Reverse Curve
Transition
Curve
1. Cubic parabola
2. Spiral Curve
3. Lemniscale
1. Summit Curve
2. Valley Curve

5. Vertical curve
A vertical curve is provided when there is a sudden change in gradient of a highway or a railway.
They are provided when a highway or a railway crosses a ridge or a valley.
A vertical curve smoothens the change in gradient so that there is no discomfort to the passenger travelling in vehicles.
The gradient is expressed in percentage.
For example, +2% , means that the slope rises by 2m in every 100.
The grade changes uniformly throughout the curve.

7. Rate of change of gradient
The rate of change of gradient per chain length is equal to the algebraic difference of the two gradients meeting at the apex divided by the length of the curve.
Thus, r=

8. Advantages of vertical curve
Due to vertical curve, change in gradient is gradual.
It improves the appearance of road.
Road and railway journey becomes comfortable.

9. TYPES OF VERTICAL CURVES
There are two types of curves.
Summit curve or convex curve.
Valley curve or concave curve.

10. SUMMIT CURVE OR CONVEX CURVE
Summit curve is provided in following situations.
An upgrade (+ g1) following by a down grade (-g2).
An upgrade (+ g1) following by another upgrade (+ g2). g1 > g2.
A down grade (- g1) following by another down grade (- g2). g2 > g1.
A plane surface followed by down grade (- g1).

11. VALLEY CURVE OR CONCAVE CURVE
Valley curve is provided in following situations.
An upgrade (- g1) following by a down grade (+ g2).
An upgrade (- g1) following by another upgrade (- g2). g1 > g2.
A down grade (+ g1) following by another down grade (+ g2). g2 > g1.
A plane surface followed by down grade (+ g1).

12. Summit Curve
Valley Curve

13. Length or a vertical curve
The length of vertical curve can be obtained by dividing the algebraic difference of the two grades by the rate of change of grade.
Length of curve(L)=Total change of grade Rate of change of grade
= g2- g1 r
Where,
g1,g2 = grades in %
r = rate of change of grade (%)

14. references