**Vertical Curves**

**12.1 Introduction**

Vertical curves are used to calculate proposed road centerline level and hence provide a smooth transition from one grade to another on a road centerline.

**12.2 Types of vertical curve**

Vertical curves may be either a SUMMIT or a Valley curve, although there are other types such as HOGGING and CREST curves.

Figure 4.39 – Types of vertical curvel

These curves can be calculated as:

(a) A simple parabola - the commonest case

(b) A circular curve - this gives similar results to the simple

parabola

© A cubic parabola - used to prevent heavy earthworks

**12.3 Terminology**

IP - Intersection point. Point where two

Grades intersect.

Grade anle - An angle, quoted as a % which

Represents the total change in grade.

Grade 1 (g1%) - First grade expressed as a %

Grade 2 (g2%) - Second grade expressed as a %

BVC - Tangent point at beginning of

Vertical curve.

EVC - Tangent point at end of vertical curve

Curve length - Horizontal length between tangent

Points.

Tangent length - Horizontal length between tangent

Point and IP.

Figure 4.40 – Vertical curve terminology.

**12.4 Calculation of a vertical curve**

**(a)**

**Calculate grades from given reduced levels and chainages defining the straights by using:**

**Difference in height**

**Grade % = ------------------------------------x 100**

Difference in chainage

(b) Calculate grade angle (A) from g1% - g2%. Ignore the sign if the result is negative

(c) Determine curve length (L) from L = A x K

Where A = grade angle

K = a constant (usually 6 on housing sites) from

“Roads in urban areas”.

The curve length will probably be quoted on the drawing and this should be used.

(d) Determine chainage of tangent points from:

Chainage of IP + tangent lengths

Where tangent length – L/2

(e) Calculate grade levels at each required chainage.

(f) Calculate ordinates at each chainae. These can be calculated as follows.

(i) Simple parabola

Distance from nearest TP

Ordinate = --------------------------------- x Vo

Tangent length

Where V0 =

__A x T__

400

(ii) Circular arc

Ordinate =(

__distance from nearest TP)2__

2 x radius

where radius =

__L__x 100

A

Figure 4.41 – Vertical offset and ordinates

VERTICAL CURVE CALCULATION SHEET

VERTICAL CURVE CALCULATION SHEET

Figure 4.42 – Calculation sheet.

(a) Calculate cuve levels – see Figure 4.41

(i) Summit curve

Curve level = grade level – ordinate

(ii)Valley curve

Curve level = grade level + ordinate

**12.5 Calculation sheet**

For ease of calculation and for providing a permanent record use a calculation sheet as shown in Figure 4.42