We now consider how these are determined.

**Co-ordinates and EDM Distance**

The EDM column is used to show the straight line distance between TP1 and the point being set out. This distance is calculated using Sine of the deflection times 2R.

All these values are shown in Table 5 ( you might verify the calculation)

So at TP2 EDM = Sin 2.5 x 1800 = 78.515 (Distance along the chord from TP1 to TP2)

Table 5: EDM & Co-ordinates

If we assume that TP1 is at 100 East and 100 North and that the tangent runs due north we can calculate the co-ordinates. In practice the tangent may run either east or west of north by a given angle. In this example we keep this example simple by saying the tangent runs due north.

Co-ordinates are calculated for each point. We will look at a value mid table at chainage 370.

Using the EDM which is the hypotenuse of the triangle along with the deflection angle 1 22 7.51 we can determine the distance north and the distance east from the tangent point.

Distance north = Cos 1 22 7.51 x 42.996 = 42.984 + 100 = 142.984

Distance East = Sin 1 22 7.51 x 42.996 = 1.027 + 100 = 101.027

**Setting Out Curves: Measurement**

A common method used is halving and quartering. We can think of a curve as having a chord and a major offset thus:

Figure 12: Chord & Major Offset

Let us call the half chord (L) and the major offset (D)

To set out a curve using these parameters we use the following method:

- Establish the chord at say 50m and the major offset at 1m at the centre (L = 25 D= 1)
- Extend the lines as shown in blue and find the centre of each one (halving) (Fig 13)
- At each centre point project D/4 (quartering) as shown offset is now 250 mm
- Continue halving the sub chord an quartering the previous offset until the required curve is produced.

Figure 13

**Formulae **