## 5 Methods for Plotting a Traverse Survey

**The five main methods for plotting a traverse survey are as follows: **

1. By running parallel meridian lines through each station

2. Using Included Angles

3. Using the Central Meridian or a Paper Protractor

5. Using Chords.

**Method # 1. By Parallel Meridians through Each Station:**

It is the first and most famous **method of plotting a traverse survey**.

After properly locating the starting point, say A, draw a line representing the magnetic meridian. Then, using a protractor, plot the bearing of line AB (1) (fig 5.22), and cut AB to scale. Then, at B, draw a line parallel to the previous line representing the meridian, plot BC (2)'s bearing, and measure its length with the scale. Rep the process until all of the lines are drawn. If the traverse is closed, the last line should end at the beginning. The difference is referred to as the closing error if it does not.

This method is flawed because the **error in plotting** the direction of a single line is carried forward throughout the traverse.

**Method # 2. By Included Angles:**

Draw the meridian at starting station A, plot the bearing of line AB (1), and measure length AB to the scale (Fig. 5.23). Then, using a protractor, draw the angle ABC at B and cut off the length BC to scale. Rep the procedure at each succeeding station.

**Although the liability of a cumulative error in protracting the angles is similar to that of the first method, this is preferred over the first because:**

(i) Drawing parallel **meridians** is both necessary and inconvenient.

(ii) The liable error in the parallelism of all meridian lines is removed.

**Method # 3. ****By Central Meridian or Paper Protractor:**

In this method, a point, say O, is chosen in the center of the paper, and a meridian line is drawn through it. The bearing of all the lines is then plotted concerning this meridian using the protractor stationed at O, as shown in fig 5.24. The starting station, say A, is appropriately chosen on the sheet, line AB is drawn parallel to the respective line, and its length is cut off to scale. Continue in this manner until all of the lines are drawn.

The method is preferred over both preceding methods because the direction of all the lines is plotted from a single setting of the protractor, avoiding the possibility of error in placing the protractor at each station. However, errors may accumulate as a result of incorrect parallel line drawing.

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**Method # 4. ****By Rectangular Co-Ordinates:**

This method is commonly used for precise work, primarily closed and open **theodolite traverses**.

The positions of various points are plotted on a plan using two lines, yy1 (y-axis) and xx1 (x-axis), which are parallel and perpendicular to the meridian, respectively (Fig. 5.25). These reference lines are the axes of coordinates, and the point of intersection O is known as the origin.

The origin can be any traverse station or completely outside the traverse. A point's coordinates are the distances it has from each axe.

If a line's length and bearing are known, its projection on the y- and x-axes can be calculated and plotted.

This method is the most accurate of **all plotting methods** because it eliminates using a protractor and allows each point to be plotted independently of the others. As a result, plotting errors do not accumulate.

**Method # 5. By Chords:**

The angle between the various lines is plotted using geometrical construction and a table of natural sines. An angle's chord is twice the size of half the angle. The lengths of chords of angles corresponding to unit radius are given in various **mathematical tables**.

A meridian line is drawn through the starting station, say A, to **plot a traverse**. Draw an arc B1B2 with A as the center and a radius of 10 units, cutting the meridian in B1 (fig 5.26). The chord length B1B2 for the angle B1AB2 (the bearing of AB) is obtained from the chord table or calculated using the relationship, chord B1B2 = 2x 10. sin 1 2. Measure the chord distance B1B2 from B1, marking point B2 on the arc. Join A and B2 to represent the AB direction.

Then remove AB. Draw an arc with a radius of 10 units intersecting the AB produced in C1. The chord distance C1C2 = 2 10 sines of half the **deflection angle** at B is then scaled off from C1, resulting in the fixation of point C2. The direction of BC is determined by point C2 connected to B. Then, using the scale, cut off BC. Other lines are plotted similarly.

Because this method's use of a protractor is completely avoided, it is preferred over the first three methods. This is frequently used to plot open traverses.

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