1.21.2. Computation of coordinates

Very popular method of showing the adjustment of closing error as well as computation of coordinates is systematically done using Gale’s Traverse Table.

Gale's Traverse Table is a systematic method used for the calculation of coordinates and adjustment of closing errors in a closed traverse. This method organizes the necessary calculations in an easy-to-follow way, formatting them into a table. It helps surveyors ensure that their measurements are accurate and that any errors are corrected appropriately.

Think of Gale's Traverse Table like a recipe for baking a cake. Just like a recipe lists ingredients and steps to follow for a perfect cake, Gale's Table lays out steps for calculating coordinates and making corrections to ensure the results are right.

The computations for a closed traverse may be made in the following steps and entered in a tabular form known as Gale’s Traverse, as shown in Table 1.8.

There are several sequential steps that surveyors follow to effectively use Gale's Traverse Table. These steps include adjusting included angles, calculating adjusted reduced bearings, computing latitudes and departures, applying necessary corrections to ensure that the total latitudes and departures equal zero, and finally plotting the traverse stations.

Consider these steps like assembling a piece of furniture. First, you make sure all the parts are correct and organized (like adjusting angles), then you figure out how each piece connects (calculating bearings), make sure everything fits as it should (correcting latitudes and departures), and finally, you put everything together to see the completed piece (plotting the stations).

(i) Adjust the included angles, if the sum is not equal to (2n-4) x 900, as explained above.

One of the steps involves checking and adjusting the included angles of the traverse. The total of these angles in a closed traverse should match a specific calculation based on the number of sides. If they don’t match, adjustments must be made to correct the angles for accurate results.

This is similar to ensuring a group of friends standing in a circle form a perfect shape. If one friend is out of place and the total angles don’t add up correctly, you would need to ask that friend to adjust their position to restore the intended circular shape.

(ii) Calculate the adjusted RB of all traverse lines, as explained above.

After adjusting the angles, the next step requires calculating the adjusted reduced bearings for each line of the traverse. This ensures that the bearings accurately reflect any changes made during the angle adjustments. Proper bearings are crucial for the correct plotting of points.

Think of this like recalibrating a compass after adjusting a map's orientation. You need to ensure the compass points correctly in relation to the new angles represented on the map before proceeding with navigation.

(iii) Compute the latitudes and departures (consecutive coordinates) of traverse lines, as explained above.

Surveyors compute the latitudes and departures for each line in the traverse. These calculations help determine the exact position of each point based on the adjusted bearings and the traversed distances. Latitudes indicate the north-south position, while departures indicate the east-west position.

Imagine you are setting waypoints on a treasure map. Each latitude and departure is like a marked spot that tells you exactly where to look for buried treasures, helping you navigate precisely.

(iv) Apply the necessary correction to the latitude to the latitudes, and departures so that the sum of the corrected latitudes is zero and sum of corrected departures is equal to zero.

Surveyors must ensure that every latitude and departure calculated sums up to zero overall for a closed traverse. Any discrepancies may indicate errors in the earlier measurements, which need correction before finalizing results.

This process can be likened to balancing your bank account. If your transactions don’t add up to zero, you need to identify where an error might have occurred and correct it to ensure math accuracy in your finances.

(v) By knowing the exact coordinates of a traverse point, find the independent coordinates of the remaining traverse points from the consecutive coordinates.

Once a point on the traverse has its coordinates established, the independent coordinates of other points can be determined based on their relationship to the established point. This uses previously calculated latitudes and departures.

This is much like building a neighborhood by defining one house's address first. Once that house is set, all other addresses can be derived based on their positions relative to the first house.

(vi) Plot all the traverse stations on a plan for map preparation.

Finally, once all corrections and calculations have been made, surveyors will plot the verified traverse stations on a map. This visual representation consolidates all the data collected during the traverse, allowing for effective area mapping.

This final plotting stage is like creating a detailed map for an amusement park after all the rides have been built. You need all the ride locations accurately represented so visitors can navigate easily.

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