1.21.1. Adjustment of a closed traverse

Due to errors present in the observations, the coordinates of a closed traverse stations when plotted may not close itself, but will have a small difference. The errors in the linear and angular observations therefore are to be adjusted before using them for computational purpose. It is also called Balancing a Traverse. These errors include: (a) Adjustment of angular errors (b) Adjustment of bearings. (c) Adjustment of closing error of traverse

In a closed traverse, when you collect data from various measurement points, inaccuracies or errors can emerge due to various factors. As a result, the final plotted coordinates may not coincide as expected. This discrepancy is termed the 'closing error'. To correct these errors before proceeding with calculations, adjustments are made in three main areas: angular errors (related to the angles measured), bearings (the directional readings), and closing errors (the overall difference in coordinates). Balancing a traverse ensures that the data is accurate for further analysis.

Imagine you're following a map to navigate through a city but misread some directions along the way. When you arrive at the final destination, you realize that you're a block away from where you intended to be. Adjusting your path based on the initial mistakes is like balancing a traverse; you're correcting your route to ensure you end up where you need to go.

(a) Adjustment of angular error In a closed traverse, the sum of all interior angles should be equal to (2n–4) x 900, and that of the exterior angles should equal (2n + 4) x 900, where ‘n’ is the number of sides in a closed traverse. The difference between this sum and the sum of the measured angles in a closed traverse is called the angular error of closure. The angular error of closure should not exceed the least count of theodolite (x) used, i.e., x √n. If it exceeds, observations are to be repeated. These permissible errors are shown in Table 1.6.

Every closed traverse has a specific expectation for the sum of its interior angles, calculated using the number of sides (n) in the traverse. If the sum of the measured angles deviates from this expected total, this difference is known as the angular error of closure. To ensure accuracy, this error must stay within certain limits; if it falls outside, it's necessary to repeat the observations. The permissible error thresholds can vary depending on the precision requirement of the survey.

Think of building a model with blocks. If you measure the space wrong for your corners, the structure won't fit together properly. Just as you must double-check measurements before committing, surveyors confirm that their angles align with the expected values to ensure their 'building' (the traverse) fits perfectly.

(b) Adjustment of bearings Many times, bearings of a traverse are measured, instead of angles. In such cases, the closing error in bearings may be determined by comparing the fore bearing of a line and back bearing of that line of a closed traverse, as they should differ by 1800. The difference is the error which has to be adjusted in the bearings. Alternatively, we compare the known bearing of the traverse line with the measured bearing, and difference, if found, is adjusted in the bearings.

When working with bearings instead of direct angle measurements in a closed traverse, surveyors must ensure that the fore bearing (the direction to the line) and the back bearing (the direction from the line) of the same traverse line are accurate; they should ideally differ by 180 degrees. If there's a discrepancy, it's considered a closing error that needs adjustment. By verifying and correcting these bearings, surveyors help ensure that all calculated directions are consistent and reliable.

Imagine you're at a beach with friends, and you agree to meet at a certain spot by following a marker. If one person walks the wrong way (say, they aim for the marker but aren’t looking closely), they might end up far from the group instead. Correcting their route by checking the path against the known marker is like adjusting the bearings to ensure everything aligns.

(c) Adjustment of closing error For all the sides of traverse, latitude and departure are computed using the adjusted RB of lines, and proper sign is used as per the quadrant of traverse line. Ideally, the sum of all latitudes and sum of all departures must be zero in a closed traverse. But due to errors in the field measurements (e.g., bearings, distances, etc., the sum of all latitudes and sum of all departures, individually, may not come out to be zero).

In a closed traverse, after adjusting for angular and bearing errors, it's essential to analyze the latitude (north-south distances) and departure (east-west distances) calculations for each side. Ideally, when summed up, these adjustments should balance out to zero which indicates complete closure. However, practical errors can cause these sums to differ, leading to a closing error. Identifying this discrepancy is crucial for ensuring the overall accuracy of the traverse.

Consider a relay race where each runner has to finish at the same line. If one runner takes a longer route, the final team's distance will be off. It’s essential to adjust the timing or speed of the last runner to ensure they all finish at the goal line together, similar to adjusting latitudes and departures to ensure all sides of a traverse meet accurately.

The latitudes and departures are now adjusted by applying the correction to them in such a way that the algebraic sum of the latitudes and departures should be equal to zero. Any one of the two rules (Bowditch Rules and Transit Rules) may be used for finding the corrections to balance the survey: (1) Bowditch Rule: It is also known as the Compass rule. It is used to adjust the traverse when the angular and linear measurements are equally precise. (2) Transit Rule: The Transit rule is used to adjust the traverse when the angular measurements are more precise than the linear measurements.

To effectively balance the traverse, corrections are applied to ensure that both the latitude and departure sums equal zero. Two common methods are employed for this process: the Bowditch Rule, which is suitable when all measurements are equally precise, and the Transit Rule, which is advantageous when angular measurements are more reliable than linear ones. These rules help in distributing the error corrections efficiently across the traverse.

Think about editing a group essay. If one person’s contribution is off-topic, you might need to adjust their content to ensure coherence. Using a uniform editing approach (like the Bowditch Rule) keeps it simple while selectively correcting more precise contributions (like the Transit Rule) makes for a clearer, refined final product.

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