In the similar approach Delta L, corrections for the Latitudes are calculated and tabulated. These Corrections are then added to the actual departures and latitudes to get the corrected departures and Latitudes. Further, Final co-ordinates are calculated based on these corrections. This is based on the principle of Probable error by Length and probable error by Squares and roots of lengths.
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In the similar approach Delta L, corrections for the Latitudes are calculated and tabulated. These Corrections are then added to the actual departures and latitudes to get the corrected departures and Latitudes.
Further, Final co-ordinates are calculated based on these corrections. This is based on the principle of Probable error by Length and probable error by Squares and roots of lengths. Initially, the actual departures and Latitudes are calculated based on the Sine and cosine rules.
However, there is a condition that if the sum of Departures is greater than the sum of Latitudes then the operator sign changes. A sample of the same is as shown below. Further the probable errors for Squared and roots are estimated as follows. Initially the Constants K1 and K2 are recalculated by solving the simultaneous equations as shown.
These are substituted to get the Delta values shown below. Review on Least Square method. Least square traverse adjustment is the determination of a set of traverse coordinates which makes the sum of the squares of the residuals a minimum.
The least-squares technique set out above requires at least two points in the traverse network to have fixed coordinate values before a solution for the corrections to the approximate coordinates of the other points can be determined. This constraining of the network can also be achieved by holding one point fixed and the bearing of a traverse line fixed, as well as these minimal constraints it is also possible to have additional fixed points and constrained bearings in the network as well as distances and angles constrained to certain fixed values.
Constraining bearings, distances and angles in a traverse network to specified values means the following equations must be satisfied. Traverse adjustment by the method of Least Squares allows precision estimation of the adjusted coordinates of traverse points as well as derived bearings and distances.
Least Squares is an adjustment technique founded on well-accepted principles of measurements and their errors and is regarded as superior to all other methods of adjustment.
The Least Squares method of adjustment, Variation of Coordinates, outlined above is a systematic method of determining the most likely values of traverse coordinates when the number of measurements exceeds the number of unknowns, as happens in all closed traverses. The technique is adaptable to many surveying applications such as Resections and Intersections, Triangulation and Trilateration schemes as well as combinations of these and lends itself to computer solution.
The inclusion of constraints in the form of bearings, distances and angles add a degree of flexibility to this well-proven adjustment process. The Following may be concluded with these methods. Axis Scale method has a greater effect on the Linear Values than any other method.
The a maximum change in bearing occurs at 90 degrees to the closing error and thus has a maximum linear correction Application of different methods for adjustment in various practical problems. Bowditch Method : Named after the distinguished American navigator, Nathaniel Bowditch These corrections are based on the assumption that: 1. All lengths are measured with equal care 2.
All angles are taken with approximately the same precision 3. Errors are accidental 4. Total error on any side is directly proportional to the length of the traverse. This is an approximate method but can be easily adapted for closing the traverse very easily.
It is mostly adapted in Road, Irrigation, Infrastructure and other projects where accuracy is not required to very high precision. Transit Wilsons Method : No sound theoretical foundation since it is purely empirical Not commonly used but best suited for surveys where traverse sides are measured by stadia or sub tensed bar. These corrections are based on the assumption that: 1.
Angular measurements are more precise than linear measurements 2. Errors in traversing are accidental. Crandall, Least Square Method: Least square traverse adjustment is the determination of a set of traverse coordinates which makes the sum of the squares of the residuals a minimum.
This is a more rigorous method to achieve better Accuracy and is used in the projects where accuracy of control points is of at most importance like Tunnels, Metro rail, etc. Examples The Following readings were observed in a traverse survey. Solution: Step 1: Working out the basic calculations. Find the Latitudes, Departures and Initial coordinates with assumed starting co-ordinates.
It may be noted that these calculations up to this stage are required for adjusting the traverse by any method. Step 2: Bowditch Method. Sum of the total Departures and Latitudes will give the Error in closure.
This needs to be adjusted. This Error is adjusted by dividing the Error by total Length and then multiplying with the respective distance Leg Length. Diagram represents the Angles and distances as per the table in the question. By adding all the Departures and Latitudes, these errors can be found. These errors need to be adjusted to obtain the final corrected readings using the Following Formulae.
Delta D — Adjustment Factor.
Bowditch Traverse Adjustment [Bowditch導線平差]
Miramar Any traverse, or a new section which does not commence at a point fixed in a previous section within the same set of data, must have at least one point the first instrument station specified as a fixed point refer to the heading Fixed Points under Enter Points and also close onto a fixed point in order that the section be able to be adjusted; if the start point is not fixed or held fixed from a previous traverse section the traverse will still compute but cannot be adjusted. Untitled Document No variation to the method of linear adjustment is made for traverses computed on spheroid — it is considered that the method described is adequate for engineering-type surveys. When the start of a new traverse section is detected by the software, all points prior to the new start bowditfh held as fixed for the purpose of allowing the adjustment if necessary of subsequent sections — i. When the finishing point coincides with the starting point, then it is called as a closed traverse. Present techniques used in traversing using total station as a open traverse. The current traverse section is re-run, applying the required correction to each traverse bowdtch.
Software for Traverse Correction – Excel Solution