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Traverses
Fieldwork In Traversing
Control By Traversing
Angular Closure
Linear Closure
Adjustment Of Traverses
Function Of Traverses
Missing Data
Bearing And Distance Of
One Line
Bearing Of One Line,
Distance Of Another
Lengths Or Bearings Of
Two Lines
Bearing of One Line, Distance of Another
Once again the assumption is made that the missing data closes the traverse. If there are any errors or mistakes in the original data all of this will be transferred into the missing line, so it is very important that all checks and corrections are applied to the original traverse measurements.
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In the diagram, the two thick lines show the known data and the two dotted lines are sides of the traverse with missing elements. There are two solutions to the calculations, one involves rotating the bearings so that one of the unknown lines has a cardinal bearing (hence SDE or SDN will be zero); the other involves calculating the vector that closes the known data and using the sine or cosine rule to solve for the data in the triangle with the missing data. |
| For example: | |
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In order to solve for the missing distance on the bearing 311°27’ and the bearing for the line length 41.14 we first calculate the vector between the two known traverse sides by performing a closure calculation. This gives a distance of 39.013 and a bearing of12°48’ (or 192°48’), which means that the other two traverse lines that have data missing must give the same result in order to close the traverse. Reducing the remaining data to a triangle gives: |
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The triangle has two known distances, one angle. The remaining elements can be solved using the sine and cosine rules. The alternative approach is to rotate the bearings of the original data so that one of the missing lines has a cardinal direction. In the example, if we added 48°33’ to the bearings the line with the missing distance becomes 0°00’ (contributing nothing to the eastings, and all of its distance to the northings). It does not matter whether the lines with the missing data are contiguous or not, the mathematical solution is the same. We can move known traverse lines around so they form one continuous series of vectors, and then perform our traverse closure on this new network. The missing data is still what is required to close the figure. |