Module 4: Boundary Retracement, Computation, and Monumentation - Worked Examples

A clearly identifiable old concrete monument is 0.25 m from a coordinate computed from a current office plot. The adjacent record distances measured from the monument are close to the approved plan.

Two adjacent parcel corners are recovered and consistent with the approved record, but the intervening rear corner monument is not found.

An iron pin is found near the expected corner but is loose, leaning, and located in recently excavated ground.

A checked course begins at P1 with $E_1=5000.000\text{ m}$ and $N_1=10000.000\text{ m}$. Its horizontal distance is $D=100.000\text{ m}$ and its azimuth is $\alpha=35^\circ00'00''$, measured clockwise from north. Compute P2.

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Two observed corner coordinates are $E_1=5000.000$ m, $N_1=10000.000$ m and $E_2=5030.000$ m, $N_2=10040.000$ m. Compute their inverse distance.

A recovered monument differs from a comparison coordinate by $\Delta E=+0.060$ m and $\Delta N=-0.080$ m. Compute the residual magnitude.

A four-corner training parcel has local plan coordinates in metres, ordered around the boundary: A $(0.000,0.000)$, B $(40.000,0.000)$, C $(40.000,30.000)$, and D $(0.000,30.000)$, where each pair is $(E,N)$. Compute the coordinate area.

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A synthetic four-course traverse has total measured length $\sum L=250.000\text{ m}$, northing misclosure $f_N=+0.012\text{ m}$, and easting misclosure $f_E=-0.016\text{ m}$. Compute the linear misclosure and express the relative closure ratio.

Four identifiable parcel monuments all plot approximately 1.20 m east of supplied spreadsheet coordinates, while their measured inter-corner distances and bearings agree closely with the approved plan.

A closed field traverse has acceptable internal observation quality, but one approved-record distance differs from all field and adjoining evidence by 8.0 m.

A four-course training traverse has a total length of 140.000 m. Before adjustment, the coordinate sums are $f_N=+0.028$ m and $f_E=-0.021$ m. Course 1 is 40.000 m long. Assume the observations have passed blunder checks, the closure meets the applicable project or agency acceptance criterion, and the Compass/Bowditch model is appropriate for this example.

A four-course training traverse has course lengths $40.000$, $30.000$, $40.000$, and $30.000\text{ m}$, for $\sum L=140.000\text{ m}$. After blunder checks, its unadjusted coordinate sums are $f_N=+0.028\text{ m}$ and $f_E=-0.021\text{ m}$. Assume the closure meets the applicable project or agency acceptance criterion and the Compass/Bowditch model is appropriate; compute every course correction.

A corner is accepted after the monument, adjacent record lines, and field observations reconcile.