Solved problems · 8 problems
Boundary retracement
Generic retracement computations: proportionate measurement, aliquot subdivision of a section, and reconciling record and measured dimensions.
- Lost corner restored by single proportionate measurementA section corner on a straight range line is lost between two existent original corners. Restore it by single proportionate measurement, working in coordinates and proving the record ratio is preserved.
- Lost interior section corner by double proportionate measurementAn interior section corner is lost with existent corners a mile or so in each of the four cardinal directions. Restore it by double proportionate measurement and verify that the record latitude and departure ratios are preserved.
- Center of section by intersection of the quarter-corner linesA section is subdivided from eight recovered monuments. The center of section is fixed by intersecting the north-south and east-west quarter-corner lines, and the four quarter-section areas are computed and checked against the whole.
- Areas of government lots on a north township boundaryThe north tier of lots in a fractional section is computed from a retracement of the north boundary, with the deficiency of the mile falling in the last half-mile.
- Record chains reconciled against a measured distanceThree record calls in chains between two existent monuments do not sum to the measured distance. Distribute the difference proportionately and report the restored positions in both feet and chains.
- Laying out the SW¼ of the NE¼ from section corner coordinatesFrom four section corner coordinates, protract the quarter corners, fix the center of the section and the center of the north-east quarter, then lay out the SW¼ of the NE¼ and compute its area.
- Retracing a metes-and-bounds description that will not closeA four-course deed fails to close by more than nine feet. Locate the error from the direction of the misclosure, decide what to hold, correct the record, and adjust the retraced parcel by the compass rule.
- Corner position recovered from two bearing-tree tiesTwo original bearing trees are found and coordinated. The corner is computed independently from each recorded tie, the discrepancy is examined, and the accepted position is checked against the record distance between the trees.
Other categories
All problems- Curve stakingHorizontal and vertical curves solved from plan data and taken all the way to the stakes: stations, deflection angles, chords, offsets and grade elevations.
- Traverse adjustmentClosed traverses computed from field notes: angular closure, azimuths, latitudes and departures, misclosure and precision, compass-rule adjustment, final coordinates.
- Area & partitioningAreas by coordinates and by DMD, curved boundaries, and the partition problems that split a parcel to a required area by a line of given direction or through a given point.
- Error propagationRandom error carried through sums, series, products and functions; weights and weighted means; the precision a procedure can actually deliver.
- Levelling loopsDifferential and trigonometric levelling reduced from notes, loop closure against a tolerance, and distribution of the misclosure.