Solved problems · 9 problems
Levelling loops
Differential and trigonometric levelling reduced from notes, loop closure against a tolerance, and distribution of the misclosure.
- Differential level circuit reduced from field notesReduce a four-setup differential level run from BM-1 to BM-2 through three turning points, then prove the page with the sum of backsights against the sum of foresights.
- Closed level loop tested against a tolerance and adjustedA four-leg level loop returns to its starting benchmark 0.060 ft out. Test the misclosure against a C times root-M tolerance, then distribute it in proportion to leg length and compute adjusted elevations.
- Level net of three loops adjusted by inspectionThree benchmarks and an interior junction point are connected by six level lines forming three independent loops. Adjust the net by inspection, distributing each loop misclosure by line length and iterating until every loop closes.
- Profile levelling reduced to a profile and a grade lineReduce a profile level run with intermediate foresights to ground elevations at six stations, then compute a grade line at -1.20 percent and the cut or fill at each station.
- Cross sections reduced to end areas and an earthwork volumeTwo roadway cross sections in cut are reduced from slope-stake notes to end areas by the coordinate method, and the volume between them is computed by average end area.
- Trigonometric levelling with the curvature and refraction correctionA single long total-station shot is reduced to an elevation, carrying instrument and target heights and the combined correction for earth curvature and atmospheric refraction.
- Two-peg test worked to a collimation correctionA two-peg test on a level is reduced to a collimation error per unit sight length, expressed in seconds of arc, and then used to correct a pair of unbalanced sights and recover a turning-point elevation.
- Reciprocal levelling across a river crossingA 1,360 ft river crossing is levelled reciprocally from both banks; the mean of the two differences removes the systematic error, and the half-difference is compared with the predicted curvature and refraction.
- Benchmark carried on two routes and reconciled by weighted meanA new benchmark is levelled from two published control points over routes of different length. Test the discrepancy, weight each route inversely with its length, and compute the weighted mean elevation and its standard deviation.
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.
- Boundary retracementGeneric retracement computations: proportionate measurement, aliquot subdivision of a section, and reconciling record and measured dimensions.