Solved problems · 12 problems
Traverse adjustment
Closed traverses computed from field notes: angular closure, azimuths, latitudes and departures, misclosure and precision, compass-rule adjustment, final coordinates.
- Closed-loop traverse from field angles to compass-rule coordinatesA five-sided loop traverse is taken from raw interior angles and taped distances through angular closure, azimuths, latitudes and departures, misclosure and precision, to compass-rule adjusted coordinates.
- Transit-rule adjustment compared with the compass ruleThe same five-sided loop is readjusted by the transit rule, which distributes the closure in proportion to each latitude and departure rather than to course length, and the two sets of coordinates are compared.
- Closed-link traverse between two pairs of control monumentsA four-course traverse runs from one control pair to another. Azimuth closure comes from the two published control azimuths and position closure from the published coordinates of the far monument.
- A traverse that fails its precision specification, and what to do about itA four-sided traverse closes at 1:2,538 against a 1:10,000 requirement. The direction of the closure line points straight at the course carrying the blunder, which is remeasured and the traverse recomputed.
- Omitted measurement: the missing bearing and distance of one sideFour sides of a five-sided parcel are recovered but the fifth runs through a swamp. Both its bearing and its length are computed from the condition that the traverse must close.
- Traverse with two missing lengths solved from the closure conditionsTwo sides of a five-sided traverse have known directions but no measured lengths. The two closure conditions give a pair of linear equations that solve both lengths at once.
- Angular closure with a suspected blunder in one angleA six-sided traverse misses its angular closure by 2′36″ against a 37 second tolerance. The size of the misclosure identifies a single blunder, which is traced in the field book and removed before any adjustment.
- Closed traverse with the area required as well as the closureA six-sided parcel traverse is closed and adjusted, then its area is computed twice, once by the coordinate method and once by double meridian distances, so the two can be made to agree.
- Closed traverse computed from deflection anglesA five-sided loop observed with deflection angles rather than interior angles. The closure condition becomes 360 degrees rather than (n − 2) times 180, and azimuths advance by simple addition.
- Reducing a ground traverse to grid with a combined factorA link traverse measured on the ground is tied to state plane control. The combined factor is built from the grid scale factor and the elevation factor, and the closure is computed with and without it.
- Locating a new point by intersection from two traverse stationsA point on the far side of a river is fixed by directions observed from two established traverse stations, then verified independently by the sine rule and by a third-angle check.
- Metes and bounds deed traverse: closure, precision and areaA five-call deed description is reduced to a traverse. It closes at 1:4,958, which is examined against what a deed of that vintage should be expected to deliver, then adjusted and its area compared with the recited acreage.
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.
- 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.
- Boundary retracementGeneric retracement computations: proportionate measurement, aliquot subdivision of a section, and reconciling record and measured dimensions.