Solved problems · 9 problems
Error propagation
Random error carried through sums, series, products and functions; weights and weighted means; the precision a procedure can actually deliver.
- Standard deviation, standard error and a rejection decision on repeated distancesTen EDM observations of one baseline, reduced to a residuals table, a standard deviation and a standard error of the mean — and one suspect observation tested against a criterion that can actually reject it.
- Error in a taped distance measured in n tape lengths, against a single EDM shotThe same 648 ft line measured two ways. Series propagation over seven tape settings against one EDM observation with a constant-plus-ppm specification, and what the comparison says about when taping is still adequate.
- Error propagated into a computed area from errors in two sidesA rectangular parcel measured on two sides, and the uncertainty those two measurements put into the acreage — with the fractional form of the same result as a check and the worst case as a bound.
- Error propagated into latitude and departure from errors in an angle and a distanceOne course, one distance uncertainty and one azimuth uncertainty, carried through the general propagation formula with partial derivatives — and a rotation argument that checks the answer without repeating it.
- Weighted mean of three observations of differing precisionThree crews, three standard errors, one distance. Weights as the inverse of the variance, the weighted mean, the standard deviation of unit weight, and what it means when that comes out well above one.
- Predicted traverse closure error against the observed misclosureWhat misclosure should a five-course traverse produce, given the instrument that ran it? Propagate the per-course errors, predict the closure, and compare it with what the field actually returned.
- Level-loop misclosure judged against a C√M tolerance and distributedA four-leg differential level loop that fails to return to its benchmark by 0.040 ft. Test it against C√M for two orders of accuracy, distribute the misclosure by leg length, and carry the adjusted elevations round.
- Angular closure of a seven-sided traverse against a k√n toleranceSeven interior angles that sum 21 seconds over the geometric condition. Test the misclosure against the k√n tolerance a 10-second instrument justifies, then distribute it equally and prove the adjusted angles close.
- Combining a systematic correction with a random errorA tape 0.012 ft short and thirteen settings of it. The systematic part is removed by arithmetic and the random part is carried as an uncertainty — and the two must never be combined in quadrature, which is the mistake the problem exists to prevent.
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.
- 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.