FS Surveying cheat sheet

Research sequence: gather subject deed and plat, adjoiner deeds, prior surveys, and public records first; written record evidence never outranks an original monument that the deed calls for.

Pre-mobilization instrument checks: peg test for level line of sight, plate/lircular bubble adjustment, optical plummet check, and EDM comparison against a calibrated baseline.

Collimation error by two-face observation: error = (reading FL − reading FR ± 180°)/2 for horizontal angles; the mean of faces cancels the error.

Coordinate metadata that must be identified before using any control: datum and realization, epoch, projection and zone, linear unit, and order/class of accuracy.

Control-network selection depends on required accuracy order: traverse for corridor work, static GNSS for long baselines and open sky, RTK/VRS where a single receiver must be positioned quickly.

In the United States, call 811 before any excavation or monument setting; most states require the locate request two to three working days before work begins.

Corner-record statutes typically require the monument material and dimensions, a cap stamped with the surveyor's license number, and filing of the record within a stated period.

Field safety controls: MUTCD-compliant traffic control, high-visibility apparel, fall protection above six feet, and hazard communication for fuels and herbicides.

Land-entry authority must be documented; a right-of-entry, permit, or written permission protects the surveyor against trespass claims and supports the final report.

Peg test: take the elevation difference between two points with the level set midway (true difference), then re-observe with the instrument near one point; the discrepancy is the collimation error for that sight length.

Curvature and refraction in leveling: combined correction ≈ 0.0675 K² meters with K in kilometers; refraction offsets roughly one-seventh of the curvature effect and is subtracted from the rod reading.

EDM accuracy is stated as ±(a mm + b ppm); atmospheric correction uses temperature, pressure, and humidity, with the correction changing roughly 1 ppm per 1 °C.

Total-station angles are turned clockwise from the set zero; a zenith angle of 90° is horizontal and 0° is directly overhead.

Direct and reverse (face left/face right) observations cancel horizontal collimation, trunnion-axis, and vertical-index errors; the mean of the two faces is the accepted value.

Traverse types: closed-loop returns to the starting point, closed-link begins and ends on known control, open traverse has no closure check and is avoided for boundary work.

Angular misclosure of an n-sided closed polygon = measured angle sum − (n − 2)(180°); distribute the misclosure equally or in proportion to instrument weights before computing coordinates.

Instrument error sources: residual level-bubble error, optical plummet misalignment, EDM zero and prism constant, and axis non-perpendicularity.

Natural error sources: atmospheric refraction, thermal expansion, wind-induced vibration, tripod settlement, and unstable instrument points.

Evidence hierarchy: natural monuments outrank artificial monuments, which outrank courses and distances, which outrank area; quantity yields to quality.

Senior rights: an earlier conveyance prevails over a later one for the same land, so a junior deed conveys only what the senior deed left unconveyed.

Public Land Survey System: a township is 36 sections in a 6-by-6 arrangement, each section nominally one mile square and 640 acres; original government-set corners are controlling monuments.

Lost-corner reestablishment uses single proportionate measurement between the nearest existent corners on the same line unless the position can be restored from independent accepted evidence.

Tidal boundary waters are generally bounded by mean high water; non-tidal navigable waters are commonly bounded by the ordinary high water mark, with title extent set by state law.

Accretion and reliction are gradual and move the boundary with the water; avulsion is sudden and leaves the boundary where it was before the event.

Unwritten rights that can control a boundary include practical location, acquiescence, estoppel, and adverse possession, regardless of deed language.

Adverse possession elements: actual, open and notorious, exclusive, hostile, and continuous for the statutory period.

A meander line is evidence of the water's location at the time of survey; it is not a boundary line and does not limit the conveyance.

Photograph scale S = f / (H − h), with f the focal length, H the flying height above datum, and h terrain elevation; scale varies across a single vertical photo with relief.

Relief displacement d = r·h / H, where r is the radial distance from the principal point; displacement is zero at the nadir point and increases outward.

Parallax height equation: h = H·Δp / (P + Δp), with Δp the parallax difference between points and P the parallax at the reference elevation.

Air base between exposures B = (1 − endlap fraction) × ground coverage of one photograph along the flight line; side spacing = (1 − sidelap fraction) × ground width.

Ground sample distance = pixel size × (H / f), equivalently pixel size times the photo-scale denominator.

An orthophoto is differentially rectified to remove tilt and relief displacement, giving a uniform map scale suitable for measuring positions.

A DTM/DEM represents bare-earth elevations; a DSM includes buildings and vegetation; LiDAR classification separates ground returns from canopy and structures.

Airborne topographic LiDAR is specified by point density (points per square meter) and vertical accuracy as RMSEz, commonly 5–15 cm for modern sensors.

Representative satellite resolutions: Landsat multispectral 30 m, Sentinel-2 10 m, WorldView-3 panchromatic about 0.31 m.

Height relationship: h = H + N, where h is ellipsoidal height, H is orthometric height above the geoid, and N is the geoid undulation.

NAD83 is referenced to the GRS80 ellipsoid; NAD27 used the Clarke 1866 ellipsoid; NAVD88 provides orthometric heights derived from tide-gage observations.

Grid distance = ground distance × combined factor; combined factor = grid scale factor × elevation factor, with elevation factor ≈ R / (R + h).

Universal Transverse Mercator: 6°-wide zones, central-meridian scale factor 0.9996, false easting 500,000 m, zero false northing in the northern hemisphere.

Grid azimuth = geodetic azimuth − convergence angle, with convergence approximately Δλ · sin φ measured from the central meridian.

Datum transformation uses a similarity (Helmert) model with seven parameters: three translations, three rotations, and one scale factor.

Astronomic and geodetic azimuths differ by the Laplace correction, which depends on the deflection of the vertical.

Coordinates must carry a realization and epoch, for example NAD83(2011) at epoch 2010.00, because plate motion changes coordinates with time.

Spherical excess of a geodetic triangle equals its area divided by R² in radians and is applied to close triangles observed on the ellipsoid.

Latitude = distance × cos(azimuth); departure = distance × sin(azimuth); azimuth is measured clockwise from north.

Linear error of closure = √[(Σlatitude)² + (Σdeparture)²]; relative precision = closure / total traverse length, stated as 1:N.

Bowditch (compass) rule distributes misclosure in proportion to course length; the transit rule distributes it in proportion to the absolute latitudes and departures.

Least squares minimizes Σv²; normal equations are N = AᵀWA and X = (AᵀWA)⁻¹AᵀWL, which also yield residuals, a variance factor, and error ellipses.

Weighted mean = Σ(wx)/Σw with weights w = 1/σ²; the weight of the mean equals the sum of the weights.

Error propagation for independent variables: σz² = (∂z/∂x)²σx² + (∂z/∂y)²σy².

Horizontal curve formulas: T = R tan(Δ/2); L = RΔ in radians; LC = 2R sin(Δ/2); M = R[1 − cos(Δ/2)]; E = R[sec(Δ/2) − 1].

Degree of curve, arc definition: R = 5729.578 / D; chord definition: R = 50 / sin(D/2).

Area by coordinates: 2A = Σ(Xi·Yi+1 − Xi+1·Yi), taken in order around the traverse; the sign indicates the direction of travel.

Scale as a representative fraction is dimensionless: 1:1,200 means one map unit equals 1,200 ground units, and 1 in = 100 ft is the same as 1:1,200.

Contour interval is chosen so adjacent contours remain legible at the plotted scale and match the map's purpose; larger-scale maps support smaller intervals and finer terrain depiction.

Plat content: basis of bearing, bearings and distances, curve data (radius, arc, chord, central angle), area, monument descriptions, adjoiner names, and the surveyor's seal and signature.

Map accuracy is reported as RMSE under NSSDA/ASPRS-style standards; horizontal accuracy is tied to map scale and vertical accuracy to contour interval.

Maps on a projected grid show grid distances and grid north; ground distances must be converted using the combined factor before comparison.

Metes-and-bounds parcels must mathematically close; the misclosure and the area computed by coordinates are typically tabulated on the face of the plat.

Digital submissions should separate boundary, easement, improvement, and annotation layers and be georeferenced to the datum, realization, and epoch stated on the map.

Vertical information on a map requires contour lines, spot elevations, and benchmarks referenced to a stated vertical datum such as NAVD88.

Easements and rights-of-way are shown graphically and tabulated with bearings, distances, widths, and the document reference of record.

Cut/fill at a point = design elevation − existing ground elevation; a positive result is cut and a negative result is fill.

Grade stakes carry the cut or fill dimension at the stake; hubs with tacks mark the offset line and are referenced to a project benchmark.

Square a building corner with the 3-4-5 relationship and confirm by comparing diagonals, which must be equal for a true rectangle.

A temporary benchmark is set outside the construction influence zone and checked into existing vertical control before any layout.

Offsets from control lines to structure faces are set with batter boards or hubs placed clear of excavation and backfill.

Slope stakes require the catch point where the design side-slope plane intersects existing ground, found by trial computation along measured offsets.

As-built surveys compare constructed to designed positions; typical tolerances are about ±0.02–0.05 ft for structures and ±0.1 ft for earthwork.

Site GNSS RTK layout needs a local base or network correction and a site calibration to the project's local control and grid.

Earthwork volumes come from average end area, prismoidal, or cross-section methods and are compared to design quantities to support payment.

Common compensation structures: lump sum, time and materials, cost plus fixed fee, and unit price; scope, deliverables, and exclusions belong in writing.

Standard of care is the degree of skill and care ordinarily exercised by reputable surveyors under similar circumstances; failing it establishes negligence.

Responsible charge means the licensed surveyor who directs and controls the work; most jurisdictions require that person's seal and signature on final documents.

Indemnification and hold-harmless clauses for a party's own negligence are limited or void in many states, and anti-indemnity statutes may override contract language.

A statute of limitations runs from the injury or its discovery; a statute of repose bars claims after a fixed period regardless of when the injury is discovered.

Field notes, computations, and correspondence should be retained under contract and state requirements, commonly five to ten years or longer for boundary work.

Board rules generally prohibit contingent compensation tied to a boundary location opinion and require disclosure of conflicts of interest to clients.

Professional liability (errors and omissions) insurance covers negligent professional services; commercial general liability policies typically exclude them.