NE Land Surveyor cheat sheet

Priority of evidence (federal PLSS practice): natural monuments > artificial monuments > courses and distances > area; written record yields to undisturbed original monument evidence.

Adverse possession elements (typical): actual, open and notorious, exclusive, continuous for the statutory period, and hostile; statutory periods vary by state (commonly 10–20 years).

Prescriptive easement requires use that is open, notorious, adverse, continuous, and under claim of right; exclusivity is generally not required.

Riparian boundary: accretion (gradual, imperceptible) moves the boundary; avulsion (sudden, perceptible) does not; reliction is land exposed by receding water.

Meander line is not a boundary of record; it is an evidential line for computing area of fractional lots; the water boundary controls.

PLSS aliquot parts: quarter-quarter section = 40 acres; 1/8 of a section = 80 acres; fractional lots along correction lines are numbered and area-computed.

Missing corner: proportioning (single or double proportion) restores position from surviving corners; double proportion uses two known corners on each line.

Unwritten rights: easement by necessity requires unity of title and strict necessity; easement by implication requires prior use that is apparent and reasonably necessary.

Boundary retracement measures record angles and distances between found monuments; it does not create new lines absent written intent.

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

Vertical curve: elevation = PVC elev + g1·x + ((g2 − g1)/2L)x², with x measured from PVC; K = L/|A| where A = g2 − g1 in percent.

Sight distance on crest vertical curve (US customary, S < L): L = A·S²/2158; sag curve (S < L): L = A·S²/(400 + 3.5S).

Stationing: 1 station = 100 ft; metric practice uses 1 station = 1 km or 20 m intervals; station equations adjust for line changes.

Earthwork: average end area V = L(A1 + A2)/2; prismoidal correction = L(A1 − A2)²/(12·A_m) for three-level sections.

Grade = rise/run expressed in percent; slope stake set where cut/fill equals the design template offset from centerline.

Superelevation: e + f = V²/(gR); in US customary, e + f = V²/(15R) with V in mph and R in feet.

Construction layout tolerances are set by specification, not by survey instrument precision; check as-built against design coordinates, not offsets alone.

Horizontal layout by bearing-bearing intersection, bearing-distance, or distance-distance; distance-distance has two solutions unless side is specified.

Stake offset = measured distance − design distance; positive/negative convention must be stated in the field book and on the stake.

Set control (baseline, traverse, or GNSS-derived pairs) outside the construction influence zone and reference by azimuth and distance from at least two points.

Vertical layout: HI = BM elevation + backsight; stake elevation = HI − foresight; check closure against a second benchmark.

Total station setup: occupy known point, backsight known point, verify with a third known point (residual should be within project tolerance).

Machine control and UAS-derived surfaces require independent check shots on known features before acceptance of grade.

For batter boards and offsets, record the reference line azimuth and the perpendicular offset distance; never rely on unrecorded string lines.

As-built reporting distinguishes design coordinate, computed coordinate, and measured coordinate; misfit is reported in both components.

Ellipsoid parameters: a (semi-major), f (flattening); b = a(1 − f); e² = 2f − f²; GRS80 a = 6,378,137 m, 1/f = 298.257222101.

Geodetic vs geocentric: latitude/longitude/height on the ellipsoid versus Earth-centered XYZ; convert with standard ECEF formulas.

State Plane: Lambert Conformal Conic for east-west zones; Transverse Mercator for north-south zones; scale factor differs from 1 except on standard parallels or central meridian.

Combined factor = grid factor × elevation factor; elevation factor ≈ R/(R + h) using mean radius and orthometric height.

NAD83(2011) and NATRF2022 are terrestrial reference frames; NAD27 is a legacy datum differing by tens to hundreds of meters.

Geoid model (e.g., GEOID18) converts ellipsoid height h to orthometric H: H = h − N.

Azimuth types: true (geodetic), grid, magnetic; convergence γ = grid azimuth − geodetic azimuth, varies with longitude from the central meridian.

UTM: 6° zones, central meridian scale 0.9996, false easting 500,000 m; zone boundaries create discontinuities requiring re-projection.

Vector topology rules: no gaps/overlaps in polygon coverage, no dangling nodes in networks, no self-intersections; violations reported by validation tools.

Raster cell size controls resolution; area of a cell = cellsize²; resampling methods: nearest (categorical), bilinear/cubic (continuous).

Map projection choice: equal-area for density/area statistics, conformal for navigation and shape, equidistant for distance measurement from a point.

Attribute join requires a key with matching type and uniqueness; one-to-many joins duplicate features and inflate area/perimeter sums.

Metadata standard elements: coordinate reference system, accuracy, lineage, source scale, and date of imagery.

Buffer distance in a projected CRS is planar; in a geographic CRS buffer uses degrees and produces distorted results.

LiDAR-derived DEM vertical accuracy is reported as RMSEz; check against independent checkpoints, not the point cloud itself.

Geodatabase feature class vs shapefile: shapefile has 2 GB limit, no true curves, field names limited to 10 characters.

Chart datum: Mean Lower Low Water (MLLW) in US waters; soundings and charted depths are referenced to MLLW, heights to MHW.

Tidal datum computation uses a 19-year National Tidal Datum Epoch; short-term series are reduced by comparison to a control station.

Multibeam: swath width ≈ 2 × depth × tan(beam angle/2); coverage and resolution degrade with depth and beam angle.

Sound velocity errors refract beams; a profile at the transducer is required; uncorrected errors appear as systematic depth bias or bowl effect.

Vertical reference: reduce soundings by observed tide or by separation model; ellipsoid-referenced surveys require a separation surface to chart datum.

Hydrographic positioning standards pair horizontal and vertical uncertainty; total vertical uncertainty combines depth-dependent and constant terms.

Side-scan sonar detects features and texture; it does not give reliable depths without additional calibration.

USACE hydrographic survey tolerances are specified per project; check the project specification rather than assuming a universal value.

Currents and vessel motion (heave, pitch, roll) are corrected with an IMU; uncorrected motion produces periodic depth artifacts.

Site plan elements: property lines, setbacks, buildable area, impervious coverage, parking counts, drainage, and utility easements.

Parking: stall dimensions and drive aisle widths are set by local code; accessible stalls require access aisles and van-accessible dimensions per ADA.

Stormwater: Rational method Q = CiA (US customary, Q in cfs, A in acres); time of concentration sets the design storm duration.

Detention/retention sizing compares pre- and post-development peak flows and volumes; post-development peak must not exceed allowable release rate.

Grading: minimum slopes for positive drainage (commonly 1–2% for paved, 2% for turf) are set by local standards; verify in the code.

Lot area and frontage are measured to the property line or right-of-way line as the ordinance specifies; do not mix the two.

Right-of-way vs easement: ROW is dedicated public access; easements convey specific use rights and do not transfer title.

Subdivision plat must show bearings, distances, curve data, monument locations, and dedications; approval is by the reviewing authority.

Floodplain: regulatory flood elevation (e.g., Base Flood Elevation) restricts fill and construction; check the effective FIRM panel.

Scale of a vertical photo: S = f/H, where H is flying height above ground; larger scale means smaller denominator.

Relief displacement: d = r·h/H, radial from the principal point; taller objects and larger radial distance displace more.

Overlap: 60% endlap and 20–30% sidelap are typical for stereo mapping; insufficient overlap prevents stereo compilation.

Parallax difference relates to elevation difference: Δh = Δp·H/(b·f) using base b and focal length f.

Aerotriangulation (bundle adjustment) solves camera stations and tie points; control points constrain the solution.

Orthophoto removes relief displacement using a DEM; errors in the DEM appear as local distortion or seam artifacts.

Ground sample distance (GSD) = pixel size on the ground; smaller GSD improves detail but increases data volume.

Analytic stereo plotting requires interior, relative, and absolute orientation; check residual statistics before accepting the model.

Camera calibration (focal length, principal point, distortion) must be current; uncorrected lens distortion biases coordinates.

LiDAR returns: first, last, and intermediate; bare-earth DEM requires classification and filtering of vegetation and structures.

Point density = pulses per unit area; multiple returns can yield higher point density than pulse density.

Vertical accuracy of LiDAR is reported as RMSEz against independent checkpoints; classify and remove gross errors before reporting.

UAS photogrammetry requires ground control points or RTK/PPK positioning; without them, absolute accuracy degrades to several meters.

Flight planning: overlap, altitude, GSD, and wind limits; check airspace authorization before flight (e.g., controlled airspace).

NDVI = (NIR − Red)/(NIR + Red); values range from −1 to 1; vegetation typically above 0.3.

LiDAR intensity is a relative return-strength value; it is not a calibrated reflectance unless corrected.

UAS-derived point clouds are photogrammetric (surface) unless LiDAR-equipped; vegetation penetration is limited.

Change detection requires co-registered datasets; misregistration produces false changes at edges.

Statute of frauds: conveyances of land must be in writing and signed; oral boundary agreements generally fail unless an exception applies.

Recording acts: race, notice, and race-notice statutes determine priority among competing interests; a later purchaser may prevail under notice statutes.

Easement appurtenant benefits a dominant parcel; easement in gross benefits a person or entity and is not tied to a parcel.

Prescription requires the statutory period of adverse use; adverse possession requires the statutory period of adverse possession plus the elements.

Boundary by agreement requires a dispute or uncertainty and a meeting of minds; it is not a substitute for a survey.

Monument priority: original government monuments control over record distances and areas; retracement surveys follow the original footsteps.

Description sufficiency requires a locatable starting point and a closed boundary; ambiguities are resolved by rules of construction.

Professional liability: the surveyor's standard of care is that of a reasonably prudent surveyor in the same community and practice.

Title vs boundary: a surveyor locates boundaries and reports evidence; title opinions and title insurance are provided by attorneys and title companies.

Priority of evidence: natural monuments > artificial monuments > courses and distances > area; undisturbed original monuments control record measurements.

Adverse possession elements: actual, open and notorious, exclusive, continuous for the statutory period, and hostile; periods vary by state.

Accretion (gradual, imperceptible) shifts the riparian boundary; avulsion (sudden, perceptible) does not move the boundary.

Meander line is an evidential line, not a boundary of record; the water boundary controls the fractional lot.

PLSS aliquot parts: quarter-quarter section = 40 acres; 1/8 section = 80 acres; fractional lots are numbered and area-computed.

Missing corner restoration: single or double proportion from surviving corners; double proportion uses two known corners on each line.

Easement by necessity requires unity of title and strict necessity; easement by implication requires prior apparent and reasonably necessary use.

Retracement measures record angles and distances between found monuments; it does not create new lines absent written intent.

Boundary evidence hierarchy is applied before any new monument is set; setting a new corner does not override original evidence.

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

Vertical curve elevation = PVC elev + g1·x + ((g2 − g1)/2L)x², with x from PVC; K = L/|A|, A = g2 − g1 in percent.

Crest sight distance (S < L, US customary): L = A·S²/2158; sag: L = A·S²/(400 + 3.5S).

Stationing: 1 station = 100 ft in US customary; metric practice uses 1 km or 20 m intervals; station equations handle line changes.

Earthwork: average end area V = L(A1 + A2)/2; prismoidal correction uses (A1 − A2)²/(12·A_m).

Grade = rise/run as a percent; slope stakes are set where cut or fill equals the design template offset from centerline.

Superelevation: e + f = V²/(15R) in US customary with V in mph and R in feet.

Layout tolerances come from project specifications, not instrument precision; as-builts compare design coordinates to measured coordinates.

Curve data on plans must include Δ, R, L, T, and PC/PT stations; missing elements prevent field layout.

Horizontal layout methods: bearing-bearing intersection, bearing-distance, and distance-distance; distance-distance has two solutions unless the side is specified.

Stake offset = measured distance − design distance; the sign convention must be recorded in the field book and on the stake.

Set control outside the construction influence zone; reference by azimuth and distance from at least two known points.

Vertical layout: HI = BM elevation + backsight; stake elevation = HI − foresight; verify closure against a second benchmark.

Total station setup: occupy a known point, backsight a known point, and verify with a third known point within project tolerance.

Machine control and UAS surfaces require independent check shots on known features before grade acceptance.

Batter boards and offsets must record the reference line azimuth and the perpendicular offset distance; unrecorded string lines are not evidence.

As-built reporting distinguishes design, computed, and measured coordinates; misfit is reported in both components.

Layout checks repeat the measurement from a different setup; a single setup does not detect orientation blunders.

Ellipsoid: b = a(1 − f); e² = 2f − f²; GRS80 has a = 6,378,137 m and 1/f = 298.257222101.

Geodetic coordinates (lat, lon, h) convert to Earth-centered XYZ (ECEF) with standard closed-form equations.

State Plane: Lambert Conformal Conic for east-west zones; Transverse Mercator for north-south zones; scale factor is 1 only on standard parallels or the central meridian.

Combined factor = grid factor × elevation factor; elevation factor ≈ R/(R + h) using mean Earth radius and orthometric height.

NAD83(2011) and NATRF2022 are terrestrial reference frames; NAD27 is a legacy datum differing by tens to hundreds of meters.

Geoid model converts ellipsoid height to orthometric height: H = h − N (e.g., GEOID18).

Azimuth types: true (geodetic), grid, and magnetic; convergence γ = grid azimuth − geodetic azimuth varies with longitude from the central meridian.

UTM: 6° zones, central meridian scale 0.9996, false easting 500,000 m; zone boundaries create discontinuities requiring re-projection.

Scale factor at a point differs from the zone's central scale; grid distance = ground distance × combined factor.

Vector topology rules: no gaps or overlaps in polygon coverage, no dangling nodes in networks, no self-intersections; validation tools report violations.

Raster cell size sets resolution; cell area = cellsize²; resampling: nearest for categorical, bilinear or cubic for continuous data.

Projection choice: equal-area for density and area statistics, conformal for shape and navigation, equidistant for distance from a point.

Attribute joins need a matching key type and uniqueness; one-to-many joins duplicate features and inflate area and perimeter sums.

Metadata elements: coordinate reference system, accuracy, lineage, source scale, and imagery date.

Buffer distance is planar in a projected CRS; in a geographic CRS the buffer uses degrees and is distorted.

LiDAR-derived DEM accuracy is reported as RMSEz against independent checkpoints, not against the point cloud itself.

Shapefile limits: 2 GB size, no true curves, field names limited to 10 characters; geodatabase feature classes avoid these limits.

Coordinate transformation between datums requires a published transformation and its accuracy statement; naive reprojection introduces error.

Chart datum: Mean Lower Low Water (MLLW) for soundings and charted depths in US waters; heights reference Mean High Water (MHW).

Tidal datums use a 19-year National Tidal Datum Epoch; short-term series are reduced by comparison to a control station.

Multibeam swath width ≈ 2 × depth × tan(beam angle/2); coverage and resolution degrade with depth and outer beam angle.

Sound velocity errors refract beams; a profile at the transducer is required; uncorrected errors appear as systematic depth bias or bowl effect.

Vertical reference: reduce soundings by observed tide or a separation model; ellipsoid-referenced surveys need a separation surface to chart datum.

Hydrographic uncertainty standards pair horizontal and vertical uncertainty; total vertical uncertainty has depth-dependent and constant terms.

Side-scan sonar detects features and texture but does not give reliable depths without calibration.

USACE hydrographic survey tolerances are project-specific; check the project specification rather than assuming a universal value.

Heave, pitch, and roll are corrected with an IMU; uncorrected motion produces periodic depth artifacts.

Site plan elements: property lines, setbacks, buildable area, impervious coverage, parking counts, drainage, and utility easements.

Parking stall dimensions and drive aisle widths come from local code; accessible stalls require access aisles and van-accessible dimensions per ADA.

Rational method Q = CiA (US customary, Q in cfs, A in acres); time of concentration sets the design storm duration.

Detention and retention sizing compares pre- and post-development peak flows and volumes; post-development peak must not exceed the allowable release rate.

Minimum drainage slopes (commonly 1–2% paved, 2% turf) are set by local standards; verify in the adopted code.

Lot area and frontage are measured to the property line or right-of-way line as the ordinance specifies; do not mix the two.

Right-of-way is dedicated public access; easements convey specific use rights and do not transfer title.

Subdivision plats show bearings, distances, curve data, monument locations, and dedications; approval is by the reviewing authority.

Floodplain regulation uses the Base Flood Elevation from the effective FIRM panel; fill and construction are restricted below it.

Vertical photo scale: S = f/H with H measured above ground; a larger scale means a smaller denominator.

Relief displacement d = r·h/H is radial from the principal point; taller objects and larger radial distance displace more.

Typical stereo mapping overlap: 60% endlap and 20–30% sidelap; insufficient overlap prevents stereo compilation.

Parallax difference relates to elevation: Δh = Δp·H/(b·f), using base b and focal length f.

Aerotriangulation (bundle adjustment) solves camera stations and tie points; ground control constrains the solution.

Orthophoto removes relief displacement using a DEM; DEM errors appear as local distortion or seam artifacts.

Ground sample distance (GSD) is the ground size of one pixel; smaller GSD improves detail and increases data volume.

Analytic stereo plotting requires interior, relative, and absolute orientation; check residual statistics before accepting the model.

Camera calibration (focal length, principal point, distortion) must be current; uncorrected lens distortion biases coordinates.

LiDAR returns: first, last, and intermediate; a bare-earth DEM requires classification and filtering of vegetation and structures.

Point density is points per unit area; multiple returns can produce higher point density than pulse density.

LiDAR vertical accuracy is reported as RMSEz against independent checkpoints; remove gross errors before reporting.

UAS photogrammetry needs ground control points or RTK/PPK positioning; without them absolute accuracy degrades to several meters.

Flight planning sets overlap, altitude, GSD, and wind limits; airspace authorization is required before flight in controlled airspace.

NDVI = (NIR − Red)/(NIR + Red), ranging from −1 to 1; vegetation is typically above 0.3.

LiDAR intensity is a relative return-strength value, not calibrated reflectance unless corrected.

UAS point clouds are photogrammetric surface models unless LiDAR-equipped; vegetation penetration is limited.

Change detection requires co-registered datasets; misregistration produces false changes at edges.

Statute of frauds: land conveyances must be written and signed; oral boundary agreements generally fail unless an exception applies.

Recording acts: race, notice, and race-notice statutes set priority among competing interests; a later purchaser may prevail under notice statutes.

Easement appurtenant benefits a dominant parcel; easement in gross benefits a person or entity and is not tied to a parcel.

Prescription requires adverse use for the statutory period; adverse possession requires the elements plus the statutory period.

Boundary by agreement requires a dispute or uncertainty and a meeting of minds; it is not a substitute for a survey.

Monument priority: original government monuments control over record distances and areas; retracement follows the original footsteps.

Description sufficiency requires a locatable starting point and a closed boundary; ambiguities are resolved by rules of construction.

Standard of care: that of a reasonably prudent surveyor in the same community and practice.

Surveyors locate boundaries and report evidence; title opinions and title insurance come from attorneys and title companies.