OR Land Surveyor cheat sheet

Latitude = distance × cos(bearing); departure = distance × sin(bearing). Closure in latitude/departure must sum to zero for a closed traverse; linear misclosure = √(Σlat² + Σdep²).

Relative precision = linear misclosure ÷ total traverse length (e.g., 0.15 ft / 5,000 ft = 1:33,333). Compare against the standard for the survey class, not a fixed universal value.

Compass rule (Bowditch) correction: correction in lat or dep = −(total misclosure in that component) × (course length ÷ perimeter). Transit rule distributes corrections proportional to the component magnitudes instead.

Balancing angles of a closed polygon: sum of interior angles = (n − 2) × 180°. Angular misclosure is distributed equally among angles when they are observed with equal weight.

Azimuth = bearing measured clockwise from north, 0°–360°. Convert quadrant bearings: NE = azimuth; SE = 180° − bearing; SW = 180° + bearing; NW = 360° − bearing.

Back azimuth = forward azimuth ± 180° (add if < 180°, subtract if ≥ 180°). Deflection angle = 180° − interior angle, with right/left sense recorded explicitly.

Horizontal curve: T = R tan(Δ/2); L = RΔ(radians) = 100Δ/D for degree-of-curve D; M = R[1 − cos(Δ/2)]; E = R[sec(Δ/2) − 1]; LC = 2R sin(Δ/2).

Vertical curve: elevation at any point = BVC elevation + g₁x + [(g₂ − g₁)/(2L)]x². Turning point (high/low) at x = −g₁L/(g₂ − g₁); K = L/A where A = |g₂ − g₁| in percent.

Leveling: BM elevation + backsight − foresight = new elevation (height of instrument method: HI = BM + BS; elevation = HI − FS). Misclosure in a closed loop is compared to the allowable tolerance for the order of survey.

State plane coordinates use a conformal projection (Lambert conformal conic or transverse Mercator); scale factor = grid distance ÷ ground distance, and combined factor = grid factor × elevation factor, where elevation factor ≈ R/(R + h).

Horizontal distance from a total station slope distance: H = S × sin(zenith angle) or H = S × cos(vertical angle); vertical difference V = S × cos(zenith) = S × sin(vertical angle).

Traverse station adjustment by least squares minimizes the sum of squared residuals; the redundancy number = (number of observations − number of unknowns) must be positive for a solution.

Area by coordinate method (shoelace): 2A = Σ(Xᵢ × Yᵢ₊₁ − Xᵢ₊₁ × Yᵢ), taken in absolute value; coordinates must be in consistent units and the polygon traversed in order.

Area by DMD (double meridian distance): DMD of first course = departure of that course; each subsequent DMD = previous DMD + previous departure + current departure; double area = Σ(DMD × latitude).

GPS/GNSS: a minimum of 4 satellites is needed to solve X, Y, Z, and receiver clock bias; PDOP quantifies geometric dilution, with lower values indicating better geometry.

RTK requires a fixed integer ambiguity solution; a float solution is less precise. Network RTK corrects for distance-dependent errors (ionosphere, troposphere, orbit) over longer baselines.

Monumentation and boundary: unwritten rights such as adverse possession, prescription, and practical location can alter record lines; priority of calls generally favors natural monuments over artificial monuments, then courses and distances, then area.

Horizontal datum: NAD83 is the current horizontal datum in the U.S. (NAD27 differs by up to hundreds of meters); vertical datum NAVD88 supersedes NGVD29. State plane zones are defined per datum - never mix coordinates across datums.

Earth curvature and refraction: combined correction ≈ 0.0206 × D² (D in thousands of feet, result in feet) or 0.0675 × D² (D in km, result in meters), applied as a negative correction to rod readings.

Level-loop misclosure tolerance commonly scales with √(loop length); random errors accumulate as the square root of the number of setups, while systematic errors accumulate linearly and must be eliminated by procedure.

Total station: horizontal angle is measured in the horizontal plane; zenith angle is measured from the vertical axis. Instrument and target heights must be recorded to reduce slope distances to elevations.

Construction staking: stationing is measured along the baseline; offset is measured perpendicular. Cut = existing ground − design elevation (positive means excavate); fill is the opposite.

Photogrammetry/remote sensing: scale = f ÷ H (focal length over flying height above terrain); overlap of about 60% endlap and 20–30% sidelap is typical for stereo mapping.

Legal descriptions: metes and bounds uses bearings and distances from a point of beginning (POB); lot-and-block references a plat; aliquot parts reference the PLSS (section, township, range).

PLSS: a normal township is 6 × 6 miles containing 36 sections of 1 square mile each, numbered 1–36 beginning at the northeast corner and proceeding boustrophedon; correction lines and standard parallels absorb convergence error.

Error propagation: for a sum or difference, variances add (σ² = σ₁² + σ₂²); for independent observations of equal precision, the mean has standard error σ/√n.

Weighted mean: x̄ = Σ(wᵢxᵢ)/Σwᵢ, with weights inversely proportional to variance (w = 1/σ²). Use it to combine observations of differing precision.

Standard deviation of a single observation: s = √[Σ(vᵢ²)/(n − 1)], where vᵢ are residuals from the mean. Standard deviation of the mean = s/√n.

Coordinate geometry: distance between points = √[(ΔX)² + (ΔY)²]; azimuth from point A to B = atan2(ΔX, ΔY), normalized to 0°–360°.

Intersection by two distances or two bearings: solve the triangle or use coordinate equations; a unique solution requires two independent geometric conditions and a check on the third.

Resection (three-point problem) determines the instrument station from angles to three known points; the danger circle is the locus of stations where the three points and the station are concyclic, producing an indeterminate solution.

Stakeout coordinates: compute the point on the design line nearest the station, then offset distance and direction; verify with an independent check measurement before setting the final monument.

Tolerance tables: NGS and most state DOTs specify accuracy standards by order/class (e.g., relative closure and elevation misclosure), and the survey must be designed and documented to meet the specified order.

Curve data relationships: for a degree of curve defined by the arc definition, D = 5729.578/R (R in feet); for the chord definition, D = 2 arcsin(50/R). State which definition is used.

Compound and reverse curves share a common tangent at the PCC/PRC; spiral (transition) curves provide gradual superelevation and are defined by length and spiral angle.

Vertical curve geometry: BVC and EVC stations are at L/2 from the PVI; the curve is symmetric for equal-tangent design; K = L/A gives the length per 1% change in grade.

Sight distance and stopping sight distance on crest vertical curves depend on K, design speed, and driver eye/reaction values; sag curves are controlled by headlight and comfort criteria.

Earthwork: average end area volume = L × (A₁ + A₂)/2; prismoidal formula = L/6 × (A₁ + 4Aₘ + A₂). Use the prismoidal correction when areas change rapidly.

Cross sections: area by coordinates or by the trapezoidal rule; borrow and waste volumes are tracked separately from cut and fill, and shrinkage/swell factors adjust for material type.

Horizontal alignment: station equations (e.g., 10+00 = 10+50) create a negative or positive equation; always resolve equations before computing distances along the centerline.

Superelevation: e + f = V²/(15R) with V in mph and R in feet gives the relationship among rate of superelevation, side friction, speed, and radius.

Coordinate transformation: a 2D Helmert (similarity) transformation uses four parameters - two translations, one rotation, one scale - and needs at least two common control points.

Least-squares adjustment output: residuals, a posteriori variance of unit weight, covariance matrix, and error ellipses; a large standardized residual flags a possible blunder or an incorrect observation weight.

Confidence region: the standard error ellipse axes are derived from the eigenvalues of the 2×2 covariance submatrix; the 95% ellipse is about 2.45 times the standard ellipse area.

GNSS observation types: code (pseudorange) and carrier phase. Carrier phase is far more precise but requires ambiguity resolution; cycle slips must be detected and repaired.

Differential correction: single difference removes satellite clock errors, double difference removes receiver clock errors, and triple difference resolves the integer ambiguity between epochs.

Coordinate systems: geodetic (latitude, longitude, ellipsoid height) versus geocentric (X, Y, Z) versus grid (N, E). Convert with datum transformations that specify the ellipsoid and shift parameters.

Traverse design: closed-loop traverses provide a geometric check; connecting traverses tie to higher-order control. Angular closure should be checked before linear closure to isolate the error source.

Quality control: independent check measurements, redundant observations, and documented field notes are the required evidence that a survey meets its stated accuracy standard.

Boundary evidence hierarchy (general rule): natural monuments, then artificial monuments, then adjoining property lines and acreage, then courses and distances, then area or quantity.

Adverse possession elements typically include actual, open and notorious, exclusive, hostile, and continuous possession for the statutory period; the specific elements and period are set by state law.

Easements: an easement appurtenant benefits a dominant tenement; an easement in gross benefits a person or entity. Prescriptive easements require use that is open, adverse, and continuous for the statutory period.

Riparian and littoral boundaries: the ordinary high water mark and meander lines are not boundary lines; accretion belongs to the riparian owner, while avulsion does not change the boundary.

Record versus measured evidence: a surveyor must retrace the original survey, not create a new one. Original monuments control over later measurements, and the record bearing/distance is evidence of the original location.

PLSS special cases: fractional lots along the north and west tiers of a township, meander corners at water bodies, and the closing corner where a township line meets a standard parallel.

Professional practice: the surveyor's seal and signature certify the work; field notes and calculations should be retained per state record-retention rules, and the survey report should state the basis of bearings and datum used.

Ethics and liability: a surveyor owes duties to the client and the public; disclosing known boundary discrepancies and avoiding conflicts of interest are professional obligations, and statutes of limitations vary by state.

Units and conversions: 1 mile = 5,280 ft = 80 chains = 320 rods; 1 chain = 66 ft = 100 links; 1 acre = 43,560 ft² = 10 square chains; 1 hectare = 10,000 m² = 2.471 acres.

Angles: 1° = 60′ = 3,600″; converting decimal degrees to DMS requires carrying the fractional minute into seconds. A 1″ error at 1 mile is about 0.025 ft.

Trigonometry identities useful in traverse work: sin²θ + cos²θ = 1; tanθ = sinθ/cosθ; the law of sines a/sinA = b/sinB = c/sinC; the law of cosines c² = a² + b² − 2ab cosC.

Coordinate geometry checks: the sum of latitudes and departures around a closed figure must be zero; the sum of double meridian distances × latitudes equals twice the area and must match the shoelace result.

Field note standards: record instrument station, backsight, foresight, HI, rod readings, weather, and the observer; notes must be legible, in ink, and corrections struck through rather than erased.

Instrument checks: a level's line of sight must be parallel to the bubble tube (two-peg test); a total station's vertical index error and horizontal collimation error are checked and stored as instrument constants.

Scale and precision: map scale 1:24,000 means 1 in = 2,000 ft; a plotted position is only as good as the map's stated accuracy, so do not derive boundary coordinates from a small-scale map.

Safety and field logistics: traffic control, utility locating (call 811 before digging), and monument preservation are part of the survey plan and are documented in the field record.

Coordinate geometry for curves: compute PC and PT from the PI, then set stations by deflection angle δ = (arc length)/(2R) in radians or by chord offsets. Long chords and subchords must be handled separately when the curve is staked by increments.

Spiral curve elements: spiral angle θs = Ls/(2R) in radians; shift p and long tangent X and Y are tabulated or computed from θs; the spiral is inserted between tangent and circular curve at the TS, SC, CS, and ST points.

Vertical curve high/low point station = BVC station + x, where x = g₁L/(g₁ − g₂) in the same units; the elevation there is computed from the curve equation, not by linear interpolation.

Grade and slope: percent grade = (rise/run) × 100; convert between percent grade and vertical angle with tan(angle) = grade/100. A 2% grade over 500 ft changes elevation by 10 ft.

Volume from contours or grid: average the elevations at grid nodes, multiply by the cell area, and sum; the prismoidal correction applies to rapidly changing terrain, and the choice of method should be documented.

Horizontal curve sight distance: for a curve with an obstruction at offset m from the centerline, the available sight distance is computed from the geometry of the chord and the obstruction; check against the design stopping sight distance.

Alignment checks: the tangent length T plus the curve length L plus the remaining tangent must equal the total PI-to-PI distance, and stations must be continuous across the PC and PT.

Datum and projection: state plane coordinates are grid distances; convert ground distances to grid with the combined factor before computing closures on grid coordinates, and back again for stakeout.

Measurement uncertainty: report results with the correct number of significant figures and an explicit uncertainty statement; a coordinate without a stated accuracy is not a survey product.

Blunder detection: a single large residual in a traverse usually indicates a misread or transposed angle/distance. Check angular closure first, then linear closure, to localize the error.

Reciprocal observations: measuring an angle in both faces (direct and reverse) cancels instrumental errors such as collimation and vertical index error; the mean of the two faces is the accepted value.

Leveling errors: refraction and curvature are reduced by balancing backsight and foresight distances; rod settlement, tripod settlement, and bubble drift are systematic errors that balancing does not remove.

EDM corrections: apply atmospheric correction (temperature and pressure), prism constant, and instrument/reflector height. Slope distance must be reduced to horizontal and then to the datum for grid coordinates.

GNSS accuracy: accuracy degrades with multipath, poor satellite geometry (high PDOP), and long baselines. A fixed solution with good geometry and short baselines is required for control-grade work.

Map projections: the scale factor is 1 along the standard parallel(s) and grows away from them; combined with the elevation factor it gives the combined factor used to move between ground and grid distances.

Documentation: a survey report should state the datum, basis of bearings, accuracy standard, methods, equipment, and any discrepancies found, so a later surveyor can retrace the work.

Area and volume units: 1 ft³ = 7.48 gallons; 1 yd³ = 27 ft³; 1 acre-ft = 43,560 ft³. Earthwork quantities are usually reported in cubic yards.

Slope staking: the catch point is where the design side slope intersects existing ground; the horizontal distance from centerline is w/2 + (cut or fill) × side slope ratio.

Construction layout tolerances: building corners are typically staked to tighter tolerances than roadway centerlines; the tolerance must match the purpose and be stated in the contract documents.

Horizontal control: traverse or GNSS static networks provide control; vertical control uses differential leveling or GNSS with a geoid model. Never mix control of different orders without documenting the adjustment.

Coordinate systems for construction: a local assumed coordinate system is common on site; record the transformation to the state plane or record system so the work can be tied back.

As-built surveys: measure the constructed feature and compare to design; report deviations with the measurement uncertainty, not just a pass/fail statement.

Monument records: record the monument type, cap, and ties (distance and bearing to at least two references) so the monument can be reestablished if disturbed.

Professional responsibility: the surveyor must not certify work outside their competence, must disclose conflicts, and must follow the state board's rules on seals, signatures, and continuing education.

Angle measurement: a repeating theodolite or total station measures an angle multiple times to reduce random error; the mean of n repetitions has standard error reduced by √n.

Direction versus angle: directions are measured from a backsight or from north; angles are the difference of directions. Record the reference direction (azimuth or bearing) for every set of angles.

Traverse computations: compute latitudes and departures, sum them, compute linear misclosure, adjust, then compute coordinates. Verify the adjusted traverse closes and the area matches an independent method.

Curve staking by offsets: the middle ordinate and tangent offset methods set points from the tangent; the deflection method sets points from the PC. Choose the method that keeps the tape or EDM within a practical distance.

Vertical curve checks: the curve elevation at the PVI equals the average of the tangent elevations at the PVI plus the external distance correction; verify the high/low point lies within the curve length.

GNSS height: ellipsoid height minus geoid separation gives orthometric height; the geoid model must match the datum (e.g., NAVD88) and the separation sign must be applied correctly.

Legal principles: a deed that is ambiguous is construed against the grantor; a call for a monument generally prevails over a call for distance, and a call for an adjoiner prevails over a call for area.

Records research: chain of title, plats, highway records, and prior surveys are the evidence base for a boundary survey; the surveyor must reconcile conflicts and document the reasoning.

Computational geometry: the perpendicular distance from a point to a line through two known points = |(X₂ − X₁)(Y₁ − Y₀) − (X₁ − X₀)(Y₂ − Y₁)| ÷ √[(X₂ − X₁)² + (Y₂ − Y₁)²].

Line-line intersection: solve the two line equations simultaneously; a near-parallel pair produces an ill-conditioned intersection with a large uncertainty, so check the intersection angle.

Circle-circle intersection: the two solutions are symmetric about the line joining the centers; the distance between centers must be between the difference and the sum of the radii for a real solution.

Coordinate rounding: carry more decimal places in intermediate computations than in the final result; rounding intermediate coordinates can introduce errors larger than the survey tolerance.

Angular units in software: verify whether the software expects decimal degrees or DMS and whether bearings are quadrant or azimuth; a unit mismatch is a common source of gross error.

Checksums: compute the area by two independent methods (shoelace and DMD) and compare; a mismatch indicates a coordinate or transcription error, not a small adjustment.

Field-to-finish: the code library must be consistent across the crew and the office; a mis-coded feature can place a monument or utility in the wrong layer and mislead the client.

Deliverables: the plat, the report, and the digital file must agree; the digital file should include the coordinate system, units, and a metadata statement so it can be used correctly.

Survey orders: control surveys are classified by order and class with specified relative accuracies; a survey must be designed, executed, and checked to meet the order required by the project.

Network design: redundant observations and a closed geometry allow a least-squares adjustment and a statistical test of the residuals; a minimally constrained network cannot detect blunders.

Datum transformations: a seven-parameter Helmert transformation (three translations, three rotations, one scale) converts between geocentric datums; a three-parameter transformation omits rotation and scale and is less accurate over large areas.

Projection distortion: the combined factor should be near 1 for ground-level work; at high elevation the elevation factor reduces grid distances, and the scale factor increases them away from the central meridian.

Quality metrics: report the misclosure, the relative precision, the standard error of unit weight, and the error ellipse for control points; these are the evidence that the survey meets its standard.

Instrument calibration: total stations and levels should be calibrated on a baseline of known length and the results recorded; an uncalibrated EDM can produce a systematic scale error.

Boundary retracement: follow the footsteps of the original surveyor, use the original evidence, and do not set a new monument on a record line without resolving the controlling evidence.

Public records: file the plat and monument records as required by state statute; a survey that is not filed may not be discoverable by later surveyors and can cause boundary conflicts.

Trig leveling: elevation difference = horizontal distance × tan(vertical angle) + instrument height − target height, with curvature and refraction correction applied for long shots.

Reciprocal trig leveling: observe the same target from both ends and average the two elevation differences to cancel curvature, refraction, and instrument height errors.

Level loop adjustment: distribute the misclosure proportionally to the number of setups or to the distance, depending on the specified method, and document the method used.

Total station stakeout: compute the design coordinates, set the instrument on control, orient to a backsight, and check the orientation on a third known point before staking.

Construction offsets: a batter board or offset stake is set at a known distance from the design line so the line can be reestablished after excavation; record the offset in the field notes.

Machine control: a 3D grade system uses a total station or GNSS to guide the machine; the design model and the coordinate system must be verified before the work begins.

Volume reconciliation: compare design quantities to as-built quantities and explain differences; a large discrepancy may indicate a survey error or a design change.

Client communication: state the basis of the survey, the accuracy, the datum, and any limitations in plain language; the client must understand what the survey does and does not certify.

Error sources: instrumental (calibration), natural (refraction, temperature), and personal (reading, pointing) errors. Systematic errors are removed by procedure, random errors are reduced by repetition.

Refraction: the line of sight bends toward the earth, so a rod reading is too high; balancing backsight and foresight distances cancels the effect in leveling, and the correction is applied in trig leveling.

Temperature: steel tapes and EDM atmospheric corrections depend on temperature; record the temperature and apply the correction when the effect exceeds the tolerance.

Tension and sag: a tape supported only at the ends sags, making the measured distance too long; apply tension and sag corrections or use a supported tape.

Alignment: a tape not aligned with the line measures too long; the error is proportional to the cosine of the misalignment angle, so small misalignments have a small effect.

Plumb and centering: instrument centering error and target centering error propagate into angles and distances; use optical plummets and check the centering before each set.

Observation strategy: observe at the best time of day to minimize refraction (avoid midday heat shimmer), and use the shortest practical sight distances consistent with the design.

Documentation: record the corrections applied and the assumptions made, so the survey can be independently checked and reproduced.

Coordinate systems: a local grid is defined by an origin, a rotation, and a scale relative to the state plane or record system; record the transformation parameters with the project.

Control densification: set secondary control from the primary network, check the new points against at least one independent primary point, and adjust the network as a unit.

Traverse station selection: choose stations with intervisible lines, stable ground, and safe access; a station that cannot be occupied or seen is useless regardless of its geometry.

Angle geometry: a traverse with angles near 180° (straight lines) has weak angular strength; a traverse with angles near 0° or 180° is ill-conditioned for intersection, so check the geometry.

Distance geometry: a traverse with short courses and long courses mixed has uneven precision; weight the observations by their actual precision rather than assuming equal weights.

Check measurements: measure a known distance or angle between two control points at the end of the survey; a check that agrees within tolerance confirms the survey, and a check that disagrees localizes the error.

Field notes: record the raw observations, not just the reduced values; the raw data allow a later surveyor to recompute and verify the work.

Safety: a survey plan includes traffic control, personal protective equipment, and a communication plan; the field crew must have the authority to stop work when conditions are unsafe.

Map scale: a scale of 1:1,000 means 1 unit on the map equals 1,000 units on the ground; a map distance of 5 cm represents 50 m. Choose a scale that supports the required positional accuracy.

Contours: the contour interval is the vertical distance between adjacent contours; a steep slope has closely spaced contours, and a flat area has widely spaced contours.

Digital terrain: a TIN is built from irregular points and breaklines; a grid DEM is built from a regular grid. Breaklines must be included to preserve ridges, valleys, and edges.

Photogrammetric accuracy: the accuracy of a photogrammetric map depends on the flying height, camera focal length, and control; it is not improved by plotting at a larger scale.

LiDAR: point density and classification determine the usable accuracy; ground points must be classified before generating a bare-earth DEM, and vegetation and structures must be removed.

GIS data: the coordinate system, datum, and units must be recorded in the metadata; a GIS layer without metadata is not reliable for survey-grade work.

Data transfer: check the file format, units, and coordinate system when moving data between field and office; a mismatch is a common source of gross error.

Deliverable review: check the plat, report, and digital file against each other and against the field notes before delivery; a discrepancy found after delivery is a professional liability.

Statutes and rules: state boards regulate licensure, seals, and practice; the surveyor must know the state's minimum standards for boundary surveys and the filing requirements for plats and monument records.

Continuing education: most states require continuing education units for license renewal; the requirement and the accepted subject areas are set by the state board.

Business practice: a survey contract should define the scope, the standard of care, the deliverables, and the fee; an unclear scope is a common source of disputes.

Liability: the surveyor is liable for negligence and for errors that cause foreseeable harm; professional liability insurance and careful documentation are risk-management tools, not substitutes for competence.

Expert witness: a surveyor may testify on boundary and measurement matters; the testimony must be based on evidence and sound methodology, not on advocacy for a party.

Ethics: the surveyor must avoid conflicts of interest, must not misrepresent qualifications, and must report known errors to the affected parties.

Records retention: retain field notes, calculations, and correspondence for the period required by state law and the contract; these records are the evidence of the work performed.

Public safety: a survey that affects public infrastructure or safety must be reviewed and signed by a qualified professional, and any unsafe condition observed in the field should be reported.

Horizontal angles: an angle to the right is measured clockwise from the backsight to the foresight; an angle to the left is measured counterclockwise. Record the sense explicitly to avoid a 180° error.

Azimuth computation: azimuth of a line = azimuth of the previous line + angle to the right − 180°, normalized to 0°–360°. Check the closing azimuth against the starting azimuth.

Coordinate computation: northing = previous northing + latitude; easting = previous easting + departure. Latitude = distance × cos(azimuth); departure = distance × sin(azimuth).

Inverse computation: distance = √(ΔN² + ΔE²); azimuth = atan2(ΔE, ΔN) normalized to 0°–360°. Check the quadrant of the result before using it.

Curve stationing: station = station of PC + arc length along the curve; the station of the PT must equal the station of the PC plus the curve length.

Vertical curve stationing: station = station of BVC + x; the elevation at the EVC must equal the elevation computed from the forward tangent.

Adjustment check: after adjustment, the sum of latitudes and departures must be zero and the computed area must match the independent area; a residual indicates an arithmetic error.

Report: state the basis of bearings, the datum, the adjustment method, and the final misclosure so the survey can be evaluated and retraced.

GNSS positioning: the receiver measures pseudorange and carrier phase to at least four satellites; the position solution is in the WGS84/ITRF frame and must be transformed to the project datum.

Static versus RTK: static surveys occupy points for long sessions and post-process the data for high accuracy; RTK provides real-time positions with accuracy that depends on baseline length and correction quality.

Network RTK: a network of reference stations models the atmospheric and orbit errors over an area; the rover receives corrections that are valid within the network's service area.

Ambiguity resolution: a fixed solution requires enough satellites, good geometry, and short baselines; a float solution is less precise and should not be used for control-grade work.

Multipath: signals reflected from buildings, water, or metal cause multipath errors; avoid these environments, use a choke-ring antenna, and observe longer sessions to reduce the effect.

Geoid: the geoid model converts ellipsoid height to orthometric height; using the wrong model or the wrong sign of the separation produces a systematic height error.

Coordinate transformation: transform GNSS positions to the project datum with a documented transformation and check the result against known control points before using it.

Quality control: record the PDOP, the number of satellites, the solution type, and the baseline length for each GNSS observation; these are the evidence that the position meets the required accuracy.

Leveling instruments: an automatic level uses a compensator to keep the line of sight horizontal; a digital level reads a bar-coded rod and reduces reading errors.

Rod handling: keep the rod vertical with a bubble or plumb line; a rod out of plumb by 1° over 10 ft introduces about 0.0015 ft of error, and the error grows with the rod reading.

Turning points: a turning point must be stable and must be used for both a foresight and the next backsight; a disturbed turning point invalidates the loop.

Loop closure: a closed level loop should return to the starting benchmark within the allowable misclosure; a large misclosure indicates a blunder or a disturbed benchmark.

Benchmark checks: check the starting benchmark against a second known benchmark before beginning; a wrong starting elevation propagates through the entire loop.

Trig leveling: use it for rough or inaccessible terrain, and apply curvature and refraction; it is less precise than differential leveling and should not be used for control.

Vertical control: NAVD88 is the current vertical datum in the U.S.; record the datum and the benchmark used for every vertical survey.

Documentation: record the instrument, the rod, the benchmark, the loop route, and the misclosure; the record allows the survey to be checked and repeated.

Boundary survey process: research the record, recover the evidence, evaluate the evidence against the record, and then set or hold monuments; the process is retracement, not original creation.

Evidence evaluation: original monuments set by the original surveyor control over later monuments; a later surveyor's monument that conflicts with the original evidence does not control.

Conflicts: when the record and the evidence conflict, the surveyor must resolve the conflict using the rules of construction and document the reasoning; the client should be informed of the conflict.

Unwritten rights: adverse possession, prescription, and practical location can create rights that are not in the record; the surveyor must investigate and disclose known claims.

Water boundaries: the boundary is generally the ordinary high water mark or the thread of the stream, depending on state law; accretion and reliction change the boundary, while avulsion does not.

Plat and lot: a lot-and-block description depends on the plat; a discrepancy between the plat and the monument is resolved by the same evidence hierarchy.

Monument preservation: a found monument should be preserved and referenced; if it must be removed, it should be replaced and the replacement tied to the original location.

Report: the survey report should describe the evidence found, the reasoning, and the boundary as determined, so the client and later surveyors can understand the basis of the survey.

Area computation: for a closed polygon, the area is half the absolute value of the sum of the cross products of consecutive coordinates; the result is in square units of the coordinates.

Coordinate order: the cross-product formula requires the points in order around the polygon, either clockwise or counterclockwise; an out-of-order list produces a wrong area.

Curve area: the area between a curve and its chord is the segment area, computed from the central angle and the radius; the area between the curve and the tangents is the external area.

Volume computation: the average end area method is exact for prismoids with parallel end areas; the prismoidal formula is exact for prismoids with a linear area change.

Borrow and waste: borrow is material brought in, waste is material removed; track them separately and apply the appropriate shrinkage or swell factor.

Contours: the area within a contour is computed by the same coordinate method; the volume between contours is computed by the average end area or prismoidal method.

Check: compute the area by two independent methods and compare; a mismatch indicates a coordinate or transcription error.

Units: report area in the units required by the contract (square feet, acres, square meters, hectares) and state the units explicitly.

Instrument setup: set the tripod firmly, level the instrument with the foot screws, and check the optical plummet over the station; a poorly centered instrument introduces angle and distance errors.

Backsight orientation: orient to a known point with a known azimuth, and check the orientation by measuring to a third known point; a misorientation rotates the entire survey.

Angle measurement: use the direct and reverse faces and average the results; the difference between faces reveals collimation error and reading errors.

Distance measurement: measure to a prism with the correct prism constant and apply the atmospheric correction; a wrong prism constant produces a scale error in every distance.

Field checks: measure a known distance and a known angle at the start and end of the survey; a check that agrees within tolerance confirms the work.

Data recording: record the raw observations and the instrument constants; the office reduction must be reproducible from the field record.

Equipment care: protect the instrument from shock, moisture, and extreme temperature; a damaged instrument may produce systematic errors that are not obvious in the field.

Calibration: calibrate the instrument on a baseline of known length and record the results; an uncalibrated instrument can produce a scale error that grows with distance.

Horizontal curve layout: the PC and PT are computed from the PI, the tangent length, and the curve length; the station of the PI is the station of the PC plus the tangent length.

Deflection angles: the deflection angle to a point on the curve is half the central angle to that point; the total deflection to the PT is half the total central angle.

Chord and arc: the chord is shorter than the arc; for small central angles the difference is negligible, but for large angles the chord must be used for staking by chord.

Compound curves: the PCC is the point where two curves of different radii join; the tangent at the PCC is common to both curves.

Reverse curves: the PRC is the point where the curve reverses direction; a reverse curve requires a tangent or a spiral between the curves for safe operation.

Spiral curves: the spiral provides a gradual change in curvature and superelevation; the spiral angle and the shift are computed from the spiral length and the radius.

Sight distance: check the available sight distance on the curve against the design stopping sight distance; an obstruction inside the curve can reduce the sight distance below the design value.

Documentation: record the curve data, the staking method, and the checks; the record allows the curve to be reestablished.

Error ellipse: the semi-major and semi-minor axes are the square roots of the eigenvalues of the covariance matrix; the orientation is the eigenvector direction.

Standard error of unit weight: computed from the residuals and the redundancy; a value near 1 indicates that the observation weights are consistent with the actual precision.

Residual analysis: a standardized residual greater than about 3 is a strong indication of a blunder or an incorrect weight; investigate before accepting the adjustment.

Redundancy: the number of redundant observations is the number of observations minus the number of unknowns; a small redundancy gives a weak check on the observations.

Datum defect: a network with no fixed control has a datum defect; the adjustment must constrain at least one point (or use a free-network adjustment) to define the datum.

Confidence level: the standard error ellipse is about 39% confidence; the 95% ellipse is about 2.45 times the area of the standard ellipse.

Report: report the adjusted coordinates, the covariance matrix, the error ellipses, and the standard error of unit weight; these are the evidence of the adjustment quality.

Software: verify the software's weighting, constraint, and output conventions; a misunderstanding of the software's conventions is a common source of adjustment errors.

Deed interpretation: the rules of construction guide the interpretation of ambiguous deeds; the surveyor applies them to the evidence, not to the surveyor's preference.

Priority of calls: natural monuments, artificial monuments, adjoining boundaries, courses and distances, and area, in that general order; the order can vary by state and by the specific deed language.

Senior rights: the senior conveyance controls over the junior conveyance when the two conflict; the surveyor must determine the order of conveyance from the title record.

Practical location: a long-accepted location of a boundary can control over the record if the parties have treated it as the boundary; the surveyor must investigate the history of possession.

Easements: an easement is a nonpossessory right; the surveyor must locate the easement from its description and show it on the plat without implying ownership.

Encroachments: an encroachment is a physical intrusion onto a property; the surveyor must show it and inform the client, but the legal remedy is for the parties or the court.

Monumentation: set monuments at the corners determined by the survey, and reference them to the record and to the evidence; the monument is the physical evidence for the future.

Report: the survey report should state the basis of the boundary determination and the evidence relied on, so the client and later surveyors can evaluate it.

Project planning: define the purpose, the required accuracy, the datum, and the deliverables before starting; the survey design follows from these requirements.

Reconnaissance: inspect the site, locate the control, and identify the hazards before the field work; a reconnaissance can reveal problems that change the survey design.

Control: establish control before the detail survey; the control must be of higher accuracy than the detail it supports.

Field methods: choose the method (total station, GNSS, leveling) that meets the accuracy requirement at the lowest cost; do not use a method that cannot meet the requirement.

Checks: build redundancy and independent checks into the survey; a survey without checks cannot demonstrate its accuracy.

Data management: back up the field data, record the file names and the dates, and keep the raw data; the raw data are the evidence of the survey.

Deliverables: the plat, the report, and the digital file must be consistent and must state the datum, the units, and the accuracy.

Closeout: review the deliverables against the scope, obtain the client's acceptance, and archive the records; a survey that is not archived cannot be defended later.

Units: the U.S. survey foot (1200/3937 m) differed from the international foot (0.3048 m) by about 2 ppm; the difference is significant over long distances and must be tracked in legacy data.

State plane: each zone has a defined central meridian, standard parallels, and scale factor; the zone must be recorded with the coordinates.

Datum: NAD83 (2011) and NATRF2022 are the modern horizontal datums; NAVD88 and NAPGD2022 are the modern vertical datums. Mixing datums without transformation introduces errors.

Coordinates: grid coordinates are not ground coordinates; convert with the combined factor and record the factor used.

Elevations: orthometric heights are referenced to the geoid; ellipsoid heights are referenced to the ellipsoid; the difference is the geoid separation.

Accuracy: the accuracy of a coordinate is not the same as its precision; a coordinate reported to 0.001 ft may be accurate only to 0.1 ft.

Metadata: record the datum, the units, the projection, the accuracy, and the source for every digital deliverable.

Traceability: the survey must be traceable to the control and the record; a coordinate without a traceable basis is not a survey product.

Safety: the field crew must wear high-visibility clothing, use traffic control, and follow the utility locate rules; call 811 before any excavation or stake placement.

Utilities: locate and mark underground utilities before staking; a stake driven into a utility is a serious safety incident.

Weather: avoid working in lightning, high wind, or extreme heat; the instrument and the crew are both at risk.

Access: obtain permission before entering private property; a surveyor without permission may be trespassing, and the client relationship can be damaged.

Communication: maintain radio or phone contact between crew members; a lone worker should have a check-in schedule.

Emergency: know the location of the nearest hospital and the emergency contact; a field crew should have a first-aid kit and a plan.

Documentation: record the safety briefing and any incidents; the record supports the claim that the crew followed the safety plan.

Stop work: any crew member must have the authority to stop work when conditions are unsafe; production pressure is not a reason to accept a hazard.

Horizontal curve formulas: T = R tan(Δ/2); L = RΔ (Δ in radians); E = R[sec(Δ/2) − 1]; M = R[1 − cos(Δ/2)]; LC = 2R sin(Δ/2). The degree of curve D relates to R by D = 5729.578/R (arc definition).

Vertical curve formulas: elevation = BVC + g₁x + [(g₂ − g₁)/(2L)]x²; K = L/A; the high/low point is at x = −g₁L/(g₂ − g₁).

Traverse formulas: latitude = D cos(az); departure = D sin(az); misclosure = √(Σlat² + Σdep²); relative precision = misclosure/perimeter.

Area formulas: shoelace 2A = Σ(XᵢYᵢ₊₁ − Xᵢ₊₁Yᵢ); DMD method double area = Σ(DMD × latitude).

Leveling formulas: HI = BM + BS; elevation = HI − FS; misclosure = measured − known.

Coordinate formulas: N = N₀ + Σlat; E = E₀ + Σdep; inverse distance = √(ΔN² + ΔE²); azimuth = atan2(ΔE, ΔN).

Scale formulas: grid distance = ground distance × combined factor; combined factor = scale factor × elevation factor; elevation factor ≈ R/(R + h).

Curvature and refraction: combined correction ≈ 0.0206D² (D in thousands of ft, ft) or 0.0675D² (D in km, m), applied as a negative correction to the rod reading.

Field notes: record the date, time, weather, crew, instrument, and station; the notes must be legible and must not be erased.

Sketches: a field sketch shows the relationship of the features and the control; a sketch is often more useful than a list of coordinates.

Codes: use a consistent feature code library; a mis-coded feature can be placed in the wrong layer and mislead the client.

Photos: take photos of the control, the monuments, and the site conditions; a photo can resolve a dispute about what was found.

Backup: back up the field data at the end of each day; a lost data file can require a return to the field.

Reduction: reduce the data in the office with a documented method; the reduction must be reproducible from the raw data.

Review: have a second person review the calculations and the deliverables; an independent review catches errors that the original surveyor may miss.

Archive: archive the raw data, the calculations, and the deliverables; the archive is the evidence of the survey and is required for records retention.

Horizontal control: use a closed traverse or a GNSS static network; adjust the network and report the misclosure and the error ellipses.

Vertical control: use differential leveling or GNSS with a geoid model; check the starting benchmark against a second benchmark.

Densification: set secondary control from the primary network; check the new points against at least one independent primary point.

Monumentation: set durable monuments with caps that identify the surveyor and the date; reference each monument to at least two other points.

Preservation: preserve found monuments and reference them; if a monument must be removed, replace it and tie the replacement to the original location.

Records: file the monument records and the plat as required by state law; a record that is not filed may not be found by later surveyors.

Quality: report the accuracy of the control and the method used; a control point without a stated accuracy is not a control point.

Review: have the control network reviewed by a second qualified surveyor before the detail survey begins; an error in the control propagates through the entire project.

Construction staking: compute the design coordinates, set the instrument on control, orient to a backsight, and check the orientation on a third known point.

Offsets: set an offset stake at a known distance from the design line so the line can be reestablished after excavation; record the offset.

Cut and fill: cut = existing ground − design elevation; fill = design elevation − existing ground; a positive cut means excavation.

Slope staking: the catch point is where the design side slope intersects existing ground; the horizontal distance from centerline is w/2 + (cut or fill) × side slope ratio.

As-built: measure the constructed feature and compare it to the design; report the deviation with the measurement uncertainty.

Tolerances: the staking tolerance must match the purpose and the contract; a building corner is staked more tightly than a roadway centerline.

Documentation: record the staking data, the checks, and the as-built measurements; the record supports the acceptance of the work.

Coordination: coordinate with the contractor and the engineer before staking; a change in the design after staking can invalidate the work.

Ethics: the surveyor must be honest, competent, and objective; the client's interest does not justify a false statement.

Conflicts of interest: disclose any financial or personal interest that could affect the survey; a conflict that is not disclosed undermines the survey.

Competence: do not accept work outside your competence; a surveyor who lacks the expertise should associate with a qualified professional.

Confidentiality: protect the client's information; do not disclose it without permission or legal requirement.

Public safety: report unsafe conditions observed in the field; the surveyor's duty extends to the public.

Records: keep accurate records and do not alter them; a record that is altered is not credible evidence.

Advertising: do not misrepresent qualifications or experience; a false claim is a violation of the professional rules.

Reporting errors: report known errors to the affected parties and take corrective action; concealing an error is a serious violation.

Total station: measures horizontal and vertical angles and slope distance; the instrument constants (prism constant, atmospheric correction) must be set correctly.

Digital level: reads a bar-coded rod and reduces reading errors; the rod must be vertical and the instrument must be calibrated.

GNSS receiver: measures pseudorange and carrier phase; the solution type (fixed, float, autonomous) must be recorded.

Software: computes coordinates, areas, and adjustments; the software's conventions (units, bearing format, weighting) must be verified.

Data collector: records the field data and the codes; the data must be backed up and transferred correctly.

Calibration: calibrate the instruments on a baseline of known length and record the results; an uncalibrated instrument can produce a systematic error.

Maintenance: protect the equipment from shock, moisture, and extreme temperature; a damaged instrument may produce errors that are not obvious.

Verification: check the equipment against a known standard before and after the survey; the check is the evidence that the equipment was working correctly.

Boundary evidence: original monuments, undisturbed natural features, and the record of the original survey are the primary evidence; later monuments and measurements are secondary.

Retracement: follow the footsteps of the original surveyor; do not create a new boundary where the original can be retraced.

Conflicts: resolve conflicts using the rules of construction and document the reasoning; the client should be informed of the conflict.

Unwritten rights: investigate adverse possession, prescription, and practical location; the surveyor must disclose known claims.

Water boundaries: the boundary is generally the ordinary high water mark or the thread of the stream; accretion and reliction change the boundary, while avulsion does not.

Plat and lot: a lot-and-block description depends on the plat; a discrepancy is resolved by the evidence hierarchy.

Monumentation: set monuments at the corners determined by the survey and reference them to the record and the evidence.

Report: describe the evidence, the reasoning, and the boundary as determined, so the client and later surveyors can understand the basis of the survey.

Accuracy versus precision: accuracy is closeness to the true value; precision is closeness of repeated measurements to each other. A precise but biased survey is not accurate.

Systematic errors: errors that have a consistent sign and magnitude; they are removed by calibration, procedure, and correction.

Random errors: errors that vary in sign and magnitude; they are reduced by repetition and by averaging.

Blunders: gross errors such as misread angles or transposed digits; they are detected by checks and redundancy.

Propagation: the uncertainty of a computed value depends on the uncertainties of the inputs and the geometry of the computation; a weak geometry amplifies the input errors.

Tolerance: the allowable misclosure is set by the standard for the survey; a survey that exceeds the tolerance must be reobserved or adjusted.

Reporting: report the result with its uncertainty and the method used; a result without an uncertainty is not a complete survey product.

Review: have the calculations reviewed by a second qualified surveyor; an independent review catches errors that the original surveyor may miss.

PLSS: a normal township is 6 × 6 miles with 36 sections of 1 square mile each; sections are numbered 1–36 beginning at the northeast corner.

Correction lines: standard parallels are established at intervals to absorb the convergence of meridians; the north and west tiers of a township are fractional lots.

Meander corners: set at the intersection of a survey line with a water body; the meander line is not a boundary line.

Closing corners: set where a township line meets a standard parallel; the closing corner is not the same as a standard corner.

Aliquot parts: a description such as the NE¼ of the SW¼ of Section 12 identifies a specific parcel; the order of the fractions matters.

Monuments: PLSS corners are monumented; the original monument controls over the record bearing and distance.

Records: the plats and field notes of the original survey are the primary record; the surveyor must research them.

Report: state the PLSS evidence found and the boundary as determined; the report should be traceable to the record.

Project scope: define the purpose, the accuracy, the datum, and the deliverables; the scope drives the survey design and the fee.

Proposal: state the scope, the schedule, the fee, and the assumptions; an unclear proposal is a common source of disputes.

Contract: define the standard of care, the deliverables, the ownership of the data, and the dispute resolution; the contract should be in writing.

Schedule: plan the field work around the weather and the site access; a realistic schedule reduces the risk of errors from rushing.

Communication: keep the client informed of the progress and of any problems; an informed client is less likely to dispute the result.

Change orders: document any change in the scope and its effect on the fee and the schedule; an undocumented change is a dispute waiting to happen.

Closeout: review the deliverables against the scope, obtain the client's acceptance, and archive the records.

Liability: carry professional liability insurance and document the work; insurance and documentation are risk-management tools, not substitutes for competence.