NV Land Surveyor cheat sheet

Angular units: 1 degree = 60 minutes = 3600 seconds; 360 degrees = 400 grads = 6400 mils = 2π radians. Convert DMS to decimal degrees by dividing minutes by 60 and seconds by 3600.

Bearings are quadrant angles measured from north or south toward east or west, 0 to 90 degrees, and must name both reference meridian and direction (e.g., N 45 E). Azimuths are clockwise from north, 0 to 360 degrees.

Azimuth = bearing in NE quadrant; 180 − bearing in SE; 180 + bearing in SW; 360 − bearing in NW. Reverse (back) bearing differs by 180 degrees.

Horizontal angles are measured in a horizontal plane; vertical angles are measured from the zenith (zenith angle) or from the horizon (elevation/depression). Zenith angle + altitude angle = 90 degrees.

North references differ: true (geodetic) north, magnetic north (varies with declination and time), grid north, and assumed north. Declination east means magnetic north lies east of true north.

Accuracy versus precision: accuracy is closeness to the true value; precision is repeatability among observations. Random errors scatter; systematic (instrumental, personal, natural) errors bias results consistently.

Closure rules: sum of interior angles of a closed polygon = (n − 2) × 180 degrees. For a closed traverse, sum of deflection angles = 360 degrees and sum of exterior angles = (n + 2) × 180 degrees.

Scale: map distance / ground distance. A 1:24,000 scale means 1 unit on the map equals 24,000 of the same units on the ground; 1 inch = 2,000 ft at 1:24,000.

Leveling fundamentals: elevation difference = backsight − foresight; height of instrument (HI) = benchmark elevation + backsight; elevation of a point = HI − foresight.

Horizontal curves: tangent length T = R tan(Δ/2); curve length L = RΔ (Δ in radians) or L = 100Δ/D for degree-of-curve D; external E = R[sec(Δ/2) − 1]; middle ordinate M = R[1 − cos(Δ/2)].

Degree of curve: arc definition D = 5729.58/R (feet) and chord definition D = 2 arcsin(50/R). Use arc definition for highway curves, chord definition for railroad curves.

Vertical curves (parabolic): length L = |A| × K, where A is algebraic grade change in percent and K = L/A. Elevation at any station: y = y_PVC + g1 x + [(g2 − g1)/2L] x².

Earthwork: average end area volume V = (A1 + A2)/2 × L, with L in the same units as areas; prismoidal correction V = L(A1 + 4Am + A2)/6 for more accurate volumes.

Area by coordinates (shoelace): 2A = Σ(Xi × Yi+1 − Xi+1 × Yi), summing around the closed traverse and returning to the first point.

Horizontal distance and elevation from total station: HD = SD × sin(zenith angle); VD = SD × cos(zenith angle). For slope distance and vertical angle, HD = SD cos(α), VD = SD sin(α).

Traverse computations: latitude (northing) = distance × cos(azimuth); departure (easting) = distance × sin(azimuth). Linear misclosure = √(Σlat² + Σdep²); relative precision = misclosure / perimeter.

GPS/GNSS: at least 4 satellites for a 3D position (3 for 2D + clock). RTK provides centimeter-level positions with a base station; static GNSS is used for control networks.

Photogrammetry and LiDAR: scale of a vertical photo = flying height above ground / focal length. LiDAR returns dense point clouds; DEM represents bare earth, DSM includes surface features.

Differential leveling: HI = BM elevation + BS; FS subtracted to get point elevation. Sum of BS − sum of FS = last elevation − first elevation (level-loop check).

Level loop misclosure: compare computed closure to allowable closure (e.g., 0.05 ft × √miles for ordinary leveling); distribute error proportionally to distance or number of setups.

Traverse adjustment: compass (Bowditch) rule corrects latitude/departure in proportion to course length; transit rule corrects in proportion to latitude/departure magnitude.

Compass rule corrections: correction to lat = −(Σlat) × (course length / perimeter); correction to dep = −(Σdep) × (course length / perimeter).

Angular misclosure: compare sum of observed interior angles to (n − 2) × 180; distribute equally among angles or by setup.

Coordinates from traverse: Northing = Northing_start + Σ latitudes; Easting = Easting_start + Σ departures. Inverse between two points: distance = √(ΔN² + ΔE²); azimuth = arctan(ΔE/ΔN) adjusted to the correct quadrant.

Resection and intersection: resection determines an unknown point from known points (three-point resection); intersection determines an unknown point from angles or distances measured from known points.

Stadia: horizontal distance = f/i × (upper − lower) × cos²(vertical angle) + constant; elevation difference uses the vertical component. Modern total stations replace stadia with EDM.

Coordinate geometry (COGO): point-on-line, offset, curve stakeout, and area routines all derive from the same latitude/departure and distance/azimuth relations.

Licensure: land surveyors are licensed by state boards; licensure typically requires education, experience under a licensed surveyor, and passage of the NCEES FS and PS exams.

NCEES FS exam is computer-based, closed-book, with a provided reference handbook; the PS exam follows for licensure. Confirm current format with NCEES before testing.

Ethics: protect public health, safety, and welfare; practice only within competence; sign and seal only work you prepared or directly supervised.

Conflict of interest: disclose any financial or personal interest that could bias a survey; do not accept compensation from multiple parties for the same service without disclosure.

Records and monuments: do not disturb or remove existing monuments without legal authority; preserve evidence and note found monuments on plats and field notes.

Boundary retracement: follow the footsteps of the original surveyor; consider senior rights, original monuments, and the hierarchy of evidence (monuments over distances, distances over areas).

Contracts and liability: define scope, deliverables, and standard of care in the agreement; standard of care is what a reasonably prudent surveyor would do under similar circumstances.

Statutes and standards: state minimum standards govern plat content, accuracy, and monumentation; ALTA/NSPS surveys follow the current ALTA/NSPS standards for title and lender purposes.

Seals and signatures: apply the seal only to final work; electronic seals must comply with state rules; keep records per state retention requirements.