NSPS CST Level II cheat sheet

Boundary evidence hierarchy: written record (deed, plat, survey) outranks physical monuments only when the record is unambiguous; otherwise original monuments control over later measurements.

Traverse closure ratio = total linear misclosure / total traverse length; compute misclosure as sqrt(ΔE² + ΔN²) after summing latitude and departure legs.

Angular misclosure for an n-sided closed traverse = sum of interior angles − (n − 2) × 180°; distribute by equal correction per angle unless instrument weights justify otherwise.

Compass rule (Bowditch): correction per leg = −(total misclosure) × (leg length / total traverse length); apply separately to latitudes and departures.

Level loop misclosure in feet = 0.05 × sqrt(miles) is a common third-order tolerance; second-order class I is roughly 0.035 × sqrt(miles).

Reciprocal vertical angles between two points cancel curvature and refraction; single zenith angles require curvature-and-refraction correction of about 0.0206 × D² ft with D in thousands of feet.

Horizontal curve: T = R × tan(Δ/2); L = R × Δ(radians); M = R × (1/cos(Δ/2) − 1); PC station = PI station − T.

Vertical curve: elevation at any point = PVC elev + g1 × x + ((g2 − g1)/2L) × x²; high/low point where x = −g1 × L / (g2 − g1).

State plane coordinates require a combined factor = grid scale factor × elevation factor, where elevation factor ≈ R / (R + h) using mean Earth radius.

Coordinate geometry: bearing = atan2(ΔE, ΔN) normalized to 0–360°; distance = sqrt(ΔE² + ΔN²); invert bearings to quadrant notation for record documents.

Area by coordinates (shoelace): 2A = Σ(Xi × Y(i+1) − X(i+1) × Yi) carried around the closed loop; result is signed, so take absolute value and divide by 2.

Least-squares adjustment reports residuals v, a posteriori reference variance σ₀² = (vᵀPv)/(n − u), and covariance Qxx; a residual exceeding 3σ suggests a blunder, not random error.

Error ellipse semi-axes come from eigenvalues of the 2×2 covariance submatrix; the 95% confidence ellipse scales the standard ellipse by 2.447 for 2 degrees of freedom.

Horizontal datum transformation: NAD27 to NAD83 shifts typically 10–100 m in CONUS; never mix datum epochs in one coordinate file without explicit transformation records.

Metadata/lineage for a deliverable must record datum, epoch, projection and zone, units, combined scale factor source, and the adjustment run identifier.

Parcel closure check: a metes-and-bounds description should close to the record area within the stated precision; a gap larger than the deed's precision triggers a review of calls and monument evidence.

Volume by average end area: V = L × (A1 + A2)/2; prismoidal V = L/6 × (A1 + 4Am + A2) is preferred when areas change rapidly between sections.

ALTA/NSPS Land Title Survey table A items are optional and must be negotiated in writing; the minimum standard requirements apply regardless of which optional items are selected.

Instrument setup order: level the tribrach with the plate bubble, then refine with the electronic level; forced-centering errors of 1 mm at 100 m produce about 2 seconds of angular error.

Traverse station spacing rule of thumb: keep legs roughly equal in length and avoid legs under 50 ft, which inflate angular error propagation.

Set-collection practice: observe directions in direct and reverse for each set; the mean of the two faces removes collimation error.

For GPS/GNSS RTK, horizontal precision is typically reported as 0.008 m + 1 ppm horizontally and 0.015 m + 1 ppm vertically; verify with a known check point each session.

PDOP above 6 degrades GNSS position quality; record PDOP and number of satellites with each observation for defensibility.

Differential leveling: balance sight distances to cancel curvature, refraction, and collimation; keep maximum sight length within the instrument's stated range.

Record field notes in waterproof ink with no erasures; strike through errors so the original entry remains legible.

Map scale ratio: 1 in = 100 ft equals 1:1,200; a plotted line of 0.03 in at that scale represents 3 ft on the ground.

Contour interval selection: interval should not exceed one-tenth of the map's required vertical accuracy, and index contours are labeled every fifth line.

Point cloud/DEM deliverable metadata: horizontal and vertical datum, resolution, classification scheme, and accuracy statement per ASPRS positional accuracy standards.

Coordinate file QA: check for duplicate point numbers, mixed units, and station/offset versus coordinate mismatches before release.

Legal description drafting: begin at a corner of record, cite the monument, give calls in bearing and distance, and close back to the point of beginning with area stated.

Deliverable review checklist: datum consistency, closure within tolerance, scale and legend correct, north arrow, and signature/seal block complete.