CA Surveying cheat sheet

Deed call priority, strongest to weakest: natural monuments, artificial monuments, courses and distances, then area or quantity.

Proportional conveyance: a grantor who conveys two parcels out of a larger tract by deeds calling for the same monuments conveys a proportionate share of any excess or deficiency to each grantee.

Accretion is gradual and imperceptible addition of land by water and belongs to the riparian owner; avulsion is sudden, and the boundary stays at the former water line.

On non-navigable streams riparian ownership normally extends to the thread (centerline); on navigable waters the state generally owns the submerged bed below ordinary high water.

A meander line only approximates the water boundary for area computation and never limits a riparian conveyance; the actual water line controls.

Adverse possession generally requires possession that is actual, open and notorious, exclusive, hostile, and continuous for the statutory period.

PLSS: a normal section contains 640 acres (one square mile), a quarter section 160 acres, and aliquot parts are described with halves and quarters such as NE1/4 of SW1/4.

Original undisturbed monuments outweigh later evidence; lost corners are restored by proportioning record distances between the nearest existing original corners on the line.

Title and boundary are distinct questions: the surveyor locates and monument the boundary on the ground, while ownership is a matter of law decided by a court.

Arc-definition degree of curve: R = 5729.58 / D, where D is the central angle subtended by a 100-ft arc.

Horizontal curve: T = R tan(Δ/2); L = 100Δ/D = RΔ (Δ in radians); LC = 2R sin(Δ/2); E = R(sec(Δ/2) − 1); M = R(1 − cos(Δ/2)).

Deflection angle to any point on the curve: δ = (l × D)/200 degrees, where l is arc length measured from the PC.

Vertical curve elevation: y = (A/2L)x² + g1x + Elev(PVC), with K = L/A; the high or low point occurs at x = −g1L/A.

Crest sight distance when S < L: L = A·S²/2158; sag vertical curve when S < L: L = A·S²/(400 + 3.5S), with S and L in feet.

Combined scale factor = grid factor × elevation factor; ground distance = grid distance ÷ combined factor.

Traverse relative precision = total linear misclosure ÷ total traverse length, stated as 1:N (0.10 ft in 5,000 ft is 1:50,000).

Average end area volume: V = L(A1 + A2)/2, with L in the same length units as the areas; the prismoidal correction refines the result for strongly varying sections.

Stake cut/fill = design elevation − existing ground elevation; a positive value is fill, a negative value is cut.

Ellipsoid height relation: h = H + N, where h is ellipsoidal height from GNSS, H is orthometric height, and N is the geoid undulation.

GRS80: a = 6,378,137 m and 1/f = 298.257222101; WGS84 uses the same semi-major axis with 1/f = 298.257223563.

UTM: 60 zones each 6° of longitude wide, central meridian scale factor 0.9996, false easting 500,000 m, false northing 0 in the northern hemisphere.

State Plane Coordinate System: Lambert Conformal Conic for zones elongated east-west; Transverse Mercator for zones elongated north-south.

Curvature and refraction: subtract 0.0206 D² ft (D in hundreds of feet) or 0.0675 K² m (K in kilometers) from the rod reading in differential leveling.

Elevation factor = R/(R + h) using mean Earth radius and height above the ellipsoid; the grid (projection) factor comes from the zone's scale at that location.

Least squares adjustment minimizes the weighted sum of squared residuals and yields adjusted coordinates with standard deviations and error ellipses.

Azimuth is measured clockwise from north, 0° to 360°; a bearing is an acute angle from the north or south meridian with a quadrant letter and never exceeds 90°.

Vertical aerial photo scale: S = f/H, with f the focal length and H the flying height above mean ground; 6 in at 6,000 ft gives 1:12,000.

Relief displacement: d = r·h/H, where r is radial distance from the principal point, h the object height, and H the flying height above datum.

Contours never cross except at an overhang, run perpendicular to the steepest slope, are close together on steep ground and far apart on gentle ground, with index contours every fifth line.

DEM is a bare-earth elevation grid; DSM includes vegetation and structures; DTM is a bare-earth model built from breaklines and mass points.

Vertical exaggeration = horizontal map scale ÷ vertical scale; 1:2,000 horizontal with 1:200 vertical is 10× exaggeration.

Scale conversion: 1 in = 200 ft is RF 1:2,400 (200 × 12); ground distance = map distance × scale denominator.

A TIN honors breaklines and fits planes to triangles of mass points; a gridded DEM interpolates by bilinear or nearest-neighbor methods and can smooth ridges and channels.

ASPRS accuracy reporting: horizontal RMSE × 1.7308 and vertical RMSE × 1.96 give the 95% confidence values for tested map accuracy.