FS Module 4: Surveying Principles & Geodesy

What is the geoid?

An equipotential surface of the Earth's gravity field that closely approximates mean sea level. It is irregular due to variations in mass distribution within the Earth. The geoid is the reference surface for orthometric heights (elevations). Water flows from higher to lower geoid heights.

What are NAD 83 and NAVD 88?

NAD 83 (North American Datum of 1983): the current horizontal datum for North America, based on the GRS 80 ellipsoid. Defines geodetic latitude, longitude, and ellipsoidal height. NAVD 88 (North American Vertical Datum of 1988): the current vertical datum, based on a single tidal benchmark (Father Point, Rimouski, Quebec). Defines orthometric heights.

What is the combined effect of Earth curvature and refraction on leveling?

Curvature causes a point to fall below a horizontal line of sight: c = 0.667M^2 (feet) where M = distance in miles, or c = 0.0785D^2 (m) where D = distance in km. Refraction bends the line of sight downward by about 1/7 of curvature. Combined correction: h_cr = 0.574M^2 (feet) or h_cr = 0.0675D^2 (m). Balanced sights (equal BS and FS distances) eliminate this error.

What is NAD 27 and how does it differ from NAD 83?

NAD 27 (North American Datum of 1927): the previous horizontal datum, based on the Clarke 1866 ellipsoid with origin at Meade's Ranch, Kansas. It was a regional adjustment. NAD 83 differences: uses the GRS 80 ellipsoid, is geocentric (Earth-centered), was a continental adjustment, and includes ellipsoidal heights. Coordinates between NAD 27 and NAD 83 can differ by tens of meters.

What is a Lambert Conformal Conic projection?

A conformal projection that projects the earth onto a cone intersecting the ellipsoid along two standard parallels. Scale is exact along the standard parallels, compressed between them, and expanded outside. Used for SPCS zones wider in the east-west direction. Meridians appear as straight lines converging at a point; parallels appear as concentric arcs.

How do you convert a geodetic azimuth to a grid azimuth?

Grid azimuth = Geodetic azimuth - convergence angle + (t-T) correction. Or simplified for short lines: Grid azimuth = Geodetic azimuth - convergence angle. The convergence angle (gamma) is positive east of the central meridian and negative west of it (for north-oriented grids).

What is the combined scale factor (CSF)?

CSF = grid scale factor x elevation factor. It converts between grid (projection) distances and ground distances. Grid scale factor: accounts for map projection distortion (varies with position in the zone). Elevation factor: R / (R + h), accounts for height above the ellipsoid. Ground distance = grid distance / CSF.

What is GEOID18 (or current geoid model)?

A model published by NGS that provides the separation (N) between the NAD 83 ellipsoid and the geoid at any point. It is used to convert GNSS-derived ellipsoidal heights to orthometric heights: H = h - N. Updated periodically as gravity data improves (GEOID03, GEOID09, GEOID12B, GEOID18).

What is the significance of the (t-T) correction?

The (t-T) correction, also called the arc-to-chord correction or second-term correction, accounts for the fact that a geodesic (shortest path on the ellipsoid) projects as a curve on a map grid, while surveyors compute with straight grid lines. It is applied to convert geodetic azimuths to grid azimuths along long lines. It is negligible for short lines.

What is the relationship between orthometric height (H), ellipsoidal height (h), and geoid undulation (N)?

H = h - N Orthometric height (H) = height above the geoid (what leveling gives you, related to mean sea level). Ellipsoidal height (h) = height above the reference ellipsoid (what GNSS gives you). Geoid undulation (N) = separation between the geoid and ellipsoid at that location. In the contiguous U.S., N ranges from about -8 m to -53 m (geoid is below the ellipsoid).

What is the reference ellipsoid?

A mathematically defined smooth surface (oblate spheroid) that approximates the shape of the Earth. The GRS 80 ellipsoid (used by NAD 83) has a semi-major axis of 6,378,137 m and a flattening of 1/298.257222101. It is the reference surface for geodetic coordinates (latitude, longitude) and ellipsoidal heights.

What is the convergence of meridians?

The angular difference between geodetic north at a point and grid north of the map projection. All meridians converge toward the poles, so grid north and geodetic north only coincide along the central meridian of a map projection zone. The convergence angle increases with distance from the central meridian and with latitude.

What is the difference between astronomic north and geodetic north?

Astronomic north: determined by the direction of gravity (plumb line) and observations of celestial bodies. It is referenced to the geoid. Geodetic north: determined mathematically as the direction along the meridian on the reference ellipsoid. The difference is the deflection of the vertical, caused by local gravity anomalies. It is typically small (a few arc-seconds) but can be significant in mountainous areas.

What is the deflection of the vertical?

The angular difference between the direction of gravity (plumb line/geoid normal) and the ellipsoid normal at a point. It has two components: xi (north-south) and eta (east-west). It affects astronomic observations and must be corrected to obtain geodetic positions from astronomic observations.

What is the scale factor at the central meridian of a UTM zone?

0.9996. This means distances at the central meridian are slightly reduced on the grid (by 0.04%, or about 1:2,500). This reduction allows the scale factor to be closer to 1.0 at the zone edges, minimizing overall distortion across the 6-degree-wide zone.