Principles and Practice of Surveying Exam (PS) Geodesy, Datums, and Coordinate Systems Syllabus

Geodesy, Datums, and Coordinate Systems syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Geodesy, Datums, and Coordinate Systems in Principles and Practice of Surveying Exam (PS), not a summary of it.

1. 1

   Reference Surfaces and Datums

   4 topics

   • Ellipsoid, geoid, and topographic surface relationships
     • Geoid undulation and deflection of the vertical
   • Horizontal datums (NAD 27, NAD 83) and realizations
   • Vertical datums (NGVD 29, NAVD 88)
     • Orthometric, ellipsoidal, and geoid heights
   • Modernized National Spatial Reference System and datum transition
2. 2

   Map Projections and Plane Coordinates

   4 topics

   • Projection fundamentals and distortion
     • Conformal projections and scale factor
   • State Plane Coordinate Systems
     • Lambert conformal conic versus transverse Mercator zones
     • Grid versus geodetic azimuth and convergence
   • UTM coordinate system
   • Grid-to-ground and ground-to-grid reductions
     • Combined factor (scale factor and elevation factor)
3. 3

   Geodetic Computations

   4 topics

   • Geodetic versus astronomic versus grid azimuths
   • Forward and inverse geodetic position computations
   • Convergence, arc-to-chord (t-T) corrections
   • Local datum and assumed coordinate systems
4. 4

   GNSS Positioning and Reference Frames

   4 topics

   • GNSS principles and observable types
     • Code versus carrier phase positioning
     • Static, RTK, and network RTK methods
   • Reference frames (WGS 84, ITRF) and epochs
   • OPUS and CORS network utilization
   • GNSS error sources and quality control
     • Multipath, ionospheric, and tropospheric effects
     • PDOP and satellite geometry

Geodesy, Datums, and Coordinate Systems flashcards for Principles and Practice of Surveying Exam (PS)

24 of 60 cards from the Geodesy, Datums, and Coordinate Systems deck — real questions with worked answers.

1. Define the geoid and state which physical quantity its surface follows.

   The geoid is an equipotential surface of the Earth's gravity field that best approximates global mean sea level. Every point on it has the same gravity potential, so the geoid is everywhere perpendicular to the direction of gravity (the plumb line).

2. What is a reference ellipsoid and how does it differ from the geoid?

   A reference ellipsoid is a smooth mathematical surface (an ellipse of revolution) used as the geometric reference for horizontal/geodetic coordinates. Unlike the geoid, it is purely geometric and does not follow the gravity field; the geoid undulates above and below it.

3. Define geoid undulation $N$ and give the relationship among ellipsoid height $h$, orthometric height $H$, and $N$.

   $N$ is the separation between the geoid and the ellipsoid (positive when the geoid is above the ellipsoid). The relationship is $$h = H + N$$ where $h$ is ellipsoidal height (from GNSS) and $H$ is orthometric height (referenced to the geoid).

4. What is the deflection of the vertical?

   The deflection of the vertical is the angular difference between the direction of the plumb line (true gravity vertical, normal to the geoid) and the ellipsoidal normal at a point. It is usually split into a north-south component $\xi$ (xi) and an east-west component $\eta$ (eta).

5. List the three primary surfaces in geodesy and what each represents.

   (1) Topographic surface — the physical land/ocean surface where measurements are made; (2) Geoid — equipotential gravity surface, reference for heights; (3) Ellipsoid — geometric reference surface for horizontal positions and ellipsoidal heights.

6. What two parameters fully define the shape of a reference ellipsoid, and give the flattening formula.

   The semi-major axis $a$ and the flattening $f$ (or semi-minor axis $b$). Flattening is $$f = \frac{a-b}{a}$$ For GRS 80, $a = 6{,}378{,}137$ m and $1/f \approx 298.257222101$.

7. Which ellipsoid underlies NAD 27 and which underlies NAD 83?

   NAD 27 uses the Clarke 1866 ellipsoid. NAD 83 uses the GRS 80 ellipsoid (geocentric).

8. What was the origin/datum point of NAD 27 and how was it defined?

   NAD 27 was a non-geocentric, horizontal-only datum fixed at Meades Ranch, Kansas. It was oriented to best-fit the Clarke 1866 ellipsoid to the geoid across North America rather than placing the ellipsoid center at the Earth's mass center.

9. How does NAD 83 differ fundamentally from NAD 27 in terms of origin?

   NAD 83 is geocentric (ellipsoid center at the Earth's center of mass) and was established using satellite/Doppler and VLBI data, whereas NAD 27 was a regional best-fit datum anchored at Meades Ranch. NAD 83 also covers ellipsoidal heights, not just horizontal.

10. What does a NAD 83 realization label such as NAD 83(2011) epoch 2010.00 specify?

    It specifies the adjustment/realization (the 2011 multi-year CORS solution) that fixes the coordinate values, and the reference epoch (2010.00) at which the published coordinates are valid, accounting for crustal motion over time.

11. Define a 'realization' of a datum.

    A realization is a specific set of physical reference station coordinates and velocities that gives practical access to an otherwise abstract datum/reference frame. Successive realizations (e.g., NAD 83(1986), (HARN), (CORS96), (2011)) refine those values with better data.

12. What is NGVD 29 and what reference defined it?

    The National Geodetic Vertical Datum of 1929, originally the Sea Level Datum of 1929. It was defined by holding mean sea level fixed at 26 tide gauges (21 U.S. and 5 Canadian) and adjusting the leveling network to them.

13. What is NAVD 88 and how was it defined?

    The North American Vertical Datum of 1988. It was established by a minimally constrained adjustment of leveling, holding fixed a single primary benchmark — Father Point/Rimouski, Quebec — rather than multiple tide gauges.

14. Why does NAVD 88 differ from NGVD 29, and roughly how do heights compare?

    They use different fundamental references (single tide gauge vs. 26) and different adjustments. NAVD 88 heights are typically a few centimeters to a few decimeters higher than NGVD 29; the difference varies geographically (commonly tens of cm in the conterminous U.S.).

15. Distinguish orthometric height from dynamic height.

    Orthometric height $H$ is the distance along the curved plumb line from the geoid to the point. Dynamic height is a geopotential-based height (geopotential number divided by a constant normal gravity) so that points on the same equipotential surface have equal dynamic height; useful for water-level studies.

16. What is a geopotential number?

    The geopotential number $C$ of a point is the difference in gravity potential between the geoid and that point, $C = W_0 - W_P$, expressed in geopotential units. It is path-independent and forms the basis for orthometric and dynamic heights.

17. What is the Modernized National Spatial Reference System (NSRS) replacing the current datums?

    NOAA/NGS is replacing NAD 83 and NAVD 88 with new geometric terrestrial reference frames (e.g., a North American plate-fixed frame) and a new geopotential (gravimetric geoid-based) vertical datum, defining heights from GNSS plus a precise geoid model (GEOID model) rather than passive leveled benchmarks.

18. In the modernized NSRS, what replaces leveled passive benchmarks as the basis for orthometric heights?

    GNSS-derived ellipsoidal heights combined with a high-resolution gravimetric geoid model. Orthometric height is obtained as $H = h - N$, removing reliance on the deteriorating passive benchmark/leveling network.

19. Why is the U.S. transitioning away from NAD 83?

    NAD 83 is not truly geocentric (its origin is offset from the Earth's mass center by ~2 m) and does not rigorously model plate motion. The new frames will be geocentric, consistent with the ITRF/GNSS, and explicitly time-dependent (with epochs and velocities).

20. What is a map projection and why is distortion unavoidable?

    A map projection is a mathematical transformation from the curved ellipsoid/sphere to a flat plane. Because a curved surface cannot be flattened without stretching or tearing (it is not developable), every projection introduces distortion in distance, area, angle, or shape; only some properties can be preserved.

21. Distinguish conformal, equal-area, and equidistant projections.

    Conformal: preserves angles/local shape (scale same in all directions at a point) — used for surveying. Equal-area: preserves area but distorts shape. Equidistant: preserves true distance along certain lines. No projection is both conformal and equal-area.

22. Name the two conformal projections used in the U.S. State Plane Coordinate System and when each is chosen.

    Lambert Conformal Conic — for zones that extend mostly east-west. Transverse Mercator — for zones that extend mostly north-south. (Oblique Mercator is used for the Alaska panhandle.)

23. What is a developable surface? Give the surfaces used for the common projections.

    A developable surface can be unrolled flat without distortion: a cone (Lambert Conformal Conic), a cylinder (Mercator / Transverse Mercator), or a plane (azimuthal). The ellipsoid is projected onto these and then unrolled.

24. Define scale factor $k$ in a projection.

    The scale factor $k$ is the ratio of projected (grid) distance to true (ellipsoidal) distance at a point: $$k = \frac{\text{grid distance}}{\text{geodetic distance}}$$ On a secant projection $k<1$ between the standard lines and $k>1$ outside them.

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