FS - Fundamentals of Surveying Geodesy and Coordinate Systems Questions and Answers — Questions and Answers
Question 1: A surveyor uses a GNSS receiver to determine the height of a benchmark. The receiver outputs an ellipsoid height (h) of 212.55 meters. A geoid model for the area indicates that the geoid is 31.15 meters below the ellipsoid. What is the approximate orthometric height (H) of the benchmark?
- 181.40 m
- 31.15 m
- 212.55 m
- 243.70 m (Correct answer)
Correct answer: 243.70 m
Orthometric height (H), which is approximately height above mean sea level, is calculated by subtracting the geoid separation (N) from the ellipsoid height (h). The relationship is H = h - N. Since the geoid is below the ellipsoid, the geoid separation (N) is negative (-31.15 m). Therefore, H = 212.55 m - (-31.15 m) = 243.70 m.
Question 2: Which of the following is a key characteristic of the Universal Transverse Mercator (UTM) coordinate system?
- It uses a Lambert Conformal Conic projection for each zone.
- It applies a scale factor of 0.9996 to the central meridian of each zone. (Correct answer)
- It divides the Earth into 120 zones, each 3 degrees of longitude wide.
- The scale is perfectly true (1.0) everywhere within a single zone.
Correct answer: It applies a scale factor of 0.9996 to the central meridian of each zone.
The UTM system uses a secant Transverse Mercator projection for each 6-degree zone. To minimize distortion across the zone, a scale factor of 0.9996 is applied to the central meridian. This creates two standard lines of true scale (scale factor = 1.0) approximately 180 km on either side of the central meridian.
Question 3: A surveyor finds a historical survey monument with published coordinates based on the North American Datum of 1927 (NAD 27). When occupying the same monument with a modern GPS receiver providing coordinates in the North American Datum of 1983 (NAD 83), a significant difference in coordinate values is observed. What is the primary reason for this difference?
- Changes in magnetic declination over time.
- The use of different units, such as feet versus meters.
- NAD 27 is a local datum referenced to a single point on the surface, while NAD 83 is a geocentric datum referenced to the Earth's center of mass. (Correct answer)
- Progressive accumulation of random errors in the original NAD 27 network.
Correct answer: NAD 27 is a local datum referenced to a single point on the surface, while NAD 83 is a geocentric datum referenced to the Earth's center of mass.
The fundamental difference causing the datum shift is that NAD 27 is a local, non-geocentric datum with its origin point at Meades Ranch, Kansas, and based on the Clarke 1866 ellipsoid. NAD 83 is a geocentric datum, with its origin at the Earth's center of mass, based on the GRS 80 ellipsoid. This change in origin and reference ellipsoid causes a systematic shift in coordinate values across the continent.
Question 4: A conformal map projection is specifically designed to preserve which of the following properties at any given point?
- True distance to all other points on the map.
- Equal area for all features across the map.
- Local angles and shapes of small features. (Correct answer)
- True direction from the center point to all other points.
Correct answer: Local angles and shapes of small features.
Conformal projections, such as the Lambert Conformal Conic and Transverse Mercator used in State Plane and UTM systems, are designed to preserve local angles. This ensures that the shape of small features is maintained correctly, which is critical for surveying, navigation, and engineering applications.
Question 5: When working in a map projection like a State Plane or UTM system, the angular difference between geodetic north (true north) and grid north at a specific point is known as the:
- Magnetic declination
- Geoid separation
- Deflection of the vertical
- Convergence angle (Correct answer)
Correct answer: Convergence angle
The convergence angle (also called mapping angle) is the angle at a specific point between the direction of geodetic north (the meridian) and the direction of grid north (the northing lines of the map projection). This angle is zero on the central meridian of the projection and increases with distance east or west from it.
Question 6: The Global Positioning System (GPS) provides its raw positional calculations and coordinates natively referenced to which geodetic reference system?
- North American Datum of 1983 (NAD 83)
- World Geodetic System 1984 (WGS 84) (Correct answer)
- International Terrestrial Reference Frame (ITRF)
- North American Vertical Datum of 1988 (NAVD 88)
Correct answer: World Geodetic System 1984 (WGS 84)
The GPS is operated by the U.S. Department of Defense and uses the World Geodetic System 1984 (WGS 84) as its fundamental reference system. All raw GPS positions are computed on the WGS 84 ellipsoid. Coordinates in other datums, such as NAD 83, are derived through mathematical transformations from WGS 84.
FS - Fundamentals of Surveying Geodesy and Coordinate Systems Questions and Answers
A surveyor uses a GNSS receiver to determine the height of a benchmark.
The receiver outputs an ellipsoid height (h) of 212.55 meters.
A geoid model for the area indicates that the geoid is 31.15 meters below the ellipsoid.
What is the approximate orthometric height (H) of the benchmark?