Certified Photogrammetrist Surveying Principles & Spatial Analysis — Questions and Answers
Question 1: A GNSS receiver reports an ellipsoid height (h) of 152.40 m at a point where the geoid height (N) is -30.10 m. What is the orthometric height (H)?
- 122.30 m
- 182.50 m (Correct answer)
- 152.40 m
- -182.50 m
Correct answer: 182.50 m
Orthometric height is H = h - N, so 152.40 - (-30.10) = 182.50 m.
Question 2: Which reference ellipsoid is used by the North American Datum of 1983 (NAD83)?
- Clarke 1866
- WGS 84
- GRS 80 (Correct answer)
- International 1924
Correct answer: GRS 80
NAD83 is defined on the GRS 80 ellipsoid, which differs only negligibly from WGS 84.
Question 3: What is the scale factor along the central meridian of a Universal Transverse Mercator (UTM) zone?
- 0.9996 (Correct answer)
- 1.0000
- 0.9999
- 1.0004
Correct answer: 0.9996
UTM uses a central meridian scale factor of 0.9996 to balance distortion across the 6-degree zone.
Question 4: To convert a horizontal ground distance to a State Plane grid distance, the ground distance is multiplied by which factor?
- The convergence angle
- The geoid separation
- The elevation factor only
- The combined factor (grid scale factor times elevation factor) (Correct answer)
Correct answer: The combined factor (grid scale factor times elevation factor)
The combined factor accounts for both reduction to the ellipsoid and projection scale distortion.
Question 5: In the State Plane Coordinate System, which projection is typically used for states with a predominantly east-west extent such as Tennessee?
- Transverse Mercator
- Lambert Conformal Conic (Correct answer)
- Oblique Mercator
- Polyconic
Correct answer: Lambert Conformal Conic
Lambert Conformal Conic minimizes distortion along east-west bands between its standard parallels.
Question 6: What does the convergence angle represent on a conformal map projection?
- The angle between grid north and geodetic north (Correct answer)
- The angle between magnetic north and geodetic north
- The deflection of the vertical
- The angle between two standard parallels
Correct answer: The angle between grid north and geodetic north
Convergence (mapping angle) is the angular difference between grid north and true geodetic north at a point.
Question 7: Which vertical datum is the current official datum for orthometric heights in the conterminous United States?
- NGVD 29
- NAD 27
- IGLD 85
- NAVD 88 (Correct answer)
Correct answer: NAVD 88
NAVD 88 is the official vertical datum for CONUS until replaced by NAPGD2022.
Question 8: A set of repeated distance measurements clusters tightly together but is consistently 0.15 m longer than the true value. How are these measurements best described?
- Accurate but not precise
- Neither precise nor accurate
- Precise but not accurate (Correct answer)
- Both precise and accurate
Correct answer: Precise but not accurate
Tight clustering indicates precision, while the consistent offset from truth indicates a lack of accuracy.
Question 9: A steel tape standardized at 20 degrees C is used on a hot day without correction. What type of error results?
- Systematic error (Correct answer)
- Random error
- Blunder
- Instrumental noise that averages out
Correct answer: Systematic error
Thermal expansion follows a predictable physical law and biases every measurement in the same direction.
Question 10: A distance is measured in three segments, each with an independent standard error of +/-0.02 m. What is the standard error of the total distance?
- +/-0.060 m
- +/-0.035 m (Correct answer)
- +/-0.020 m
- +/-0.012 m
Correct answer: +/-0.035 m
For a sum of independent errors, the total is sqrt(3 x 0.02^2) = +/-0.035 m.
Question 11: What quantity does a least squares adjustment minimize?
- The largest single residual
- The sum of absolute residuals
- The number of observations
- The sum of the squares of the weighted residuals (Correct answer)
Correct answer: The sum of the squares of the weighted residuals
Least squares yields the most probable values by minimizing the sum of weighted squared residuals.
Question 12: In a weighted least squares adjustment, how is the weight of an observation related to its standard deviation?
- Directly proportional to the standard deviation
- Inversely proportional to the variance (Correct answer)
- Equal to the standard deviation
- Independent of the standard deviation
Correct answer: Inversely proportional to the variance
Weights are taken as inversely proportional to variance, so more precise observations carry more influence.
Question 13: What should the sum of the interior angles of a closed six-sided traverse equal?
- 540 degrees
- 1080 degrees
- 720 degrees (Correct answer)
- 900 degrees
Correct answer: 720 degrees
The sum is (n - 2) x 180 = (6 - 2) x 180 = 720 degrees.
Question 14: A closed traverse with a total perimeter of 5,000 ft has a linear misclosure of 0.25 ft. What is its relative precision?
- 1:20,000 (Correct answer)
- 1:2,000
- 1:12,500
- 1:50,000
Correct answer: 1:20,000
Relative precision is 0.25 / 5,000 = 1:20,000.
