Surveying Principles & Spatial Analysis Flashcards

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)?

Answer: 182.50 m

Orthometric height is H = h - N, so 152.40 - (-30.10) = 182.50 m.

Which reference ellipsoid is used by the North American Datum of 1983 (NAD83)?

Answer: GRS 80

NAD83 is defined on the GRS 80 ellipsoid, which differs only negligibly from WGS 84.

What is the scale factor along the central meridian of a Universal Transverse Mercator (UTM) zone?

Answer: 0.9996

UTM uses a central meridian scale factor of 0.9996 to balance distortion across the 6-degree zone.

To convert a horizontal ground distance to a State Plane grid distance, the ground distance is multiplied by which factor?

Answer: The combined factor (grid scale factor times elevation factor)

The combined factor accounts for both reduction to the ellipsoid and projection scale distortion.

In the State Plane Coordinate System, which projection is typically used for states with a predominantly east-west extent such as Tennessee?

Answer: Lambert Conformal Conic

Lambert Conformal Conic minimizes distortion along east-west bands between its standard parallels.

What does the convergence angle represent on a conformal map projection?

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.

Which vertical datum is the current official datum for orthometric heights in the conterminous United States?

Answer: NAVD 88

NAVD 88 is the official vertical datum for CONUS until replaced by NAPGD2022.

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?

Answer: Precise but not accurate

Tight clustering indicates precision, while the consistent offset from truth indicates a lack of accuracy.

A steel tape standardized at 20 degrees C is used on a hot day without correction. What type of error results?

Answer: Systematic error

Thermal expansion follows a predictable physical law and biases every measurement in the same direction.

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?

Answer: +/-0.035 m

For a sum of independent errors, the total is sqrt(3 x 0.02^2) = +/-0.035 m.

What quantity does a least squares adjustment minimize?

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.

In a weighted least squares adjustment, how is the weight of an observation related to its standard deviation?

Answer: Inversely proportional to the variance

Weights are taken as inversely proportional to variance, so more precise observations carry more influence.

What should the sum of the interior angles of a closed six-sided traverse equal?

Answer: 720 degrees

The sum is (n - 2) x 180 = (6 - 2) x 180 = 720 degrees.

A closed traverse with a total perimeter of 5,000 ft has a linear misclosure of 0.25 ft. What is its relative precision?

Answer: 1:20,000

Relative precision is 0.25 / 5,000 = 1:20,000.