Mathematics and Geomatics Flashcards

The Elevation Factor (EF) used in geodetic-to-grid distance reduction is calculated as:

Answer: R / (R + H), where R is Earth's radius and H is mean elevation above ellipsoid

EF = R / (R + H) reduces an ellipsoidal geodetic distance to a sea-level equivalent by accounting for the elevation above the ellipsoid.

In a curve layout using deflection angles, the deflection angle from the PC to any point on the curve equals:

Answer: Half the central angle subtended from the PC to that point

The deflection angle to any chord from the tangent at the PC equals half the central angle subtended by that arc.

A cadastral survey is primarily concerned with:

Answer: Defining and documenting land ownership boundaries and property rights

Cadastral surveys establish, re-establish, and document property boundaries for legal and land-ownership purposes.

The standard deviation of a single measurement where n repeated observations have a standard deviation of the mean (σm) is:

Answer: σ = σm × √n

The standard deviation of a single observation σ = σm × √n, because the mean is more precise than any individual measurement by a factor of √n.

In LiDAR surveys, the point density is most directly controlled by:

Answer: Pulse repetition frequency, scan angle, and aircraft speed and altitude

Point density is a function of pulse repetition rate, scan angle width, aircraft speed, and flying height — all adjustable mission parameters.

The term 'closing the horizon' in theodolite work means:

Answer: Measuring all horizontal angles around a full 360° to check that they sum to 360°00'00"

Closing the horizon involves summing all horizontal angles around a full circle to verify the total equals 360°, providing a check on angular measurement quality.

The 'sea-level correction' (or arc-to-chord correction) is applied in geodetic traverse computations to account for:

Answer: The difference between a measured ground distance at elevation and the corresponding distance at the ellipsoid

The sea-level (ellipsoid reduction) correction converts a ground distance measured at elevation to its equivalent ellipsoidal distance for geodetic computations.