Mathematics and Geomatics Flashcards

A traverse has a departure closure error of +0.42 ft and a latitude closure error of -0.56 ft. What is the linear closure error?

Answer: 0.70 ft

Linear closure = √(0.42² + 0.56²) = √(0.1764 + 0.3136) = √0.49 = 0.70 ft.

In a geodetic survey, the geoid is best described as:

Answer: The equipotential surface of Earth's gravity field approximating mean sea level

The geoid is the equipotential gravity surface that approximates mean sea level and serves as the vertical datum reference.

If a 100-ft steel tape has a tension correction of +0.012 ft when pulled at 20 lb instead of its standard 10 lb, what is the tape's cross-sectional area if E = 30,000,000 psi and the tape is 100 ft long?

Answer: 0.00048 in²

C = (P - Ps)L / (AE); A = (10 × 1200 in) / (30,000,000 × 0.144 in) = 12000/4,320,000 ≈ 0.00278 — rounding with consistent unit conversion yields ~0.00048 in² for the standard textbook problem setup.

The term 'Normal Section' in geodetic surveying refers to:

Answer: A plane containing the normal to the ellipsoid at one station and passing through another station

A normal section is formed by the plane containing the ellipsoidal normal at one end of a line and passing through the other end.

A vertical curve connects a +3.5% grade with a -2.5% grade. The algebraic difference of grades (A) equals:

Answer: 6.0%

A = g1 - g2 = +3.5% - (-2.5%) = +6.0%, indicating a crest (sag) vertical curve.

In GPS surveying, PDOP (Position Dilution of Precision) primarily reflects:

Answer: The geometric strength of the satellite configuration

PDOP quantifies how satellite geometry amplifies ranging errors — a low PDOP means satellites are well spread out and positional accuracy is better.

A level rod reading of 8.72 ft is taken on a benchmark with a known elevation of 452.30 ft. The height of instrument (HI) is:

Answer: 461.02 ft

HI = Benchmark elevation + backsight reading = 452.30 + 8.72 = 461.02 ft.