Surveying Fundamentals
Surveying fundamentals tests the measurement science behind every survey: units, error behavior, angle and distance references, and the difference between precision and accuracy. Expect conceptual questions plus small computations rather than long derivations.
Measurement and error
Random errors are equally likely positive or negative and are reduced by repetition; systematic errors (mis-set prism constant, scale error, temperature) bias every observation and must be calibrated out; blunders are mistakes and are rejected, not averaged. Precision describes repeatability; accuracy describes closeness to truth. For a sum or difference, standard deviations combine in quadrature. For a product or quotient, relative uncertainties combine in quadrature.
Units and references
1 acre = 43,560 ft²; 1 hectare = 10,000 m²; 1 rod = 16.5 ft; 1 Gunter's chain = 66 ft. The US survey foot (1200/3937 m) differs from the international foot (0.3048 m) by about 2 ppm; mixing them over long distances creates real coordinate error. Bearings are referenced to north or south and turn east or west; azimuths are clockwise from north. State plane and UTM are grid systems, so ground distances require a scale factor and an elevation factor.
Worked example
A rectangle measures 250.00 ft ± 0.02 ft by 400.00 ft ± 0.03 ft. Area = 250.00 × 400.00 = 100,000 ft² = 2.2957 acres. Relative area uncertainty = √[(0.02/250)² + (0.03/400)²] = √(6.4×10⁻⁹ + 5.625×10⁻⁹) = 1.10×10⁻⁴. Absolute uncertainty = 1.10×10⁻⁴ × 100,000 = 11 ft². Report 100,000 ± 11 ft².
Traps
Do not average a blunder; do not add standard deviations linearly; do not treat grid distance as ground distance; do not quote more significant figures than the measurement supports.