Engineering Mathematics, Basic Sciences, and Survey Instrumentation
Mathematics and statistics applied to surveying
Expect plane and spherical trigonometry, coordinate geometry (bearing and distance between points, line intersection, area by coordinates), and basic error statistics: mean, standard deviation, standard error of the mean, and the most probable value as the weighted mean with weights inversely proportional to variance. Unit fluency matters: 1 hectare = 10 000 m squared, 1 acre = 4 046.86 m squared, 1 grad = 0.9 degree, 1 mil = 0.05625 degree, and a radian = 206 265 seconds.
Instruments and their corrections
Theodolite and total station errors include horizontal collimation (line of sight) error, vertical index error, vertical axis tilt, plate bubble adjustment and eccentricity; the two-peg test checks a level's line of sight. EDM work requires prism constant, zero (additive) constant, and atmospheric corrections expressed in parts per million from temperature and pressure.
Earth curvature and refraction
For a horizontal line of sight, curvature lowers the far point and refraction raises the apparent reading; combined, the correction is approximately 0.0674 K squared metres when K is in kilometres (0.0674 K squared feet with K in thousands of feet). The sign is positive when reducing an observed reading to the level surface.
Traps
Applying the curvature correction in the wrong direction, using the curvature term alone without refraction, mixing units in 0.0674 K squared, and forgetting the difference between flying height above datum and above ground in other subjects.
Worked example. For a sight of 1.2 km, combined correction = 0.0674 x 1.44 = 0.097 m, which is subtracted from the staff reading to reduce it to the instrument's level surface.