18-Geom-A1 Surveying · May 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — 04-Geom-A1 Surveying, May 2019. Closed-book; approved Casio or Sharp calculator permitted. Format: nine (9) questions of varied value totalling 100 marks constitute a complete paper; all nine are solved below. Elevations are referenced to the Canadian vertical frame (CGVD2013) and azimuths to NAD83(CSRS) unless the printed question states otherwise.
Reference texts: Wolf & Ghilani, Elementary Surveying: An Introduction to Geomatics (15th ed., Pearson); Ghilani, Adjustment Computations: Spatial Data Analysis (6th ed., Wiley); Kavanagh & Slattery, Surveying with Construction Applications (8th ed.); Federal Geodetic Control Subcommittee, Standards and Specifications for Geodetic Control Networks (1984).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
(a) Zero / additive-constant error of an EDM (3 marks). Every EDM carries a fixed additive constant (also called the zero or index error) — the algebraic sum of the electrical and mechanical offsets of the instrument and its reflector from their nominal reference points — which is added to every distance the instrument measures. It is isolated by the three-point (baseline) method:
Set out three stable, collinear marks A, B and C on flat, firm ground so that AC is a single straight line of convenient length (say 60–120 m). Using the same instrument and reflector throughout, measure the whole line $AC$ and the two segments $AB$ and $BC$. Because the true whole equals the sum of the true parts, and each observation carries the same constant $z$, the observed values give
$$ (AC_m - z) = (AB_m - z) + (BC_m - z) \;\Rightarrow\; \boxed{\,z = AB_m + BC_m - AC_m\,} $$
Repeat over several placements of B (and, ideally, over more than one baseline) and average, so that the reflector is oriented identically each time. The mean $z$ is entered as the instrument/prism constant so that every subsequent measurement is corrected. The test also checks the cyclic (phase) error if B is stepped in even increments of the unit length.
(b) Collimation error in a total station (4 marks). A total station has two collimation checks, and both use the same idea: point at one target on face left (FL) and again on face right (FR), because each error changes sign when the telescope is transited.
If either value is outside the manufacturer’s tolerance (typically a few seconds), run the instrument’s electronic calibration routine, which stores $c$ and $i$ and applies them to every later reading. The alternative is a mechanical reticle adjustment by a service centre. The same session usually checks the trunnion-axis tilt (with a steeply inclined target) and the compensator index. Whatever is stored, critical work is still measured on both faces and meaned, because that cancels any residual $c$ and $i$.
(c) Two-peg test (3 marks). This checks a level for collimation error — a line of sight that is not truly horizontal when the bubble is centred. Drive two pegs A and B on level ground about 50–60 m apart.
If $\Delta H' = \Delta H$ the instrument is in adjustment. Otherwise the discrepancy $e = \Delta H' - \Delta H$ is the collimation error over the sight length to B; the correct reading that B should give in Setup 2 is $b_2^{corr} = a_2 - \Delta H$. Bring the horizontal cross-hair onto $b_2^{corr}$ using the adjusting screws (tilting screw or reticule screws, per instrument), then re-test.
