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.
The problem of underground orientation is to carry a known surface azimuth (bearing) and position down a shaft so that a tunnel driven underground stays on its designed alignment. Several established procedures exist; the classical geometric methods use plumb wires, and modern practice adds gyro and optical instruments.
(1) Two-shaft (or two-wire, wide-base) method. Where two shafts connect to the same underground level, a fine wire carrying a heavy plumb-bob (steadied in a drum of oil or water to damp swing) is hung down each shaft. Their two surface positions are coordinated from the surface control network, so the azimuth of the surface baseline between the wire tops is known. Underground, the same two wires are picked up and a traverse is run between them: because the wires are vertical, the underground line joining them has the identical azimuth as the surface baseline. This transfers orientation over a wide base and is the most accurate wire method (illustrated below).
(2) Single-shaft Weisbach-triangle method. When only one shaft is available, two plumb wires are hung close together in that shaft (the shorter the base, the greater the care needed). A theodolite set up underground, slightly off the line of the wires, observes the very small angle they subtend, forming a long, thin Weisbach triangle. Because the offset angle is tiny, the sine rule lets the underground instrument line be related to the near-vertical wire plane, and the surface azimuth (established over the same two wires on top) is carried down. The wires must be steadied and read repeatedly; the geometry is deliberately kept near-collinear to minimise error propagation.
(3) Gyro-theodolite / optical methods. A gyro-theodolite (surface-calibrated) measures true azimuth directly underground, independent of any wire, and is now the usual production method for orientation; an optical or laser plummet transfers position vertically down the shaft, and the two together fix both position and azimuth. Co-planing (aligning the theodolite in the vertical plane of two wires) is a further refinement of the wire methods.
In every method the essentials are the same: establish the orientation on a firm surface base tied to the control network, transfer it vertically by physically plumb elements (wires, optical plummet) or by an azimuth-measuring instrument (gyro), damp all oscillation, and observe redundantly so the underground bearing can be checked before the heading is committed.
