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18-Geom-A2 Adjustment of Observations: December 2018

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Weighted Least-Squares Adjustment of a Level Net
  2. Question 2 Weighted Adjustment of a Level Net with Four Fixed Benchmarks
  3. Question 3 Linearized Observation Equation for a Distance
  4. Question 4 Parametric Adjustment of a Six-Section Level Net
  5. Question 5 Traverse Departures, Latitudes, Closure and Balancing
  6. Question 6 Loop Levelling Adjusted by Number of Instrument Setups
  7. Question 7 Linearized Observation Equation for an Angle

Start with Question 1 →

National Exams — December 2018 — 04-Geom-A2, Adjustment of Observations and Data Analysis. Three-hour, CLOSED-BOOK exam; an approved Casio or Sharp calculator is permitted. Format: seven questions are given and any five (20 marks each) constitute a complete paper — all seven are solved below for completeness. Adjustments are carried out in the Canadian survey frame (heights on CGVD2013, horizontal work on NAD83(CSRS)); US-foot units are retained in Q6 wherever the printed question uses them.

Reference texts: Ghilani, Adjustment Computations: Spatial Data Analysis (6th ed., Wiley, 2017); Wolf & Ghilani, Elementary Surveying: An Introduction to Geomatics (15th ed., Pearson, 2015); Mikhail & Gracie, Analysis and Adjustment of Survey Measurements (Van Nostrand, 1981).

Method note. Every weighted least-squares result below is formed from the normal equations $N\hat{x}=A^{\mathsf T}W\ell$; the reference (unit-weight) standard deviation is $s_0=\sqrt{v^{\mathsf T}Wv/(n-u)}$ with $n$ observations and $u$ unknowns, and station precisions come from $\Sigma_{xx}=s_0^2 N^{-1}$.