Abstract
M.Phil. (Engineering Management)
This study investigates the development and testing of an alternative method for the Mine Surveyor to calculate meridian convergence. Meridian convergence is the angular deviation between Grid-South/North and the corresponding South/North longitudinal line (Meridian) at a specific geographical point of interest. Meridian convergence is thus the angular connection between a South/North meridian orientated angular direction and the associated Grid-South/North angular direction at a specific spatial point of interest on the surface of the ellipsoidal earth. The management benefit of the research includes the lowered risk of computational error as a result of human error, through the proposal of an alternate methodology to meridian convergence. The alternate is based on variables that are familiar computational “language” to the Mine Surveyor.
In this study, an experiment is conducted to establish how accurate an alternative method performs against traditional methods of meridian convergence calculation used by the Mine Surveyor. The spatial study is defined by the geographical range of the existing geodetic tables (a traditional method), ranging from 70 km south of Ndola (Zambia) to 10 km north of De Aar (South Africa). Lateral (East/West) range is not considered since it is not a constraint regarding the geodetic tables.
The sample size is established under the constraint of an infinite population since the number points that can be sampled within the geographical range of interest are infinite. Visual inspection of scatterplots and the execution of regression analysis confirm a linear trend between traditional - and alternative outcomes. Linear regression in collaboration with the hold-out validation technique is adopted as a strategy to statistically refine the alternative method of calculation. Specific to this study, the application of the alternative method is limited to the geographical range under statistical analysis.
The computational outcomes of the refined alternative method in comparison to the unrefined alternative method are predominantly closer to the outcomes of traditional methods. Computational outcomes specific to the hold-out validation set demonstrate a maximum variance of a partial arc second (0.827”) to existing methods, while the identical hold-out validation set subsequent to model refinement indicate an improved maximum sub-1” variance of 0.650”. A sub-variance of 0.650” is tolerable specific to South African Mine Survey limits of error. The subsequent clustering of variances at specific variances intervals coincidently indicate similarities to comparative studies conducted by T. Soler and R.J. Fury with respect to meridian convergence. The research thus delivers on an alternate...