Methodology for dimensioning the hoisting shaft using mathematical and graphical methods

The opening of deep ore bodies is most rapidly accomplished using vertical shafts. Shaft construction is the most economically demanding process, so despite providing the fastest access to deep ore bodies, the high capital costs involved in construction mean that determining the cross-sectional dimensions of the shaft is a complex and very important step in the design of the shaft and the entire underground mine. An inadequate cross-sectional area can have negative impacts: a small area limits the mine's capacity, while a large area increases construction costs and affects shaft stability. In modern mining practice, shafts are mostly constructed with a circular cross-section, whose area depends on a single parameter - shaft diameter. The choice of area, or more specifically the minimum shaft diameter, is generally determined empirically using mathematical or graphical methods. If there are indications that production capacity might increase or that greater volumes of air will be required, adjustments are made, and the shaft diameter is increased. This paper will present an extended mathematical model and calculations to accurately determine the dimensions of skips for ore hoisting, followed by a graphical method for determining the shaft diameter based on the mathematical calculation.