Significance of parameters used in designing optimum airway size

Abstract

This paper presents a detailed theoretical analysis of well-known formulae for designing optimum airway sizes for both circular and rectangular excavations. It is shown that, at the optimum size, the excavation cost bears a fixed ratio to the power cost for any values of the contributing variables. An expression is developed which gives the actual cost of an installation (if errors are made in the design parameters) as a multiple of the true optimum cost. This expression is used to explore the sensitivity of the design to errors in the various parameters. It is shown that the effect of an error in a single variable is not great except in the case of the airflow rate. However, the combined effect of errors in several variables could be quite large. On the other hand, similar proportional errors in certain groups of variables tend to cancel each other out. A discussion of the individual variables and their potential for error is included. Variables discussed are: airway friction factor, airflow rate, unit power cost, cost of money parameters (interest rate and life of airway), incremental excavation cost, and efficiency of air moving equipment. The main analysis is presented in terms of a circular airway, but equations are also developed showing how the size of a rectangular airway may be optimized for a given aspect ratio, or how the aspect ratio may be optimized if one side of the rectangle is fixed, as, for instance, if it is desired to confine the excavation to a certain seam width.