A heuristic model of the tromp (distribution) curve

Abstract

A five-parameter mathematical model for the Tromp curve has been derived by using heuristic arguments. It can be transformed into a four-parameter self-similar distribution or partition function for the generalized Tromp curves in a reduced specific gravity. The generalized model can be linearized for graphical curve fitting of data. For more accurate analysis, a nonlinear optimization technique is required. However, the structure of the proposed model facilitates the parameter search in four- or five-dimensional space. The model exhibits close fit to a variety of Tromp curve shapes based on plant data for various coal-cleaning equipment and permits explicit expressions for error area and probable error in terms of its parameters.