New approach to border line evaluations for whole sample of Williams pear (Pyrus communis)

In many processes of heat exchange, as well as in other processes of biomaterial handling, physical properties of fruit such as dimensions, shape, surface area and volume are of crucial importance. The objective of this work was to find a function which approximates pear border line, as precisely as possible, in order to calculate the surface area and volume of a pear by means of integral calculus. Previously described estimation of an average pear border line was based on the sixth order polynomial and proposed algorithm. Two new ways to calculate the Williams pear border line are the focus of this study. The first way includes spline functions as an estimation of a pear border line (i.e. four third order polynomials), while the second one uses regression function obtained by nonlinear regression method. The regression function has two independent variables, length and total length of a pear. The most precise approximation of a pear border line was obtained by nonlinear regression with R2 = 97.48. This was more obvious when total pear length was smaller or greater than average total pear length. Border lines of all tested pears were determined by one regression function with large precision. Therefore, it is safe to calculate surface area and volume of a pear based on regression function and total pear length, only. Calculated volumes of the pears were compared with volumes measured by Archimedes’ method. The smallest relative error has been obtained when the volumes were calculated using the regression function as approximation of pear border line.

► Surface area and volume of a pear can be calculated, based on pear length, only.
► The best pear border line function is obtained from nonlinear regression function Q.
► Just one function is enough for pear border line formation, for arbitrary pear length.
► Archimedes’ method has confirmed precision of calculated volumes based on Q.