Correlating the mass of walnut fruit to some physical characteristics

Abstract

Physical characteristics of fruits and vegetables and their relationships are necessary for the design of some postharvest processing systems such as handling, sorting and packaging machines and reducing the processing costs. For proper design of grading systems, important relationships between the mass and other properties of fruits such as length, width, thickness, volumes and projected areas must be known. The aim of this research was to measure and present some physical properties of walnut fruits. In addition, walnut fruit mass was correlated to measured physical properties using linear, the Quadratic, S-curve and power models as three different classifications: (1) single variable regressions of walnut dimensional characteristics; (2) single variable regressions of walnut mass based on projected areas and (3) estimating the walnut mass based on its volumes. The results showed that mass modeling of walnut based on width and the second projected area were the most appropriate ones in the first and the second classifications, respectively. In the third classification, the Quadratic model based on the volume of the fruit assumed as ellipsoid shape (Vellip) with R2=0.976, was the best model as: M = 6.019 + 0.001Vellip - 3.067×10-9, R2=0.965. In the economical and agronomical point of view, suitable grading system of walnut mass was ascertained based on the second projected area as the Quadratic form: M = 7.663 – 0.002PA2 + 2.468×10-6PA22, R2=0.921.