Modeling the mass of apples by geometrical attributes

Abstract

Iran has an apple production of 1.9 million tons, seventh largest in the world. However, in comparison to this production the export of apples is very small (0.19 million tons). There are some situations in which it is desirable to determine relationships between physical attributes. Models for predicting the mass of apples from their dimensions and projected area were identified. Models were divided into three categories: (1) single and multiple variable regression of apple dimensions (first category); (2) single and multiple variable regression of projected areas (second category); (3) estimation of apple shape – ellipsoid or spheroid based on volume (third category). Two different varieties of Iranian apples were selected for study. Red and Golden Delicious varieties from the four different regions of Damavand, Semirom, Maragheh and Oromiyyeh with a total of 644 observations. These models have been obtained for individual varieties as well as for mixed varieties. Among single variable models, first category, mass model with smallest diameter of apple had a strong relationship with a very high coefficient of determination, R 2, and minimum regression standard error, R.S.E., for the total observations. Therefore, the apple diameter is a good parameter for sizing. Second category mass models, with three projected areas, had maximum R 2 and minimum R.S.E. relative to others. Among the single variable models obtained from projected area, had maximum R 2 = 0.94 and minimum R.S.E. = 10.9. Third category models had the best performance, with R 2 closer to unity, followed by second and first category models. The second category models need electronics systems with cameras for projection, whereas first category models may be employed in simple mechanical systems, with the exception of multiple variable models of dimensions and third category models that require three dimensional mechatranic systems. Normal relative frequency distribution of second diameter for the total observations was graphed and the levels of sizing were identified.