Mathematical modeling of mechanical bruising parameters in some fruit varieties

Objective: The aim of this study is to determine mathematical models for estimating the damage caused by impact quince, apple, nectarine and peach fruits from different heights (20, 35, 50, 65 and 80 cm) to different surfaces (wood, steel and rubber plates). Material and Method: The study was carried out with four different fruit varieties: quince, apple, nectarine and peach. Fruits were hit on 3 different surfaces from 5 different heights, with 20 replications for each height, using a pendulum mechanism. The hardness values of the fruits were performed with a digital hardness measuring device, An incubator device was used for to determine of the moisture content values, the mass measurements were carried out with a precision balance, and the calculation of the projection area, bruise area and bruise depth values were performed with the ImageJ program. Digital caliper was used for fruit size measurements. The elasticity coefficient of the fruits was determined by using the pendulum impact test setup. Mathematical models for estimating bruise area and bruise volume are designed in two different forms as linear and nonlinear mathematical models. The data obtained for each mathematical model were subjected to Stepwise regression analysis in the Minitab package program. Coefficient of correlation (r) values were calculated to express the prediction rate of mathematical model forms. Results: The R2 values of linear and nonlinear mathematical models for quince fruit bruise area estimation were respectively, 91,96% and 96,56%, 88,57% and 97,87% for bruise volume, the regression coefficients linear and nonlinear mathematical models for apple fruit bruise area were respectively 94,97% and 98,15%, for the bruise volume 96,91% and 97,45%. Conclusion: There is a linear relationship between drop height and bruise area and bruise volume. As the fall height increased, the bruise area and bruise volume values increased. The coefficient of determination (R2) of the nonlinear mathematical models was found to be higher than the linear and nonlinear mathematical models obtained for the injury area and injury volume. Among the designed models, the impact height (h) and the modulus of elasticity of impact surfaces (E) were the parameters that contributed the most to the models. Since bruising damage was not observed in nectarine and peach fruits, bruising area and bruising volume calculations were not performed. It is thought that the data obtained from this study may be useful for making appropriate designs or modifications in equipment and machines to be used during or after harvest for quince, apple, nectarine, and peach fruits. Key Words: Mathematical modelling, Fruit, Bruising.