# Mathematical Modelling And Grand Nain Essay

2359 words - 9 pages

Mathematical modelling was done to predict mass of the banana fruit var. Grand Nain from the physical characteristics like length, width, thickness, volume, geometrical mean diameter, etc. The observed physical properties of banana were statistically analysed and their mean, standard deviation, error and coefficient of variance were presented. The fitted models were divided into three classifications. Among the first classification model, empirical equation describing the length and width (model no.4) predicts the mass with highest R2 value. In the second classification, mass models of surface area (model no.8) had a linear relationship with R2 = 0.91. Highest R2 value of 0.85 and 0.83 were found for mass models with true and ellipsoidal volume (model no. 9&10) respectively in the third classification.
Keywords: Banana fruit, mass models, physical properties, dimensions, geometrical attributes

INTRODUCTION
Physical properties of agricultural products play an important role in determining standards for designing grading, processing, conveying and packaging systems. The major physical properties of banana fruit are mass, volume, size, density, porosity, surface area etc. Among these properties, mass, projected area, volume, etc are the most important in designing grading system [16]. Surface area is important in indicating heat transfer rate, respiration rate, water loss, gas permeability per unit surface area, quantity of pesticide applied and ripeness index [4,10,26,28].
Fruits are often graded by size and it would be more economical and ease when it is graded by weight. Mass grading of fruits become more essential and it is used to attain uniform weight [19], optimum packaging configurations, reduces packaging and transportation costs [15]. Also the mass grading is recommended for the irregular shaped products. This makes the relationship between weight and the diameter more crucial [22]. Fruits with large length to diameter ratio were separated (diverging roller sizers) based on the sizing equation: P=0.25L+0.75D [15].
In weight sorter, constant density fruits can be sorted based on their volume [22]. Models suitable for sizing of the kiwi fruit [17] were determined between mass, volume, projected area and length. Volume can be used to monitor yield during harvesting and to predict harvest time [6]. Measuring dimensions by a digital caliper causes human error and is not an efficient method to estimate volume. Mathematical models involving geometric mean diameter and some common methods like water and gas displacement method are used to determine volume of different fruits [14].
Many researchers formulated empirical equations and studied relationship between volume and surface area [3], mass, diameter and surface area [8,9,13] for different agricultural produces. Based on geometrical attributes, eleven models were recommended to predict mass of an apple [24]. Mass of an orange was predicted from its projected area and dimensions [25]. High...

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