Non-destructive evaluation of the volumes of egg shell and interior: Theoretical approach

Describing the properties of table eggs requires the development of methods enabling to look inside the egg without destroying it, suggesting a thorough theoretical study including the formulation of theoretical aspects of this advanced egg-related research area. For this purpose, we developed a mathematical assay for computing the volumes of shell and interior of a chicken egg using, as input data, its main external geometric dimensions (length, maximum breadth, and the value of its shift from the centre of the horizontal axis) as well as the thickness of the shell. The shell volume can be determined as the product of the average thickness by the surface area estimated along the midline of shell section. We obtained theoretical dependences of the midline-based estimate of surface area on the values of the average shell thickness and the outer surface area of the egg. Since the volume of egg interior, in addition to the volumes of the entire egg and shell, is also affected by air cell volume, we derived theoretical formulae for computing this indicator. To calculate it, in addition to the values of the basic geometric dimensions of the egg, data on the diameter of the air cell or its height should be used, which is quite simple to measure with conventional measuring instruments like an ovoscope.