# How oviform is the chicken egg? New mathematical insight into the old oomorphological problem

Narushin, Valeriy G., Romanov, Michael N., Lu, Gang, Cugley, James, Griffin, Darren K. (2021) How oviform is the chicken egg? New mathematical insight into the old oomorphological problem. Food Control, 119 . Article Number 107484. ISSN 0956-7135. (doi:10.1016/j.foodcont.2020.107484) (KAR id:82655)

## Abstract

The chicken egg, a major food product, has been, as a model oviform object, the focus of advanced description in mathematical terms, and such a description has practical applications in engineering, industrial and biological disciplines. A precise mathematical description circumscribing major oomorphological characteristics, coupled with their non-destructive measurement, remains, to a certain extent, problematic and has not yet been achieved, hampering their effective control and use. A contour of any chicken egg can be accurately defined with Hügelschäffer's model by means of three main measures: length, L, maximum breadth, B, and a parameter w that corresponds to a distance of shifting the ellipse center to form an egg ovoid. The goal of the study was a comprehensive theoretical evaluation and development of basic geometrical formulae to define egg external traits by using Hügelschäffer's model and employing simulation modelling, digital imaging and image processing. As a result, we deduced novel geometrical formulae for the egg long circumference, C, volume, V, area of a plane curve obtained by the normal/orthogonal projection, A, surface area, S, distance parameter, w, and radius of curvature, R, at any point on the x-axis. For practical use in the poultry industry and food engineering, the proposed formulae can be instrumental in the non-destructive and accurate definition of the external parameters of any chicken egg.

Item Type: Article 10.1016/j.foodcont.2020.107484 Chicken egg quality; Oviform objects; Oomorphology; Egg geometrical parameters; Hügelschäffer's model; Simulation modelling and digital imaging Q Science > QH Natural history > QH324.2 Computational biologyS Agriculture > SF Animal culture Divisions > Division of Natural Sciences > Biosciences Food Systems, Natural Resources and Environment Mike Romanov 28 Aug 2020 08:46 UTC 08 Sep 2023 13:43 UTC https://kar.kent.ac.uk/id/eprint/82655 (The current URI for this page, for reference purposes)

## University of Kent Author Information

### Romanov, Michael N..

Creator's ORCID: https://orcid.org/0000-0003-3584-4644

### Lu, Gang.

Creator's ORCID: https://orcid.org/0000-0002-9093-6448

### Griffin, Darren K..

Creator's ORCID: https://orcid.org/0000-0001-7595-3226