Non-destructive measurement of chicken egg characteristics: Improved formulae for calculating egg volume and surface area

Mathematical progression of avian egg shape with associated area and volume determinations

“…20 Only using simulation methods and the minimum step in division of the integrated function enabled us to obtain an accurate result. 21 Formula (1) is so complex to integrate that even approximate methods do not allow for mathematical transformations (2) and surface area for eggs of any shape, especially for not quite typical ones found in the poultry industry, that is, the so-called pyriform (pear-shaped) eggs.…”

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

“…The methodological approach we have chosen (Eq. 5) in calculating V s , in our opinion, is simpler and more convenient than use of integral calculus for finding this parameter, since it can cause certain difficulties and, as a consequence, inaccuracies in the result obtained, which was demonstrated by us earlier (Narushin et al, 2020b;2021a;2021b).…”

“…This range excessively covers all possible variations for the hen's eggs. The S m values were obtained using the respective formula for the egg surface area from Narushin et al (2021b):…”

Hugelschaffer egg curve and surface

“…Egg-shaped curves and surfaces have wide applications in engineering (air, civil, food). For the calculation of A, V and S of egg-shaped curves and surfaces, mostly numerical approximations were used, such as the ones presented in works [16], [22], [25], [33], [41], [46], [49]. In this paper, we determined the formulae for calculating A, V and S in a Hügelschäffer model and we expect that the obtained result will be applicable in various engineering areas.…”

“…Analogous to the previous example, a Hügelschäffer egg-shaped curve model can be generated according to the profiles of egg-shaped pipe sewers obtained through composition of circular arcs with the shape index B/L = 2/3 or B/L = 3/4 as given in [47]. In recent years, the application of Hügelschäffer models, as well as other mathematical models for describing the shape of eggs -ovoid forms (curves and surfaces) in the poultry industry and food engineering is on the rise, as evident from papers [2], [13], [14], [16], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28].…”