Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio

Abstract

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Egg-inspired engineering in the design of thin-walled shelled vessels: a theoretical approach for shell strength

“…5. Based on the known formula for calculating the surface area of an egg, S, derive a dependence for S n by reducing the geometric dimensions (L and B) by twice the value of kT (Figure 1; Narushin et al, 2022c). As a result, a calculation formula for k can be obtained.…”

“…In the previous study (Narushin et al, 2022c), we carried out a similar theoretical procedure for the Hügelschäffer's model that resulted in the following calculation formulae:…”

“…Define the egg volume, V , as a sum of the volumes of its constituents, i.e., egg contents volume, V i , and shell volume, V s : 2. Using the known formula for calculating V , determine V i values by reducing the geometric dimensions ( L and B ) by twice the shell thickness, T ( Figure 1 , as also shown in Narushin et al, 2022c ). 3.…”

“…While Hügelschäffer’s model has been thoroughly investigated in terms of its geometric ( Petrović and Obradović, 2010 ; Obradović et al, 2013 ; Narushin et al, 2020 , 2021c , 2022b , c ) and mathematical properties ( Maulana et al, 2015 ; Narushin et al, 2020 , 2021a , b , 2022a , b ), this gap should be filled for Narushin’s model.…”

“…While indicators (ii) and (iii) can be characterized, by analogy with the parameters of a bird’s egg, as the shell volume (in other words, the material consumption of the vessel shell), V s , and volume of the interior (i.e., capacity of the vessel), V i , it is not so clear with a measure of strength (i). Based on our previous studies ( Narushin et al, 2022c ) on the geometric features of bird eggshells, however, the parameter (i) can be linked to the position of the neutral axis of the eggshell.…”