Computation of the radius of curvature R in any avian egg and identification of the location of potential load application that forms its unique asymmetric shape: a theoretical hypothesis

In avian biology, the radius of curvature, or R, has hardly ever been used to study the mechanics of birds' egg shape formation. However, it is essential for introducing important details about the form, function, and performance of an object, which is useful in biomedicine, manufacturing, and precision design. In order to determine a possible biological mechanism and the location of load application that creates the distinctive asym-metric egg shape in nature, the goal of this study was to develop a formula for computing R at any point over an egg contour. We derived a relatively simple means of computing R and identified the location that muscular compression is carried out to give the egg its characteristic form. This location (x/L), the angle (α) of compression and the relative magnitude of the load proportional to R can help identify a specific section of the oviduct and the squeezing muscle involved. Novel equations for computing R, x/L and α were proposed , based on standard geometric parameters. Our findings demonstrate how the theoretical knowledge of physical, mechanical and mathematical processes can contribute to the solution of biological problems and resonates with the fields of egg-inspired engineering.