Series Report on the National Taiwan University Research Achievements:
Newtonian Mechanics and Egg Incubation of Giant Birds -STEM Sparks Innovation

Buildings with round roofs are called “domes.” The new Sports Center of the National Taiwan University is an example. The dome resembles a giant egg, laid by a giant bird. In nature, ostriches are the largest living birds. Ostrich eggs are giant compared with those of sparrows. How are domes constructed by engineers and giant eggs laid by birds related?

Professor Jia-Yang Juang of the Department of Mechanical Engineering, advising master degree student An Yen and undergraduate student Pin-Yi Chen, and Professor Hon-Tsen Yu of the Department of Biology, advising master degree student Hsiao-Jou Wu, collaborated on a study of the relationship between the mechanics of eggshells and egg incubation. The results were published as the cover story in the August issue of the international journal Biology (MDPI) (https://www.mdpi.com/2079-7737/10/8).

Shell theory in engineering discusses the mechanical properties of shells and the load weights they bear. Both the new sports center of the National Taiwan University and the eggs of birds are shells in structure. Shell, as a load-bearing structure, has the merits of using the least materials, lightweight yet stiff and strong. Thus shell structures have been widely adopted in engineering designs such as airplanes and domes. Bird eggs are a representative case of load-bearing shell designed by nature with contradictory requirements. On the one hand, the eggshell must be sufficiently strong to bear the weight of the parent bird while incubating. On the other hand, the eggshell must be sufficiently fragile, so that the hatchling can break the shell, and will not be trapped inside and die.

Professor Juang, Pin-Yi Chen, and An Yen have discovered something interesting in a previous study (Juang et al., Sci. Rep., 7, 14205, 2017)–Although the size of bird eggs varies greatly, they appear to follow certain “design rule.” For example, the egg of the elephant bird (Aepyornis maximus, once lived in Madagascar and is now extinct) weighs 9,000 grams, while the egg of the hummingbird (Mellisuga minima) weighs only 0.3 grams, five orders of magnitude in difference.  However, after analyzing thousands of eggs of different colors, shapes, and sizes from different birds, they found that a dimensionless number C, which they defined as a function of the stiffness of the eggshell, the weight of the egg, the major and minor axes of the egg, is invariant. C is about 15,000 for all bird eggs irrespective of their size and species.

The biological implication of this result is that birds have evolved a special design for a long time. Although the weight of different birds varies greatly, their eggs have all achieved a common design principle, after adjusting to 4 factors (the stiffness of the eggshell, the weight of the egg, and the major and minor axes of the egg), with the emergence of an invariant number C. That is to say, the eggshell is a nearly perfect design, which overcomes the dilemma of incubating and hatching eggs.

However, biological diversity produced by biological evolution is even more interesting; that is, animal behavior is indirectly involved in the "eggshell adaptation" design competition, especially for birds classified as giant birds. The most familiar giant birds are of course ostriches from Africa, laying giant eggs weighing 1.2 kilograms. Ostriches and other giant birds are almost all ratites. They differ from other birds because they have flat sterna without keels, unlike the chicken we eat that have sternal crests.

In addition to ostriches from Africa, other ratites in the world include rheiform birds, emus, and cassowaries. Elephant birds and moas are also ratites, which have been hunted to extinction by humans in the past 400 years. Among these giant birds, male and female elephant birds and rheiform birds are about the same size. Male and female ostriches, emus, cassowaries, and moa are dimorphic. Male ostriches are slightly larger than females. Male emus and cassowaries are far smaller than females (rare among birds), so they adopt the strategy of egg incubation exclusively by males (the eggshell bears a lighter load this way).

Focusing on giant birds, the team set out again to obtain eggs from emus and cassowaries. The stiffness of the eggshell was analyzed using precision instruments, and was estimated using a computer simulation technique called the finite element analysis (FEA). Indeed, the strength of the eggshell can only bear the weight of males but not females. The team also analyzed several extinct moas and other giant birds, and their incubation behaviors.

FEA was originally developed for engineering analysis of man-made structures, including shell-like domes. To the amazement of paleontologists and zoologists, this technique has been creatively applied to the analysis of eggshells. Furthermore, the field of mechanics has included eggshells in the discussion of shell theory used in engineering, with the possibility of developing biomimetic applications.

In conclusion, the education sector has promoted an integrated approach to STEM (Science, Technology, Engineering, Mathematics) in recent years. Based on shell theory, the mechanics behind egg incubation of giant birds demonstrates the benefits of STEM education, by generating more interaction between science and engineering, and by combining existing knowledge and expertise for more creative sparks. As for students participating in this study, Pin-Yi Chen is a doctoral student at the Massachusetts Institute of Technology (MIT) in the US; An Yen works as an engineer at the Kinki Sharyo Co., Ltd. in Osaka, Japan, designing railroad vehicles; Hsiao-Jou Wu continues the study on dinosaur eggs, and is now a research assistant in paleontology in the Department of Geology, and plans to go to the US for further studies. Undoubtedly, all of them have benefitted from the concept of STEM education!

The full text of “Egg Incubation Mechanics of Giant Birds”, published August 1, 2021 in the journal Biology:https://doi.org/10.3390/biology10080738