The ultimate shape of any mass of materials depends critically on their structure and gravitational forces. The outline of mountains and “planets,” by definition, and simple columns are definable as to structure: As an example, and explication, Machine Elf notes (post #7):
The compressive strength of naturally occurring materials is limited, so you can only have a column of it be so tall before the rock at the bottom is overloaded and crumbles/extrudes out from under it. Take granite, for example, with a compressive strength of 29,000 psi and a density of 0.0991 pounds per cubic inch; under earth’s surface gravity, the tallest exposed cliff face you could make would be 4.62 miles tall; any taller than that, and the rock at the bottom is overloaded and will crumble…
In that thread, “egg-shapedness” of various celestial objects were calls into question.
With this kind of analysis, is it possible to determine the maximum size of an egg more or less of the materials avians create?
I found the extensively referenced “The Eggshell: Strength, Structure, and Function,” S.E. Solomon, British Poultry Science, 2010, available online, but the contents, for any real analysis, is over my head.
The maximum practical size of an egg is based more on getting oxygen to the embryo through diffusion than to any structural considerations of the material it’s made of.
The largest amniote eggs known are those of the extinct Elephant Bird, Aepyornis, which was about 13 inches long, and those of the sauropod dinosaur Hypselosaurus, which were about the same size at 12 inches long. Given that the dinosaur was far larger than the bird, and that no larger eggs have been found, suggests that these are probably near the maximum size possible physiologically.
No doubt it would be possible to construct a larger egg just based on the materials involved.
No reason you have to diffuse through the entire thickness of the shell, though. You could have 5% of the surface be a straight shot through the shell without reducing the strength much, and then on the interior have a high-surface-area shape (like alveoli) to transport the oxygen across a thin boundary. You would still eventually hit a limit but it would be much larger.
It’s not just a matter of getting oxygen through the shell. You also have to diffuse it through the entire mass of the egg, at least before a circulatory system has developed. Admittedly most of the egg will be yolk, which is not very metabolically active, but if you have an egg 12 inches in diameter you have to diffuse oxygen through 6 inches of egg white and yolk.
Yeah–though if we’re really trying to engineer a very large egg, one could come up with other solutions. The gas diffusion rate in air is much higher than in liquid, so the farther in you can get with gas cavities, the greater volume you can support. So you might have a very complex network of passages that allow air to nearly reach the center. This would have to dissolve or otherwise go away as soon as the embryo gets too big, but one could imagine solutions to this as well.
Of course if it doesn’t have to function as an egg at all, you could do a lot better–like lose the white+yolk completely, and just have structured shell material.
If you take this to one extreme, you could say that the largest egg is a female blue whale. The mother is just a very large, very complicated egg designed to acquire and transport oxygen and other nutrients.
I say that mostly in jest, but if we start considering radical redesigns of eggs, we quickly reach a point where it’s hard to be clear about what the word egg even means.