The smallest container capable of protecting an egg from breaking is... an egg! So long as the drop isn’t vertical, is over 40 ft and is onto a reasonably forgiving surface, like grass, an egg will protect its own fall. At a lower height, 3-4 feet, it will almost always break.

This was the subject of much discussion in New Scientist letter pages some years ago (11 August 1960!), I think the best replies were re-published as an article because it was the most answered letter ever.

Fans of physics explained the phenomenon by studying the structural qualities of an egg.
The aerodynamics of an egg causes it to fall largest end first, in a similar way to early space re-entry capsules. If the egg isn’t dropped from high enough the egg is more likely to fall on a weaker side.

The largest end has an area of gas trapped between the egg’s two membranes. This causes the hole in the white of your hard boiled egg; it also makes peeling one easier. Upon impact the heavier spherical yolk continues moving towards the ground. The compression of the airspace acts like an air bag for the eggs’ valuable contents. It also adds additional structural support in the form of pressure to the already incredibly strong curved eggshell.

Eggs with no yolk invariably break. This is not only because the air compression wouldn’t happen properly but also because the elasticity of the chalazae which hold the yoke in place probably has some form of dampening effect on the fall.

Evolutionary theorists couldn’t help adding an explanation as well. Apparently early birds didn’t make nests. They simply laid eggs mid-flight*. The eggs which survived the fall continued to add their genetic information to their species. This theory is supported by the relatively oval shape of land based dinosaurs. In this way the existence of sophisticated physical mechanisms within a common hen egg, which certainly don’t need drop protection, are explained.

So next time you are competing against some eager MIT professors to find the best way to protect an egg from a fall, trust evolution and physics to help you win the grand prize!

Sources:

www.picotech.com/experiments/ dropping_egg/dropping_eggs.html
http://www.asl.org.au/aslnews/v37/aslnews_v37n3_articles.htm

*It has been pointed out by rootbeer277 that this is very unlikely. Most birds can’t even excrete in flight.

Update

rootbeer277 also challenged me to conduct the experiment myself. I took three eggs outside and confidently lobbed them over a tree.
The first one hit the tree and didn’t fall out. Unperturbed I lobbed the second egg. The street lights provided beautiful illumination for the resulting spray of yolk off the damp lawn.
Damn.
Remembering all my javelin training from school I hurled the last egg with all my might.
Splat.
My breakfast now lies inedible on the floor outside. I’m suing New Scientist for making me hungry.

About once every three months I get a whole lode of "Hey, sweet! Someone likes your write-up titled "Egg Drop!"" which is great because I have to assume that there is a class somewhere that has found these write-ups useful. However it would be great, particularly if you were brave enough to try my unprotected egg drop, if you would send me a private msg with your results. All you have to do is sign up to everything2 and use the box above my write-up to contact me. Thank you!