I have documented my theory, including the optimal configuration in the carton for each number of eggs from 1-12. Here it is in Excel format and in PDF format.
The objective is to optimize the distribution such that the center of mass approaches the center of mass of a full carton, and that the moment of inertia approaches the midpoint between the minimum possible and maximum possible moments of inertia for the given number of eggs. There is an unquantified bias favoring achieving the center of mass goal over the moment of inertia goal as center of mass is the most important attribute for correct balance of the carton.
Personally, I try to minimize the moment of inertia about the geometric center (which incidentally also means keeping the center of mass centered). Fortunately, this is a very easy task to accomplish: Just take eggs from alternate sides.
I thought I was the only one who paid any attention to this.
Having dropped more than one cartoon that was grossly unbalanced, I long ago learned to distribute eggs evenly in the tray. I do it by selecting eggs to maintain balance, or rearranging them if others have done it linearly. A little fussy but entirely practical and pragmatic, imvho.
Very impressive. You should make an app for that. Take a picture of the carton and the phone tells you which egg to take next, or how to rearrange them if you’ve made poor egg decartonization choices.
I applaud the OP for bringing this issue to wider attention. Unbalanced egg-boxes are a scourge and should not be tolerated.
However, I find their solution less than optimal as it necessitates REARRANGEMENTS of existing eggs as the last few eggs are taken (worse – in the act of making such rearrangements the box becomes dangerously unbalanced (see the transition between 3 and 2 eggs) – if this is done with box in hand then eggs are needlessly put at risk).
Here is my solution with the added bonus of not being wrapped in a lop-sided PDF.
I hate to overelaborate the issue, but I have a friend who provides both chicken and duck eggs from their self-raised birds. There is little rhyme or reason to the number and variety of eggs I get in a dozen.
Duck eggs are larger and have a thicker shell. Also, the eggs I get tend to vary in size much more than the pre-sorted variety one gets at the store.
Furthermore, duck eggs have a richer flavor, and—to my taste—work best when used together with chicken eggs. When I’m simply frying or hard-boiling there isn’t so much difference, but in something like an omelet, or a recipe, or even a pan of scrambled-eggs, mixing seems to me to be the best approach.
One large duck egg might offset, weight-wise, two small chicken eggs; but then one large chicken egg might offset a small duck egg. A duck egg that is a similar size to a chicken egg will be a little more weighty (mostly due to the thicker shell). Some of the chicken eggs are dark enough, and some of the duck eggs light enough, that they can be hard to tell apart without feeling or holding them.
As a final, personal note, I will add that my aesthetic preference is for a crosswise layout so that four eggs are best arranged:
…O.O
…O.O.
…despite the fact that such an arrangement leads to an unbalanced carton. My solution to this is to put the carton lengthwise in the refrigerator with the load facing the door.
Even the pre-sorted ones can vary in size and weight to some extent, so I redistribute them to alternate large and small in the carton as they get used. Still all centred in the middle as much as possible.
Perhaps you live alone. In a house with three other people I never know which end is the heavy end and am frequently surprised. Surprises and egg cartons do not mix well. Unfortunately I have yet to train the rest of my family in classical mechanics.
Same here. And, yes, I live with others. Pretty much everyone I’ve ever lived with has done it this way, and I can’t remember ever suffering from some butterfingers dropping the carton.
Save some of those plastic Easter eggs left over from children’s egg hunts. Then, when you remove a real egg from a carton, you can replace it with a similarly weighted plastic egg. Now your carton is always evenly balanced.
I think you’re on to something here. Farmers should be using those plastic eggs for packaging instead of that fragile stuff they use now. What is that, plaster or something?