Once a year, engineers can put shell theory into practice in a less conventional way: by winning their family’s egg cracking competition (also known as egg knocking or egg tapping). On Easter Sunday, it is a tradition for Greek and Armenian families to gather and play a game of egg tapping. Similar traditions exist in many different places such as in Cajun communities in Louisiana or for other occasions, like the Persian New Year Nowruz (celebrated at the beginning of spring).
“As geometric stiffness is inversely proportional to the radius of curvature, the curvier the egg, the better it will perform.”
Here’s how the game works: everyone picks one hard-boiled egg from a basket, and the battle begins. In a knock-out tournament, several players hit their eggs against each other, first bottom-to-bottom, then when bottoms are broken – top to top. When a player’s egg is cracked on both sides, he or she is eliminated. The game continues until one player remains with an intact side of their egg, and he or she is proclaimed the winner.
But first some structural mechanics. The mechanical behavior of shells is predominantly determined by the overall shell shape. When observing the failure mechanism of the egg shells, you will see a relatively small depression with some cracks (as shown on egg B above). This failure mode in shells is called local buckling, and is caused by the sudden excessive deformation of the super thin shell due to the impact of the other shell. But why did shell B break, rather than the egg used to break it?
How much a shell deflects can be predicted through what engineers call the shell’s stiffness. Stiffness depends on two factors: material properties (material stiffness) and geometry (geometric stiffness). For egg shells, geometric stiffness dominates the behavior, especially as the material of all eggs is basically identical. Thus, the secret of winning the egg challenge can be boiled down to the (local) shape of the egg. As geometric stiffness is inversely proportional to the radius of curvature, the curvier the egg, the better it will perform: geometric stiffness ̴ 1/radius.
That gets us to strategy:
Step 1: Pick the pointiest egg in the basket. The importance of this step cannot be stressed enough. Only the top part of the egg matters. Size and thickness are of very little importance. Curvature is key, but make sure the egg has no pre-existing cracks (like egg D). For example, if you were to consider the eggs pictured below, egg C would be the best choice.
Step 2: Polish your egg. The buckling phenomenon described above is dominated by curvature. However, local buckling can be facilitated though small imperfections (like small bumps) on your egg. Try to remove as many as possible. Also, it it is nicer to win with a clean, shiny egg.
Step 3: Start hitting. Typically, you will first use the bottom of your egg, this part of the game is relatively unimportant. Consider playing strategically: try to steer the game so you can make the first hit when you get to attack the top of the egg of your opponent (see step 4).
Step 4: all bottoms of the eggs are broken, time to step up your game and get cracking with your pointy top. Make sure you hold your egg in a grip so that it can only be hit at the curviest spot on the top. Buttress the sides with the palm of your hand for extra support.
However, imagine someone picked egg C before you, and you ended up with the less desirable egg D. If you plotted well and are the hitter, you can still win: aim for the flatter area on egg C next to the top (see red arrow below). It does not matter how hard you hit the egg (remember Newton’s 3rd law of action-reaction), the location is much more important.
Good luck in your next egg face-off.
Author: Tim Michiels
P.S.: The secret to a delicious egg salad is a splash of vinegar!
