Engineering the World’s Tallest Cake
It’s my birthday tomorrow and as I approach the grand old age of 26 my mind is turning, inexorably, to cake. Being an engineer, however, I am not to be satisfied with just any cake- I demand something structural; the tallest cake in the world!
Initial load testing shows that the elastic limit (i.e. the point at which the cake does not spring back) is about one and a half wine bottles.
Currently the record for the tallest cake is 33m, which already rules out just baking some monstrosity in one of the worlds biggest ovens. Like our predecessors, the only option is to go modular; making this cake a tower of tasty masonry.
In keeping, our icing will be our mortar. Despite the many great qualities of buttercream, structural connectivity is not one of them. This means our cake needs to be gravity supporting, making it weak against lateral loads like wind- necessitating it’s indoor storage (and who, I ask, stores cakes outside anyway?).
Although the internet provides us with some information, it’s not wholly reliable and precludes the fun of doing some original (and fattening) research. So without further ado, let me introduce my lab:
A quick weigh-in leaves us with a block density (for chocolate-chip cake) of 5.7 kN/m3 somewhere in the region of pine-wood, interestingly enough. As there are no plans to inhabit the cake, the only load it needs to take is its own weight, and therefore the (relatively) light make-up is a plus.
Initial load testing shows that the elastic limit (i.e. the point at which the cake does not spring back) is about one and a half wine bottles; with an additional semi-elastic limit at two and a half. This means the elastic modulus of cake is around 7-8 kPa, giving us a block strength in the region of 2.25 kN/m2.
Beyond the elastic limit our cake beings to show plastic hardening (that is to say, as it compresses, it gets stronger). At the expense of flattening our cake by 81% we start to get to the limit of our cake’s capacity, with an enhanced block strength nearing 75 kN/m2. By this point our test cake has expanded outwards by almost as much as its compressed; a behaviour known as a Possion’s ratio of 0.5 (this is important for later).
If we stick within the elastic limits (i.e. we leave the individual sponges soft and airy) our tower can reach a measly 400 mm. Allowing our cake-bricks to flatten, however, we gain a theoretical height of 13m; although the resulting squash shortens it back down to 2.5m.
By this height, however, our tower of cake would have already fallen.
Cake is a non-conforming material, and imperfections will be rife. Small unbalances at the base will start to have greater and greater effects on the structure as it rises. Given the amount the cake will squash our tower is unlikely to make it past a meter.
This means its time to pick out a better structural form. The best place to go to rid this instability (known as slenderness) is a Pyramid. Of course, we loose economy because our cake extends out as far as it goes up- but extra cake never hurt anyone.
The Pyramid form comes with an added benefit, the distribution of pressure allows us to build three times higher; while reducing the loss of height as the bricks are confined (at an engineering judgement). This means that the grand height of my birthday cake will be 40m.
So who’s going to make this for me?