Advice on two-tier cake and height
What is the recommended height of cakes when making a two-tier chocolate mud cake? Or to get a decent height, should I make (as an example) two shallow nine-inch rounds for the bottom layer and two shallow seven-inch rounds for the top layer?
Best Answer
As a note before the post I am more scientist than baker.
The stress you can put on a structure before it severely deforms depends on a lot of things including it's Young's modulus. These are very well understood for construction materials but I came across this paper which discussed it for various cake recipes (PDF). The recipe I found for mud cake has about 27% flour so I used values accordingly for my calculation.
If we assume that we do not want more than a 5% deformation (this may seem like a small number but my estimation is an attempt at being conservative, plus it would be at the very least noticeable) then the maximum height would be about 28 inches.
Or to put it another way, your two 9 in pans for the bottom layer and the 7 in for the top would make a delicious cake with some room left over for frosting. If you are really concerned about structure I also came across this recipe which kind of talked about that as well (much more so from a baking perspective).
Other info from Epicurious.
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How tall should a 2 tier cake be?
Cake Size You need A two tier cake means you need two cakes (composed of layers) in two different sizes. The standard size is usually a 6\u2033 cake stacked on top of a 8\u2033 cake and it feeds about 40-50 people depending on how big you cut the slices.Do cake tiers need to be the same height?
If you only need a cake to serve 60, two tiers will suffice, but I would recommend a taller base tier, as a two tier cake can look unfinished if the tiers are the same height. this taller tier can be divided with a board inside the cake so that you can have two different flavours.How tall should my cake layers be?
Be sure your pans should be two to three inches high. Usually, my cakes are 3 layers. Most recipes can be adapted to other size pans, and it's best to check on the individual recipe. I like 8-inch pans because the cakes are usually taller than a 9-inch or 10-inch pan and it's the easiest size to work with.How tall should each tier of a wedding cake be?
Two layers each approximately 2 inches high with a 1/2 inch to a 1 inch layer of filling. Once the frosting and decorating is on you have about a 5-6 inch high cake.Two-Tiered Cake Sizes
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Answer 2
I do not have experience with mud cake. If it isn't a very sturdy cake, you may need to add supports (i.e. dowels and cake rounds). If it is sturdy like a yellow or white cake, you can stack them without adding supports.
Here is a picture of a cake I made using 9 inch pans for the base and 6 inch pans for the top. There were three layers of cake on each tier. 
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Images: Rachel Claire, Reem Mansour, Tim Douglas, Tim Douglas