17/9/2020
Nitya Nigam
This article is a direct result of me being hungry at the time of writing. We’ll be taking a look at the maths behind puff pastry, a deliciously light, flaky pastry made from layering dough and butter several times and then baking to crumbly perfection. It’s used in everything from dessert pies to beef wellington, and melts in your mouth. Check out this video to find out how to make it yourself. Puff pastry gets its flaky layers from a tedious rolling-and-folding process, and there are multiple techniques for this. In this article, we’ll mathematically analyse each of these techniques and discuss their advantages and disadvantages.
The first rolling-and-folding technique, the Scotch method, doesn’t actually have any folding. In this method, flour, salt and cold water are combined with walnut-sized lumps of butter and mixed together. This creates flat discs of butter dispersed through the dough, rather than the continuous sheet created by other methods. Therefore, this pastry doesn’t rise as well as the others, but it is the least tedious to make.
The second method is called the English method. This involves rolling the dough out into a rectangle, covering two-thirds of it in butter, and folding inwards as shown in the diagram on the left. The new rectangle is then rolled out to a thickness of about 12mm and folded again in the same way. Since each “fold” involves tripling the number of layers, the formula for the number of layers after n folds (we can call this L) is simply L = 3^n. The optimal number of layers is between 100 and 700 (depending on how much you want your pastry to rise). We can solve the following inequality to find our values of n.
The only integer value of n between these bounds is 5, so that is the optimal number of folds.
The third and final method is called the French method. Here, the dough is first rolled out into a square, and butter is placed in the middle of the square as shown in the diagram. F stands for fat (butter), and D stands for dough.
The four corners are then folded inwards, creating a smaller square. This is then rolled out into a 12mm-thick rectangle and folded as in the English method. The formula for these later folds is the same as above, but we have to use n-1 instead since the first fold is excluded. The first fold actually doubles the number of layers, since each corner is folded onto only one layer of dough. So for this method, L = 2(3^(n-1)). It is quite clear that this is less efficient than the previous method, but let’s find our optimal values of n in any case:
So n can be either 5 or 6 in this case.
While the English method creates more layers with less folds, it is less malleable than pastry made using the French method, since the butter was in contact with less of the dough’s surface area. Additionally, the more layers there are beyond 130, the less the pastry rises (because of the weight of all the layers), so it tends to produce a shorter pastry. Therefore it’s best used in dishes where height and texture are less important, like savoury pies where the flavour of the filling stands out. The French method is best used in delicate desserts.
