The Mathematics of Pork Pies

Having eaten a pork pie for lunch yesterday I found myself pondering an old question. I had bought two small pies, because on this occasion that represented a better deal with a free tub of potato salad thrown in, but I would normally have opted for one large pie, not just because it’s usually better value but also because of a long-held conviction that the larger the pie, the better the meat to pastry ratio.

This belief, which is superficially based on nothing more than common sense and experience, is backed up by a reductio ad absurdum argument – if one were to continually reduce the size of the pie, there would eventually be no room for the meat at all. However, having nothing better to do, I decided to test the theory mathematically.

To do so, it was necessary to make a few assumptions:

The shape of the pie was considered to be a perfect cylinder. This is clearly untrue but to assume otherwise would result in an horrendously complex calculation.

For the same reason, the pastry was assumed to be of even consistency with no flanges, crenellations or other decoration.

The meat was assumed to fit the space inside the pastry exactly, ignoring any jelly or air gaps.

An aspect ratio (diameter to height) of 4:3 was chosen as this seemed to be a reasonable figure for the average pork pie (although altering it made little difference to the outcome).

Finally, the all-important factor – the thickness of the pastry. Should it be a constant, regardless of the size, or does it increase in proportion to the overall dimensions? The former is clearly not the case, for a very large pie with no more substantial a casing than one of the cocktail variety would soon fall apart. On the other hand, the relationship is not a linear one: whereas 0.2 inches of crust might be necessary for a 2 inch diameter pie, a 1.2 inch crust on a 12 inch pie would be ridiculous. I therefore devised a formula whereby the pastry thickness increases at one tenth of the rate of increase of the diameter from a minimum of 0.2 inches.

I then calculated the percentage of meat for various sizes of pie, using the above assumptions and plotted the results in a graph.pork_pie

The grey line represents the nonsensical case where the crust thickness is directly proportional to the diameter. Predictably, when you think about it, this is a straight line.

The red curve represents a constant thickness of 0.2 inches and the blue a gradually increasing thickness.

So, there you have it. Making some approximate but entirely reasonable assumptions, a very small pork pie is less than 20% meat; the proportion rapidly increases with size but then, to use an expression currently in vogue, the curve flattens. A 12 inch diameter pie is about 78% meat; a monstrous 10 foot diameter pie (7 foot 6 tall with a crust nearly 6 inches thick) would be around 86%.