Eggs and Maths

Going to work on an egg
From a blog first posted 3 September 2011 - https://sites.google.com/site/foodieshare/

Calculating the volume of an egg and the quantity required for a quiche. 

Recently in Flan tins – Does size matter I admitted that I did not know the cubic volume of an egg. Feeling this was a critical gap in my knowledge of all things ovoid I decided to investigate...

A quick Google and it turns out that there have been many complicated and in depth papers concerning the volume of an egg. Not least among these great works is an article by that well know ornithologist F.W. Preston published in The Auk back in January 1974 with the devilishly clever and witty title 'The Volume of an Egg' (I have included a link as I think some of you will find this a fascinating and riveting read).

However for the more shallow of you I have come across a simplified explanation...

The shape of an egg can be thought of as two halves of ellipsoids with different radius dimensions. It's width is its equatorial diameter. Half of this diameter is the equatorial radius, which you can call A. The total length of the egg is its polar diameter. The distance from the equator to the nearest pole is the short polar radius of the egg; call this number B. The distance from the egg's equator to the farthest pole is the long polar radius; call this number C. Thus one ellipsoid has radii of A, A, and B; the other has radii of A, A, and C. It follows then that the formula (1/2)(4π/3)A²B + (1/2)(4π/3)A²C or (2π/3)A²(B+C) will give us the volume.

All we need now is the vital statistics of your standard egg and where better to start than the British Egg Information Service. All eggs in the UK are graded by size, great. No wrong, for size read weight. Fortunately there has been some superb work done not only on volume of an egg but also density of an egg. In the book 'The Avian Egg' A.L. Romanoff and A.J.Romanoff (1949) gave the value of 1.033 as the density of a fresh hens egg. C.V. Paganelli, A. Olszowka and A. Ar gave it as 1.038 x egg weight^0.006 but I think we should go with the Rmanoff's on this occasion. (Panganelli, Olszowka and Ar come across as a bit pedantic).

Egg facts – here in the UK we have four sizes of eggs, small, medium, large and very large. Small eggs are under 53g, medium from 53-63g, large 63-73g, very large over 73g. Which means in theory that small eggs can weigh anywhere between 0 and 53g (I understand that eggs weighing less than 1g are referred to in the trade as chick wind and are only available from specialist suppliers). At the other end of the scale very large eggs have an undefined upper limit although in practice the largest hens egg ever recorded was 340g (it was in The Telegraph so it must be true). I don't know if hens eyes usually water but I bet the poor things tear-ducts were stretched to the limit that day, along with a few othere things I expect.

Now for some maths. All we need to do is divide our chosen eggs weight by the Romanoff's density value (or should that be multiply). Not to worry, don't suppose it makes much difference. Anyway if you take each gram of egg as having a volume of 1cm³ ±0.033cm³ or 1ml ±0.033ml you are not going to be too far off.

I think I see a bit of a short cut here. If you do need to know the volume of your egg forget all the maths, just weigh your egg in grams and call it millilitres!

So to fill a 20cm flan dish it would take around 15 large eggs, less a couple to take into account of the lining pastry, less a few to take into account of the cream, less a few to take into account the solids (bacon, cheese etc.) less a few because we don't want to fill it to the very top. In fact Felicity Cloake of the Gardian goes for 4 eggs plus 2 yokes, 320ml cream and 200g of bacon for her Quiche Lorraine. That seems to workout well, I make it about 800-850ml by volume plus a couple of yokes – oh no, what is the ratio of yoke to white in an egg? Think I feel another Google coming on.

I did check the figures in this blog by measuring the eggs in my fridge and using the formula given but I have to confess I didn't sit down and do the maths with my trusty slide rule and abacus, there's a brill Egg Calculator at http://www.had2know.com/academics/egg-surface-area-volume-calculator.html. Bookmark it, you never know when you'll need it!

After thought – 'Going to work on an egg', what a brilliant concept, wonder if the Egg Marketing Board would be interested?