Applied Science and Maths 101: Honey Pi

A barrel of maths fun

Once upon a time my partner and I (both science heads) loved finding and renovating interesting things made of wood. One day he suggested we get a hogshead wine barrel and use it as a rainwater tank. We arranged for the barrel, a beauty made of French oak – to be delivered to the middle of our front lawn. A sniff at the plug hole gave a slight odour of red wine and oak but no mould or rot. We lovingly polished the barrel until it glowed with the unique golden beauty of oak wood and were very pleased with our handiwork.

The question that arose was: how to get the barrel around to the back of the house through the one narrow gateway, or the front door of the house? We measured the width of said apertures. But the problem with a hogshead is that it bellies out in the middle. Holding up a straight ruler across one side or across the top to try to measure the maximum width will not show you the right diameter (straight distance across the widest part of a circle) because parallax (contraction with distance) causes it to look smaller than it is. It looked as if it would be very close to the width of both door and gate, but it was so heavy and unwieldy that we would not try to move it without knowing exactly where we were going first.

We needed to know the straight diameter across the widest point of the barrel and all we could do was measure the circumference by running a tape measure around it. Enter a bit of high school maths:

c = π Χ d
where:
c = circumference
d = diameter
π (Pi) = 3.141592…
(I also remembered that you can obtain a rough approximation of Pi by dividing 22 by 7, magic stuff if you don’t have a calculator or maths brain!)

Switching the equation around algebraically we get:
d = c ÷ π

We knew the circumference and we know Pi, so bingo! we had our diameter, and it was ONE centimetre too big to go through either the front door or the gate! So the lovely shiny hogshead barrel remained in the middle of the front lawn, a nice decoration, and sometimes a de facto table when we had garden parties.

Nature abhors a vacuum

Pretty soon we noticed bees going in and out of the plug hole in the side. They were nice tame bees so we let them alone and they got busy. A while later you could smell the aroma of honey wafting from the plug hole, and if you put your ear close to the barrel you could hear the constant soft hum of bees at work inside. So it remained for a few years: the bees living happily in the barrel, as unconcerned about us as we were about them. As I’d go about gardening, I’d cross their flight path or even peer into the plug hole and they’d just steer around my head and keep going, sometimes brushing my face with their wings. A group of people could lean on the barrel chatting and the bees didn’t mind.

The best-laid plans of bees and men….

Then one summer we had an especially intense heat wave, and came home from the beach to find the hogshead slumped and leaning sidewise in its metal straps like the famous tower of Pisa. What? Being scientists, we set to analysing the situation. Honey and melted beeswax containing struggling and drowned bees stuck in it were flowing out through the gaps between the now loose wooden boards. The bees were in an uproar, although not against us. We realised that the hogshead timbers had been drying out and loosening up in the sunshine these last few years but were being held in shape by the massive wax constructions on the inside. Now the wax had melted in the heat and the whole thing was coming unstuck!

Being not just intellectuals but practical beings, we set to scooping up as much of the honey and wax as we could recover into jars, and rescuing living bees with a dip in fresh water. Once the flow stopped all we could do was to gently right the barrel, moisturise the timber with oils, and see what would happen. Evidently the queen bee had survived the ordeal inside her hogshead castle and the bees were able to rebuild their passages in to her. Then they swarmed across the neighbourhood, huge wildly gyrating clouds of them, much to the terror of the human residents. But our bees were gentle and well-mannered and nobody was hassled or stung by them. Off they went to find more stable lodgings, while we enjoyed the deep golden honey which had a faint tang of oak and red wine, probably quite unique. And we got to use the beeswax to make candles and polish the hallway floor!