Speedometer

It occurred to me today that I don't actually know how a speedometer works. I looked at this: https://www.explainthatstuff.com/how-speedometer-works.html Whilst mine is certain to be a modern electronic one I really liked the old electromagnetic induction idea and will try to get it into my teaching. The engine turns and pulls a magnet round with it. The magnet passes a metal cup and induces a current in the cup. This turns the cup into a kind of electromagnet. By Lenz's Law, this new electromagnet must have poles that try to oppose the original turning of the magnet. In other words, the poles are attracted to the original turning magnet, trying to drag it back. This means that the cup gets pulled round. The cup is actually attached to a rotary spring to stop it moving and the bigger the current the bigger the force so the further the spring turns. The spring is attached to a needle which is what you see.

Sunset and twilight

Back to consideration of the sunset in Normandy. There are 24 x 60 = 1440 minutes in a day. The Earth rotates 360 degrees about its axis in 24 hours. That means it takes 1440/360 = 4 minutes per degree. The Sun subtends 0.5 degrees and thus takes 2 minutes from the bottom first touching the horizon until the tip disappears. Civil twilight is defined as lasting until the Sun is 6 degrees below the horizon https://en.wikipedia.org/wiki/Sunset That means 24 minutes. Apparently night starts when the Sun is 18 degrees below the horizon, so 72 minutes after sunset. I'll need to find out why the boundaries are set thus.

Penrose Tiling in Oxford

I finally got to see the Penrose Tiling outside the Mathematical Institute in Oxford. He explains here how the pattern is formed https://www.maths.ox.ac.uk/about-us/life-oxford-mathematics/oxford-mathematics-alphabet/aperiodic-tiles

Yards in a mile: Oxford Race for Life

It was a 5km event but one participant didn't have much of an idea of how far that would be. So it is 3.1 miles. But I realised that I have never learned how many yards there are in a mile. So for the record, there are 1760 yards in a mile. So 5km is 3 miles and just under 200 yards!

Cans experiment and Newton's Law of Cooling

We did the experiment where you pour boiling water into a black tin and a shiny tin and let them cool. I had never thought about the equation of the curve but guessed it was exponential. It turns out that it follows Newton's Law of Cooling. The rate of fall of temperature is proportional to the temperature difference between inside and outside the can. In other words, a hot can cools faster. The solution is an exponential equation. https://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html I used the experimental data to plot LN graphs to get the factor k from the gradient. I did it for both black and shiny tins:

Having got the values for k, I put them back into the equation from the linked page and got the theoretical cooling curves if we had done the experiment for an hour.

Bayeux Cathedral and Gothic architecture

I have finally got my head round the advances in architecture that are called "Gothic". The ceilings became made of stone vaulting. This made the roofs much heavier. The middle pulls downwards and pushes the edges of the roof outwards. This would cause the walls to be pushed out. So something is needed to resist this outward push. Hence the flying buttresses on the upper level. The walls on the Gothic cathedrals also have large windows which weakens them.

Light effect at sunset at Merville

Once again I was able to see the green flash from the beach at Merville in Normandy. On this particular night I was unconvinced but I did film it to try to catch the moment. Reviewing the film has brought out a detail that I missed. There is a clear V shape in the light, 10 degrees up from the surface of the sea on each side.Maybe it was about particular conditions that night. I have not yet found an explanation.