Broken bridge

This bridge on Royal Deeside had been hit by a tree in flood waters and put out of action. Suppose the tree had a mass of 1 tonne (1000kg) and was travelling at 30km/h, which is about 8 m/s. That would give it a kinetic energy of 35000J. Elastic strain energy is given by 0.5kx^2 where k is the spring constant and x is the extension. Suppose the bridge is 15m long and the middle is displaced by 30cm. By Pythagoras, that means an extension of each half by about 0.5cm. That means spring constant would be 1.4 x 10^9 N/m.

Saharan dust and the jet stream

I took this photograph on the 22nd April. The dust on the car was said to be from the Sahara. Since then there have been two further events where blobs of hot air have moved north from the Sahara into Europe. I found https://www.eurekalert.org/pub_releases/2018-10/rai-pjc100218.php which suggests that it is to do with the jet stream. Weather forecasters refer to the jet stream a lot at the moment. Winds on Earth are driven by convection. At the equator, the Sun heats the air so that it expands and rises. This causes low pressure at ground level. The opposite happens at the poles. In between, the air from the equator falls down to the ground creating high pressure around the latitudes that contain deserts like the Sahara. At our sort of latitude, it is warmer than the poles so air pushed down from the Arctic by high pressure there can be warmed and rises. This means that in each hemisphere there are 3 convection cells. The polar jet stream occurs along the boundary between the two most northerly of the large scale convection cells in this hemisphere. I'm interested that it flows along the boundary rather than from one side to the other. This seems a bit like one of the hand rules for electromagnetism. Hot air is rising but the fast flow is perpendicular to this upwards flow. https://en.wikipedia.org/wiki/Jet_stream#Polar_jet_stream

Thunderstorm downdraft on Meal Fell

We were caught in a developing thunderstorm on Meal Fell. The winds suddenly rose to over 30mph out of nothing. Now I knew that thunderstorms are driven by convection. Hot air rises quickly. I assumed that the winds were caused by air rushing in from outside the area at ground level to fill the space. However it seems that downdrafts are the most likely cause. The initial rising air contains water vapour that condenses into big droplets that fall down. These droplets drag colder denser air with them. This rushing air pulls the surrounding air in to join it. This process is called entrainment and I am wondering if this is linked to the Bernoulli Effect. The mass of colder air rushing downwards results in the strong winds we experienced.

Helmholtz resonance: open car windows

In this heat wave, driving with an open car window has brought back that hammering noise you get when driving along. We thought it might be like the way water gulps when being poured from a bottle and air has to force its way in to fill the space. But apparently it is the same as blowing over the neck of a bottle that is part full of water to get a note. This is called Helmholtz resonance. https://jalopnik.com/why-do-slightly-opened-car-windows-make-that-awful-soun-1447498738

Cordierite in the Skiddaw metamorphic aureole

Amongst the rocks at the Roughten Gill bridge, you find these spotted stones.

I have learned a new word. I knew that the hornfels in which the cordierite appears is metamorphosed mudstone but the term for metamorphosed mudstones is PELITE. The crystal structure is interesting. It is made  up of a lattice of magnesium or iron atoms, then oxygen and then silicon and aluminium. There is a picture of the structure here https://en.wikipedia.org/wiki/Cordierite It would be good to link that with the stuff I've been learning about crystal structure in solid state physics. I was also interested that synthetic cordierite is used in catalytic converters.

Cordierite is

Safety switch on the hedge trimmer

My hedge trimmer has a system which means that both hands have to be firmly gripping the handle before it will cut. This is to stop me cutting my hand. I was surprised by how mechanical the system is. I had expected it to be based more on electrical contacts. My left hand pulls up on the switch shown in the bottom picture. The switch is actually a lever. The way it is pivoted suggests a "distance multiplier" - the distance moved by the tip is more than my hand moves. The top two pictures show the right hand lever. This just moves the handle closer to the red electrical switch. Both together means that the white plastic then depresses the switch and the hedge trimmer works.

RPM: lamb's chops on Whiteside

This ewe and lamb pair sat in the path with their mouths rotating as they chewed. The lamb was chewing almost twice as fast as the mother. I timed the lamb as 10 chew rotations in 5 seconds. That is 120 revolutions per minute. That means 240*pi radians in 60 seconds. That's 12.6 radians per second. I've always called this latter the "angular velocity" but I've seen it called "angular frequency" recently. Turns out that the former is a vector quantity and the latter is the magnitude https://en.wikipedia.org/wiki/Angular_frequency

Special relativity

I was listening to https://www.weltderphysik.de/mediathek/podcast/spezielle-relativitaetstheorie/ and it reminded me about the first time I really understood the reasoning behind special relativity. Einstein considered a mirror in a vehicle. If the vehicle is stationary, then light travels away from me at the speed of light, hits the mirror and comes back. When the car is moving, it becomes more problematic. Surely the light must have to travel faster than the accepted speed of light to overtake the car and reach the mirror. Einstein was aware that this would break the laws of electromagnetism as set out by James Clerk Maxwell. So perhaps the light wouldn't reach the mirror and you wouldn't be able to see the reflection. But this would mean that there would be a difference between sitting still and travelling at a constant speed, thus breaking Newton's First Law. To avoid breaking any laws of Physics, Einstein had to allow time to stretch and distances to shrink to bring the distance/time calculation back to the normal speed of light.

Hot rocks on Graystones

The rocks on the top of Graystones were warm to the touch during the recent hot spell. That suggests a rock temperature of say 30 degrees Celsius. The surface area of rock exposed was about 1 square metre. I will estimate the power of the sunlight at 1000 Watts per square metre as it will vary during the day and we are not square on to the Sun at this latitude. We can estimate the power of the black body radiation from the rock using Stefan's Law P = Stefan constant x area x (absolute temperature)^4 = 478 Watts per square metre. Supposing thermal equilibrium by this time of day (early afternoon) then the rock must be losing at a rate of about 500 Watts per square metre through other means such as thermal conduction through the rock and into the ground. I looked up a thermal conduction equation http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatcond.html I found a value for the thermal conductivity of slate as 1.16 W per square metre per degree Kelvin (we were on Skiddaw Slates) Supposing the soil beneath the rock was at 15 degrees Celsius, then for the rate of conduction to be 500W in my model, the depth of rock would be 3 cm. This seems too small.

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.