This week's Covid data

 This week's ONS data shows that up to a week ago, Covid levels in the population in England are still rising. Are the last 3 points on my log graph in a straight line, meaning exponential growth, albeit at a slower level than before?

The actual reported cases have fallen in the same time frame. This may be because the Euros are behind us and some schools had broken up in that time frame. It could also be a product of the amount of self-isolation that is going on or it could be because herd-immunity is close.

Danger: commuting adders

 

Here is a Network Rail sign at Seascale station. The adders might be a danger to commuters. As quantum physics is based on the fact that not every object is commutative under multiplication, were there any examples in which addition does not commute? Normally 3x2 = 2x3 but with matrices that need not be true under multiplication. But surely it is always true that 3+2 = 2+3. This must also work with matrices. It is clearly a question that other people are asking. I don't understand group theory well enough to fully understand this discussion.

Models of the atom at Seascale

 

The John Dalton way is marked by a symbol based on the Solar System model of the atom. Dalton is credited with cementing the modern idea of the atom. Since his day there have been many different models. I'm fond of the Plum Pudding model because it's an excuse to heat up some Christmas Pudding. The Solar System model is the easiest to picture and I like it for that reason. True ideas based on Bohr and Quantum Theory are exciting but hard to visualise and draw!

Single slit pattern with a laser

 I used a pin to scratch a narrow slit onto a microscope slide that had been painted black with Aquadag.

The laser was shone at the gap and the slide was 3 metres from the screen. The pattern above shows the wide, bright middle strip, a dark minimum band then fainter narrower side bands in a repeating pattern that gets fainter.

Wonderful Walker commemorated by a sundial

The curate of Seathwaite in the Duddon the 18th Century, immortalised as Wonderful Walker by William Wordsworth, is commemorated with this sundial by the church door. It is stuck on to a stone he allegedly used for shearing sheep, a job he did to bolster his stipend. It's a very physics thing, I think, to have a memorial sundial. We called by at nearly noon BST. That means 11am GMT, and it is the latter that is shown by the sundial. The door of the church is on the south side. As you go in, the sanctuary is on your right, the east side, the direction of the Holy Land. So I can tell that the sundial is correctly aligned.
 

Why a driven flock of sheep is like a liquid

They were clipping the sheep on Turner Hall Farm and the shorn sheep were then herded back to the fields. It struck me that they would make a great allegory for particles in a liquid. They are packed close together but not joined. The shape of the whole changes as they move. You could also say that the sheep dogs applying pressure to make them condense into the close-packed liquid state.
 

This week's Covid data

 The ONS survey data is always a week behind. This week it shows a slowing of the growth in cases, though this is one data point. My model would give the 7-day R number as 1.22. I haven't redrawn the line on the graph yet -  more data needed to show it is not just an anomaly.

Here is the graph for the actual reported cases for the same period - a week ago. The rise was "on trend". The R number for case growth figures was 1.34. Reported case numbers have fallen since then. It will be interesting to see if next week's ONS data backs that up.

How tall is the cumulus?

 

Harter Fell in the distance is 650m above sea level so 4 fingers are probably worth 500m. The tall cumulus subtends twice as many fingers so would be worth 1000m if it were the same distance away as Harter Fell. I think it was further away so would be taller. I think that they can be up to 2000m high so that's not a bad estimate.

Back to Seathwaite Tarn copper mine

 

We visited the upper level of Seathwaite Tarn copper mine. The spoil heap was mostly quartz. I found this paper about the mineralisation at the site. Apparently the adit that can no longer be seen here went in 100 fathoms. A fathom is 6 feet or 1.8 metres so the tunnel was 180 metres long. The copper minerals formed in veins of quartz, hence the spoil. I've known for a while that mineral veins form when faults in the rock caused by earth movements fill up with very hot mineral-rich fluid which crystalises out. If I've read it right, then quartz formed first in the faults. Then more earth movements fractured the quartz and the copper minerals formed in those cracks. Here the copper mineral also contained bismuth but I'm going to need to improve my chemistry to understand fully.

Sunset diffraction patterns

 Here's what sunset over Harter Fell looked like through tent fabric. It suggests maybe 3 weave directions.

The mosquito net produced this. I was expecting a cross like a net curtain so will need to look at the mesh or consider whether an oblique angle affects it.

This week's Covid report

 Friday is the day that the ONS data is reported. I have also updated the government's 7 day rolling average for new cases. Both Log graphs show the same trend so the R-values are the same as last week.

Anti-static gloves at a petrol station

 

Plastic gloves have become ubiquitous at petrol stations in the last 18 months. I assumed it was to do with Covid but it turns out they are supposed to stop static electricity producing sparks that ignite petrol vapour. I am still wondering how it works. My first theory was that they conduct electricity better than normal plastic to allow built up charge to flow away. I measured the resistance of a bag - see below - and the resistance was off the scale even with the clips close together. So that can't be the answer.

Looking at the reported daily Covid cases

 

I have previously only used Office for National Statistics survey data as this is randomised and doesn't rely on people reporting for tests. However, I decided to look at the reported daily cases for the same time frame as yesterday's post about ONS data. I got the data from https://coronavirus.data.gov.uk/details/cases. My time frame is two days out. The trend is clearly linear so the reported cases are rising exponentially. I tried hard to see the same change in gradient but I'm not convinced. If ONS is correct, it suggests that reported cases are slightly too low. The reported cases with a gradient of 0.0581 give R=1.37 in my model. If it continues to grow at this rate, it will reach 100,000 a day by the end of the month.

Another look at the Covid data

 

I have been following the Office for National Statistics weekly survey data for a year now. Last year I watched the number of deaths come down as a straight line on a log graph. Now I've chosen to take the natural logarithm of the ONS estimated number of cases in England each week. The graph above shows the data for the last 5 weeks. My model gives the gradient as being (R-1)/6.4 where 6.4 is the number of days between you catching Covid and the person you give it to catching Covid. I worked out that number in January from data in the New Scientist magazine. R is the famous R-number or reproduction rate. The red section of the line for the first half of June has gradient roughly 0.35/21 and therefore gives R=1.1. For the last two weeks, gradient is roughly 1/14 and gives R=1.46. 

Crater Lake in the Lake District?

 I found these interesting striped rocks just below Combe Door on Glaramara.

They reminded me of these rocks I found in Adam-a-Cove on Crinkle Crags.

I know that the rocks in these parts were supposed to have been laid down as sediments of volcanic ash at the bottom of a lake in a caldera. So how big was the lake? On the map, there is exactly 4 miles between the sites. That would be heading for the size of Crater Lake in Oregon. The caldera on Mount Teide on Tenerife is 7 - 12 miles.

Glaramara via Combe Gill: not a steep enough angle

 Combe Gill is the dark straight line of a ravine in the middle on the picture. In this view, it looks almost vertical. Being north facing, it seemed a good bet to be in the shade on the hottest day of the year.

It is very steep but at 12 contours per cm on the map, it's about 25 degrees. We were in baking sunshine all the way because the Sun is so high in the sky in mid summer. 

I checked for the angle of the Sun and found this. OK, we've a long way north of London but it is clear the angle of the Sun at noon will only be low enough to put Combe Gill in shade in the winter months. Unfortunately it means that shade on a north facing slope in mid summer will only be on cliffs.

40 degrees on Maiden Moor

 

We climbed Maiden Moor up Ellers Beck and Greenup. It was as steep as anything we've been up so I have been counting the contours on the map. In the section shown, I counted 15 contours in 1cm. That's an angle of 30 degrees. But it got steeper. I counted 7 contours in 3mm which comes in at nearly 40 degrees. I'd always thought 45 degrees was the steepest we'd climbed but that seems unlikely. 30 degrees now seems to be the steepest normal slope.

Why do wind turbines all turn clockwise?

 

It was only a couple of days ago that I woke up to the fact that all wind turbines turn clockwise. This suggests that it is probably an historical quirk. I don't think those who say the rotating blades give lift are correct. Propellers on a plane pull the plane forwards to create an airflow over the wings, the shape of which generate the lift. This site suggests that early Danish wind turbines turned anti-clockwise but includes some stuff about yaw and furling that I will have to look up.

Climbing rope

 

I managed to get to see the data on a climbing rope. I take it 9.8mm means the diameter which would mean a cross-sectional area of 7.5 x 10^-5 square metres. This suggests that for static elongation a standard 80kg load is applied (ie sort of a human). Stress = F/A = 10 million N/m^2 approx. If strain is 8% for this, Young Modulus = stress/strain = 130 million N/m^2.

So it's not a UFO, then.

Last night there was a sundog visible. You can see it as the bright coloured bit to the right of the Sun in the centre of the picture. It reminded me to put one of my favourite newspaper articles back on the wall of the lab. The purported UFO circles in the bottom right hand picture is actually a sundog. I was really pleased to meet the actual broken blade in person when I went to climb the wind turbine in Swaffham.