A rainbow that ends in the sea at Silloth

 

It was a good afternoon for rainbows with strong sunlight between showers. This one at Silloth ended in the sea, so with no boat, I had no chance of finding the treasure. However, it shows that the water has to be in droplet form to produce a rainbow. It is the boundary between the water and surrounding air that causes the refraction and total internal reflection combination. In the sea, there are no such boundaries so the rainbow ends at the sea's surface, even though it is water in the air that produces the rainbow.

Using an ecclesiastical candle snuffer on my birthday cake

In these Covid days, we decided blowing out the candles might be deemed risky so I was handed an ecclesiastical candle snuffer. It's an open system in that air can move freely in and out of the bottom if the cone if it wants to, so why does the candle go out? The candle's combustion reaction turns oxygen into carbon dioxide. This is warmer than the air outside due to combustion so it tries to rise upwards. A normal fire has a chimney so it can escape upwards and draw colder oxygen-rich air in at the base. That can't happen here because the rising air is trapped. It's pressure must be such that air cannot move up. Since it is warmer, it is also likely to have a higher pressure as well which in theory would tend to drive some of it downwards. Not sure if it really is hot enough for that.
 

Brian Cox is back

 The new Brian Cox series on the Universe is on the BBC iplayer https://www.bbc.co.uk/iplayer/episode/p09ybpb8/universe-series-1-1-the-sun-god-star I have watched this first episode and picked up some new ideas. I hadn't heard about the dark matter cosmic web but it makes sense as I knew that dark matter was supposed to be where the galaxies condense. I'd also managed to miss the Parker Solar Probe. 

Sediment in my wine and the Cumbrian floods

 Last week I blogged about sediment and linked to a paper on the historic flooding record as shown in the sediments in Bassenthwaite Lake. Having told my class about sediment in wine, I found some at the weekend.

Since then it has rained non-stop in Cumbria. I found this tweet yesterday. His mention of the sediment plume will be one way that events like today will show up in the record in decades and centuries to come.

Figuring out Dry Tarn - Maxwell-Boltzmann

 

I think I have thought of a solution to my question about Dry Tarn. The Maxwell-Boltzmann distribution for a constant temperature is above. Particles with high speed will have enough kinetic energy to escape from the tarn by evaporation. But that means the internal energy falls and the temperature goes down. My realisation is that there is plenty of time for thermal energy to cross the system boundary from the surroundings and bring the tarn water back up to the same temperature. This means that if there is some evaporation at a given temperature because some particles have enough energy to escape, that will always continue to be the case because of the heat from the surroundings. I should add that the evaporative cooling will mean the tarn water is at a lower temperature than the surroundings so thermal energy will flow from the surroundings into the tarn until equilibrium is reached.

Dry Tarn: some questions about evaporation and latent heat

 

We found the elusive Dry Tarn on Great Gable. It is easier to see coming down than going up because of the way it sits. I was going to calculate the energy needed to make it evaporate using the specific latent heat equation I am teaching my classes but I've realised there's a problem. In the simplified world of GCSE Physics, we calculate the energy required to raise the temperature to boiling point and then the energy to change state. The problem here is that the water evaporates without ever getting close to boiling point. This gave me some clues. I've blogged about boiling point on Great End and it is very close to that at sea level. Dry Tarn evaporates when it is dry for long periods. That must mean when the humidity is very low. Even so, saying that the most energetic particles can escape when if you wait long enough, they all escape ... is this going to be a probability problem in the end?

Trying to repeat the Karman Line calculations

 I decided to have a look at what Karman did in his calculations to find the edge of outer space. I used the equation for lift L=1/2 rho.S.v^2.C(L) were rho is air density, S is the wing area, v is speed and C(L) is the lift coefficient. Karman used the Bell X-2 so I got data from here. I got the air density vs altitude from here and speed of sound vs altitude from here.

I simplified it by assuming half full fuel tank for mass. I have no idea about lift coefficient so I fixed it by noting that the plane reached Mach 3 at about 20000m. That needs C(L) = 0.1. However, C(L) is probably not constant throughout. The aim was that v calculated is the speed needed to achieve aerodynamic lift. Karman then factored in whether or not the aircraft was overheating. For me, this was just an exercise to start to play with the numbers. If it is anything near valid, the speeds become phenomenal. 

Where does space start? Looking for The Final Frontier

 I've always loved the original Star Trek series but as you'll see from my poster, Captain Kirk wasn't my favourite.

However the news of William Shatner's trip into space this week had us asking the question "where does space start?". It turns out that it is probably governed by the Karman Line. To summarise, the lift generated over the wings of a plane is directly proportional to the density of the air but also to the square of the speed. The higher in the atmosphere you go, the less dense so to generate the same lift, you have to go faster. But faster means more heating due to air resistance. Theodore von Karman wrote a paper in 1956 in which he did the maths on this and discovered that somewhere over 80km up, a plane would overheat trying to generate enough lift. Above that height going that fast would put you into orbit. Now there seem to be two definitions. The Americans reckon space starts 80km up and the international view seems to be 100km. Space starts somewhere. 

Sedimentation and flooding events

 I took a bottle of water, added some sand and gave it a shake. The biggest particles of sand fell to the bottom immediately.

After a week, even the smallest particles had settled.

I was tipped off about this paper. It's an important one because it can help us to be sure that the climate is changing and that extreme weather events are becoming more common. Our problem is lack of weather records from beyond a couple of centuries back. The researchers were trying to find out how extreme flooding events can be traced in the sediment laid down on the bottom of Bassenthwaite Lake. One figure suggests that sediment settles at about 1cm a year. I'm still reading the paper so there'll be more on this.

Lateral moraine on the Walna Scar Road

Thanks to Keith for pointing out this band of boulders that sits like a tide line across the Walna Scar Road above Seathwaite in the Duddon. It runs north towards the reservoir road and south towards Stickle Pike. The boulders are large and quite rounded which would suggest they have had a bashing. Rocks dropped from crags would be more jagged, and anyway there are no crags in the vicinity. This looks likely to be boulders deposited from the side of the local glacier as it retreated.
 

More on FSD and resolution

 These two voltmeter readings show how changing the FSD on the scale alters the resolution of the instrument and thus the precision of the reading. In the first picture the FSD is 200V so the resolution is +-0.1V.

But a reading of 7.9V will also fit on the FSD 20V scale. This time the resolution is +-0.01V so the reading is more precise (to more decimal places). Interestingly 7.99V should surely round up to 8.0V. I'll need to consider if there is an obvious reason for this not working out.

The FSD 2000mV scale would give even more decimal places but 2000mV is 2V so we would be off the scale and get no reading.

Choosing the correct FSD

 Having been brought up in the age of analogue meters, I still refer to the maximum reading on a scale as the FULL SCALE DEFLECTION FSD. We were measuring the current through a resistor and got this reading. 1 significant figure is not good.

I changed to a FSD of 200mA and was rewarded with 3sf. The resolution was +-0.1mA.

To get a better resolution I could try the next FSD of 20mA. This should give more decimal places. Unfortunately FSD means the highest reading possible on the scale and since the reading was higher than 20mA, I got the display that means "off the scale".

Turning Points in Physics

 

This installation in the park at Ambleside reminded me of when I taught the Turning Points in Physics module in the NEAB A Level specification in the late 90s. It included the discovery of the electron, quantum physics, special relativity and low temperature physics. The quantum theory has since become part of the main AQA syallabus. The current content is here. It has changed a bit since NEAB became AQA. No low temperature physics anymore. Why turning points? I suppose that physics really did change direction in terms of its focus with relativity and quantum theory. I suppose I've always thought of each discovery as a threshold to a new world of thought - a kind of forward motion rather than a turn. Interesting to reconsider.

Logistic equation graphs

 I found my model of the logistic equation and changed the factor r. This is r = 2.6. It settles quickly to a steady population.

Then I went for r=3.0. Now we clearly have oscillation between two population sizes.

Now r=3.5. There are 4 population sizes in the oscillation. We have passed another bifurcation point.

By r=3.9 there is no repeating pattern.

My numbers don't quite match those in the book I looked at but I've noticed that I started with x=0.1 and they started at x=0.2. I wonder if that makes a difference.

Bifurcation on Bright Beck

 Bright Beck runs down into Stickle Tarn from behind Pavey Arc. Its ravine looks like an eroded fault or dyke. Near the top, the ravine splits as pictured by Wainwright in High Raise 4 - a bifurcation.

I haven't looked at bifurcation theory for years but in honour of the Nobel Prize for complexity, here goes. This theory is based on the work of Verhuist, a Belgian mathematician who in the 1840s used negative feedback to stabilise the explosive population growth of Malthus's theory. The equation he came up with is now called the logistic equation. It links the population in one generation with the population in the generation before. If x is the population size, xnext = rx(1-x). In the 1970s, Robert May found that if r=2.6, he got a stable population but above that population oscillation happens, initially between two different population sizes that swap from generation to generation predictably. This change in behaviour from one population size to two is the bifurcation. 

Nobel Prize for Physics 2021

 The Nobel Prize was announced today https://www.bbc.co.uk/news/science-environment-58790160 It's great to hear that complex systems are being recognised again. When I started my career, Chaos Theory was in vogue but it has never made it onto the curriculum unlike newer discoveries like Dark Energy. 

Solar glass: waving at my own reflection

 We found ourselves driving past the building on the way to Bridlington where we used to wave at our own reflections from the coach.

Now I suspect that the glass is so reflective because it is south facing and has been treated with a coating to stop the occupants overheating as though they are in a greenhouse whilst letting in plenty of light. They seem to call it Solar Control Glass. I couldn't find details on the specifics of the coating but I did discover info about what are called G values for glass. This is the fraction of the heat from the Sun that is transmitted through the glass and into the building. I am familiar with U-values for insulation but I've not come across that before. Click here for my source of information and here for some typical values if you scroll down. I'm guessing smaller G-value is better in this context.

A different type of arcing protection for pylons

 I've posted before about arcing horns on pylons: http://wigtonphysics.blogspot.com/2015/03/arcing-horns-in-manchester.html I saw this on the way to Bridlington

Not horns as such but almost circles - like the Iron Age torc ornaments. I was wondering how the change in design might affect it. I've drawn field lines in green on the right hand set and there will be parallel fields lines all the way round so there will be a uniform field all round insulator. That will allow arcing for problems on any side of the insulator.

Looking for the Pavey Arc Member

 I've always loved these volcanic rocks on the top of Pavey Arc. There seem to be huge lumps encased in volcanic ash. 

I'm trying to learn the vocabulary and to understand what went on to form them. In this wonderful document there a diagram on page 5 which shows the "Pavey Arc Member". Page 4 also has what I've been looking for: a map that shows the extent of the Scafell Caldera. It's even bigger than I'd suspected. So I'm guessing that my rock might well be the Pavey Arc Member. I'm inferring that the rock is particles from an explosion that flowed into the caldera lake along with ash so they are sedimentary in a sense. The document calls the rock a "breccia". Now I'd only understood that to refer to rocks shattered on fault lines and cemented by solidifying solutions but it does seem to mean any rock made of large fragments in a matrix of small particles. https://en.wikipedia.org/wiki/Breccia I also looked up "clasts" and found that this is not just to do with volcanic rocks but also sedimentary https://en.wikipedia.org/wiki/Clastic_rock

The bin bag capacitor

 

I made a capacitor out of two sheets of kitchen foil with a bin bag in between. I connected it up to several thousand volts (but VERY low current!). The two sheets attract each other. If the bin bag is cheap enough, breakdown occurs and there is a loud crack and spark, punching a hole through both foil and plastic. The breakdown voltage was about 2000V.