Copt Howe Cup and Ring markings: circles and ellipses

 This boulder in Langdale has rock art on it from perhaps 5000 years ago called "cup and ring" markings.

On inspection, the circles looked perfect. I'm impressed and was wondering how they were able to do this. Chalk on a string method perhaps??

Today I tried measuring the circles on the photographs and found that they have a bigger diameter horizontally than vertically. Now is this because of the angle of the photograph? Next time I'll take a ruler with me but I think it will be easy enough to test if viewing a circle from an angle distorts the perception of circle. I was interested if a circle like this is actually an ellipse and wondered if the ratio of perpendicular diameters gave the eccentricity. Sadly not: the formula for the eccentricity of an ellipse requires knowing the position of the foci. See this

Testing my hypothesis about the protactinium generator

 I was asked about why the protactinium produced by the decay of uranyl nitrate ends up in the organic layer. Protactinium is not soluble in water - well, at least the isotope produced in this decay chain is not. So in a way, it must precipitate out on an atomic scale. I wondered if these atoms just got picked up by the organic layer on shaking because it "sticks" to the solvent in some kind of surface tension effect. I came up with an analogue experiment. I put sand into water - it doesn't dissolve. I added a layer of oil.

Then I gave it a big shake...

Looks like it all sank to the bottom again so no evidence to support my theory here!

Parabolic reflector? Ring Ouzel song perch

 

I found a Ring Ouzel singing. It sounded close and clear but was actually most of the way up this photograph. It was using a tier of crags like a reflector to project the song. Perhaps he was at the focal point like the bulb in an old-fashioned car headlight sits at the focal point of a parabolic reflector so it can project a forward beam. Perhaps this now explains why singing Ring Ouzels always seem to be so high up. I wonder if this is a common behaviour with them.

Milli moles in the tablets

 

A mole is an old idea for the quantity of a substance that dates back before we could detect individual atoms. Then the idea was that if you got a very large number of atoms together, they could be weighed. The difference in mass between different substances would then become apparent. Now this is understood as being linked to the atomic mass number and thus the number of protons and neutrons. It has been fixed so that the atomic mass number in grams is the mass of 1 mole of the substance. Now the atomic mass number of sodium is 23 grams so that is the mass of 1 mole. A milli mole is one thousandth of a mole so would have a mass of 23 milli grams which is as on the notes.

An energy explanation for why waves slow down

 

It occurred to me that as a wave approaches the coast, it starts to get taller. I think that this is because the water is shallower so there is les space beneath the surface for the wave motion. Now the fact that the water has been pushed up higher means that it has more gravitational potential energy. This energy has to come from somewhere. The total energy of the wave will remain the same if it is a closed system. This means that the energy must come from the wave's kinetic energy. With less kinetic energy, the wave slows down.

Tree rings at Campfield Marsh

 This bog oak is at Campfield Marsh RSPB.

The tree rings are much closer together than yesterday's post. It has occurred to me since that if the stump on the beach had been in the sea, it might have expanded and that could have made the tree rings wider. It might be true that being in a bog for thousands of years could have shrunk the rings. Anyway, I was able to count up to about 100 rings again. 7000 years ago was during the Atlantic Period which was a warm and wet period. You'd expect that to encourage growth so perhaps wider rings. That needs checking.

Counting tree rings on the beach

This large, partly-burnt stump on the beach at the Merthyr Mawr end posed a challenge. The tree rings were very obvious but very far apart. The question is then whether the sea has eroded some of the intervening rings. Wide rings would be evidence of strong growth. I think that means good climate. I had a go at counting what I could see and estimate that 100 years would be a reasonable age if the rings are true. The other way of estimating the age is by girth. This source suggests a 100 year old tree might have a girth of 3m. It does give some provisos. 3m girth would mean a diameter of about 1m which is probably not far off given the burnt section. It suggests that no rings are missing.
 

Evidence of an anticline in the Black Rocks formation

 After I found the conglomerate from yesterday's post, I walked along the beach and took this picture looking back at where I'd been. Notice that the rocks are slightly tilted and angled up.

That means that the conglomerate must have been on the top of the tilted pile of rocks. These layers in the foreground are older and must be Carboniferous limestone. Then I went further along the beach and noticed that the rocks where tilted the other way. The photograph was taken facing the same way.

I can only conclude that there must have been a peak somewhere between the two photographs with the layers going up one side and down the other. Such a wave peak in folded rocks is called an anticline. It meant that now as I went further along the beach, the rocks stopped getting older and started getting younger.

Triassic conglomerate at Black Rocks near Porthcawl

 Walking along the beach from Newton towards Merthyr Mawr I found this rock that looks amazingly like concrete in the Black Rocks formation on the beach.

This map confirmed that it is Triassic. I then found this walk leaflet that explains what happened, even though the walk described is in the other direction from Porthcawl. It seems that Carboniferous limestones were eroded and washed down with sand to form a conglomerate. A similar thing happened in the Eden Valley up here. The pebbles seem quite rounded so must have been transported some distance.

VHF in Porthcawl

 

When I was a child, I was familiar with the letters VHF. Very High Frequency was what the better signal that Radio 1 shared with Radio 2 was called. It is now called FM. VHF and FM refer to different properties. FM is how the wave is changed to carry the coding for the sound. With Frequency Modulation (FM) it is the frequency that is varied slightly to encode the programme. This is a more accurate description of that radio than VHF, which just refers to a band of EM waves from 30 to 300MHz. Now channel 16 is the international distress channel (see this). It turns out that marine radio is FM. There is Amplitude Modulation (AM) VHF but that is for aviation.

Making the fuel go further

 

A couple of weeks ago The Guardian published some tips on coping with the soaring petrol prices. One suggestion was to stop driving at 80mph on the motorway but drive at 70mph instead, making a 20% saving. That's no use to me: it's illegal to drive at 80mph so I don't. But I was interested in where the statistic came from. I was going to do a full calculation based on the drag equation but then it occurred to me that when comparing between two speeds, the other terms should be the same and I just need to consider speed. I am, of course, assuming that all fuel consumption is proportional to drag. Drag is proportional to speed-squared. So I did 80^2/70^2 and got 1.31 so the fuel use at 80mph would be 1.31x higher than that at 70mph. So isn't it a 30% reduction? I normally do percentage difference as difference/true answer. In this case it might be (80^2-70^2)/80^2 = 23%, being 23% of what it WAS at 80mph. That's probably where the figure came from. Now trying a reduction from 70mph to 60mph, I get a 27% reduction! But I remember from the oil shock of the 1970s that 55mph is said to be the most fuel efficient speed. This site gives some figures to consider.

Rigs of Nigg

 

There's a wonderful programme on the engineering and social challenges of the oil rig production at Nigg available until August https://www.bbc.co.uk/iplayer/episode/m000yybp/rigs-of-nigg

Calculating the percentage yield for carbon dioxide

 I surprised myself by working out a fairly obvious way of working out percentage yield in a chemical reaction. We weighed out 2 grams of marble chips and added 40 cubic centimetres of 1M hydrochloric acid. The reaction produces carbon dioxide so we weighed the whole conical flask at the start and then at the end. It had got lighter because the carbon dioxide escapes into the air. 

By using relative formula mass we could calculate the expected mass of carbon dioxide and compare it with the actual mass, thus allowing percentage yield to be calculated.