Hoar Frost

 

As far as I can tell, hoar frost is when water vapour in the air, what is a gaseous state, turns directly into a solid without passing through the liquid phase. This happens when the water vapour touches a cold surface. As this is the opposite of sublimation, which is when a solid is heated and turns straight into a gas without becoming a liquid, it is called desublimation. Rime ice is different because the water vapour turns into a supercooled liquid first before it then turns into a solid on hitting a cold surface. Rime is thus forms on the side of an object exposed to the wind. Now I need to find phase diagrams for H2O to show this.

Bicycle dynamo

 

I found an old bicycle of a type I used in the 80s. It had a dynamo. I used to love these because your batteries never ran out. The little black wheel on it is turned because it sits on the tyre. The turning black wheel is attached to a permanent magnet that spins inside a coil of wire. By Faraday's Law, this induces an EMF and the EMF causes a current to flow. The faster you pedal, the higher the EMF and thus the higher the current and the brighter the light. This is also covered by Faraday's Law which says that induced EMF is proportional to the rate of change of flux linkage. The flux of the magnet links the coils and this changes as it spins round. The faster it spins, the bigger the EMF. Disadvantage is that when you stop at traffic lights, your lights go out, and they are dimmer going uphill!

Sunshine on a globe

 This caught my eye lying abandoned on the verge.

On closer inspection, it turned out to be a globe.

It looks as though it is meant to stand upright with the Earth's axis tilted at the correct 23.5 degrees but discarded on a slope as it is, the axis is more like 40 degrees to the vertical. This led me to think about what would happen if the Earth had a bigger tilt. That would mean that a greater number of countries would have 24 hour sunshine in the summer and 24 darkness in the winter. The seasons would then be more pronounced. This had the best explanation.

Snowflake symmetry

 Mrs B has been making snowflakes as very effective window decorations. The process reminded me that symmetry is used a lot in physics to simplify problems. I came across the idea with tensors, where symmetry across the diagonal makes hideous calculations possible by eliminating a lot of possibilities.

Today I started with a square of paper.

I folded it into four.

This simplified things because I only needed to trim one quarter to make a whole circle.

I then folded it again.

Now I only needed to cut half shapes to get the effect I was looking for.

When opened the symmetry is revealed.

I tried again with a bigger piece of paper and twice as many folds.

I got twice as many patterns.

So using symmetry made it easy to make a very complex design, an analogue for physics computational short cuts.

Car light corona through the windscreen

 We were sat waiting in the car on a rainy day. I noticed that the bright white headlights (or maybe they were LED sidelights) were giving a wonderful diffraction corona.

It proved very difficult to photograph. I think one thing is that I was holding the camera too low. The diffraction depends a lot of droplet size and that was probably variable across the windscreen. It must have been optimal at eye height!

Like Clockwork

We loved this amazing game. You wind up Santa and the reindeer and they are released at the same time. The winner is the one who gets to the middle first.

We were wondering whether anyone will know what clockwork is in the future. Winding the mechanism fills the elastic energy store of the spring by the mechanical working pathway. As the spring unwinds, it itself does mechanical work to turn a crank that turns the legs, filling their kinetic energy store. There must be something eccentric on the crank to make the feet go round in a full circle, probably something like the pedals on a bicycle but driven by the spring. Like pedals so that when one is up, the other is down.

 

The Geminids

 

I saw a shooting star tonight and it was coming from the Gemini direction although all accounts suggest it really should be too late. There is a nice picture here. Researching the Geminids, I was interested to discover that there are some close in asteroids whose orbits cross that of the Earth. I thought all the asteroids were in the asteroid belt. 

Azimuth

 

Azimuth is an installation on the sea front at Eastbourne. I knew that azimuth is to do with where the stars are in the sky but I had never bothered to learn the definition. In the polar coordinate system, you have an angle round and an angle up, as well as a distance out from the centre. Azimuth is essentially the angle round in the horizontal plane.

Kurzfristenenergieversorgungssicherungsmassnahmenverordnung

 

We really enjoyed seeing Harry Baker last week as he's another enthusiast for maths and German. He comments on the way words are put together to make long compound words, and my friend sent me this from a letter sent out whilst such advice was frowned upon here. The very long word means "short-term energy supply security regulation" and suggests that reducing the thermostat temperature by 1oC will reduce your energy consumption by 6%. This thread explains that the 6% depends on the temperature outside. I like the idea that if the thermostat is 21oC but outside is 20oC then reducing by 1oC will basically save 100%! the 6% must be based on local averages.

An odd scale on the radio

 

It was nice to see the sort of radio dial I was used to as a child. In those days, VHF used to be synonymous with FM. It's true that VHF has frequencies that are 1000x those of medium wave, but the main difference is the modulation method. Medium and Long Wave were both AM (amplitude modulation), where the height of the wave is changed to carry the signal. FM is where the frequency is shifted up and down around the carrier frequency to encode the sound. The LOG SCALE  label is confusing. Log would mean that each mark would be, say, 10x more than the last mark but for the scales above, that is clearly not the case. Looks linear to me.

Calculating the cost of Christmas lights

 

I saw a claim in a supermarket advertising magazine that a 1000 LED fairy light array would only cost 44p for the whole of December. The small print clarified that it is 6 hours a day and a Unit cost of 34p as a basis for the calculation. 44p/34p = 1.3kWh used. 31 days x 6 hours = 186 hours. That means power of the array = 1300Wh/186h =7W. For 1000 LEDs, that's 7mW each. Using data from here, a white LED running on about 3V would draw 20mA and have a power of 60mW. But if these are really dropping 230V across 1000 in series, each would get 0.23V. That would be below the threshold for most diodes and they shouldn't light. The LEDs would need to have roughly 75 groups of 12 wired, with each 12 in parallel, to get the desired voltage. This needs some thinking.

How many stones were there in Hadrian's Wall?

 

We were musing on the amount of effort that went into building the wall. All the stones are cut by hand, unlike the later drystone walls. We decided to attempt the calculation of the number of stones as a Fermi question, using data to hand and reasoned estimates. I couldn't tell whether the middle was made of cut stones or filled with rubble. My poles in the picture are 1.3m long and contain about 35 stones. That's 70 counting the other side. But the wall was said to be 4m high by Bede who would have seen it only a couple of centuries after it was abandoned. That's a factor of 3 higher so that gives us 210 stones in 1.3 metres. It was 73 miles long which is 117km. There are 90000 x 1.3m sections giving nearly 20 million stones. However, some say only 3/5 was ever in stone bringing it down closer to 10 million. This says it was built by 15000 people in 6 years. That's just over 100 stones per person per year. Sounds well within reason.

Overhead Fibre in Aikton

 

I was surprised to find this notice on the telegraph poles in Aikton. That's because I spent so long in the city where fibre is always underground cables. Turns out that in rural areas, using the existing overhead infrastructure is a good option. I found this site. Disadvantages are storm damage and the stretching forces on the fibre cables that come from being hung. Some cables are made strong enough to support themselves and some are hung from supporting wires.

Most sensitive solar cell

 It was sunset tonight: you can see the Belt of Venus on the horizon. The chef solar-powered kinetic toy was still going but the ladybird and a third toy had long since stopped.

I would say that the ladybird's panel is angled more towards the light. Maybe it is not to do with the amount of light coming in but to do with the mechanics of the mechanism. Need to think of a way to test that!

Imaging analogy on Hadrian's Wall

 

In Physics, the internal workings of something are often detected by firing waves through and then processing the image on the far side to work out what was inside. I was looking at the shadow of the low December sun on Steel Rigg. It shows where the land rises and falls but we could work out the true proportions of the land from just the shadow if we knew the angle of the sunlight.

Stationary wave on a distraction toy

 

I was given this piece of elastic at a meeting as one of those fidget toys to occupy my hands. I spent the meeting making stationary waves. At the right frequency, the outgoing wave interferes constructively with the reflected wave making a pattern when the maximum point or anti-node stays in the same place. The fundamental was easy. The first overtone or second harmonic, with two loops, was possible but much harder and very unpredictable.

Mystery metal

 

We found this piece of metal whilst on a beach clean at Crosscanonby. It looks superficially like aluminium but is heavy so I decided to try to identify it by density. Mass shown above. Dimensions are 12.6 cm x 1.9 cm x 0.45 cm which gives a density of 8.6 g/cm^3. That could be cadmium but cadmium is soft and this isn't. Best guess is that it is some kind of alloy.

Brocken Spectre and Glory on Longlands Fell

 

Only the second occasion I've ever seen this. Apparently the theory of how the Glory forms is more complicated than I thought. This article starts talking about complex angular momentum of light. I can't find much that isn't research papers on this but did find just angular momentum of light to think about.

William Brownrigg: Cumbrian scientist I'd never heard of

 

I've been reading this wonderful but very detailed history of Crosthwaite Parish, Keswick. There are some gems of information that I didn't know. One is mention of William Brownrigg meeting Benjamin Franklin. Brownrigg is credited as being the first person to recognise that platinum is a separate element.