I missed the Aurora again!

Have you seen the photographs on the BBC? http://www.bbc.co.uk/news/uk-26378027 It must have been amazing. Sadly I only found my Aurora Watch email this morning, and then again they only gave an Amber Alert! I suppose the problem is that you can never be sure even if you stay up all night and also that every good alert here seems to have come in cloudy conditions. You can sign up on the Aurora Watch website. I've met the people at Lancaster University who run it. Try Googling it.

Upper Sixth Estimation Question #2

Here's a picture of me on the swing at Whinlatter. What I want you to do is to estimate the tension in one of the supports as I swing through the equilibrium position. Remember that circular motion makes the tension bigger than it would be at rest. You'll need to use simple harmonic motion to work out my speed as I swung through equilibrium first.

Heat radiation on my hot cross buns

 

We are still a week away from the start of Lent but here I am with hot cross buns. Not very traditional - I'm supposed to wait until Good Friday but they've been on sale since Christmas! You can see the heating element on my grill in the photograph. The grill is above the buns so it can't be heating by convection because this is when air heats up, expands and rises. It transfers thermal energy up not down. It could be conduction because that can transfer thermal energy in any direction. However there is air between the heating element and the buns. Air is a good insulator because the molecules are far apart and not joined. They cannot pass on the vibration very easily. In that sense, air is an insulator. So thermal energy must be being transferred by heat radiation. This is in the form of infra-red electromagnetic waves, a type of invisible light. This travels quickly, at the speed of light. It feels warm on our skin because we have receptors cells that detect it. But don't leave your hand under the grill. Heat radiation can burn your hand as well as it will burn toast!

The aeroplanes were closer in Edinburgh

The campsite in Edinburgh was underneath the flight path for the airport. Given that I had to fit the camera in between my face and my little finger, let's say that my little finger is worth 1.5 degrees. So the plane subtends 3 degrees of my vision, which is 3/360 x 2pi = 0.05 radians. If the plane is 60 metres long it is 60/0.05 = 1200m away. Still 1km away but we were at least that distance from the airport itself.

Wind carved snow on Grisedale Pike

 

These features look related to the flutings described by Joe Simpson in his book Touching The Void. In the second picture there is a stone at the far end of the snow ridge. I was wondering whether a uniform blanket of snow fell and then the wind removed sections that weren't sheltered. I find it more likely that the snow was being fired in at speed by the wind and built up in sheltered areas. If that's the case then it will be like diffraction round objects. The wind would be being into the space behind the stone but have less energy and so deposit snow.

Glenridding Hydro

 

We walked up to Red Tarn to get to the snow. We passed the hydro-electric scheme at the old mine above Glenridding. The mine used a lot of water power in its day so this is fitting. http://www.british-hydro.org/installations/g/glenridding_hydro.html This source says that it is a 500 kW scheme that has been going for over 20 years. Oddly I don't remember noticing it before. It powers over 300 homes. I can't find details of exactly where the turbines are but it looks to me as though the concrete weir acts to create a deep pool with a constant head. This then feeds the blue pipe shown. I imagine that this takes the water downhill to a generator hall below. In the Coniston scheme about which I blogged six weeks ago, the generators were half a mile below the weir. This scheme is small and does not seem to affect the environment around - although that has been badly scarred by lead mining.

The length of the coastline from Cramond Island

 

We walked out onto Cramond Island on the outskirts of Edinburgh. It was a calm day and the views were fantastic. It reminded me of an important question in Physics: How long is the coastline of the UK? According to a recent edition of Physics World magazine, this started with a piece of research by a pacifist who wanted to show that there was a proportionality between the length of a country's borders and the likelihood of war. But the problem is one of what do you measure and when do you measure it? If you stop to measure round every stone the length goes up and up. And the distance changes as the tide changes. In fact, you get a distance that tends towards a huge number (not infinite as far as I know) but with an area that is finite. That is, if you stop to measure round every grain of sand. This research was one of the early works that led to fractal geometry that is itself key to Chaos Theory. A straight line has one dimension and a flat plane has two dimensions. In some sense the wiggly coastline has a dimension in between, some fraction of a dimension, hence fractal.