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.

Heel strike

 

I suffer pain in my knees coming down hill. The problem is the force on my heel transferring its way up my leg. This is called heel strike. It's a problem on the way down because I'm moving faster. I have the same mass but greater speed means more momentum. There is a bigger change in momentum in approximately the same time as I put my foot down. Bigger rate of change of momentum means bigger force which hurts. The moral of the story is to slow down!

Rime on Grisedale Pike

We were up on Grisedale Pike above Keswick today enjoying the snow. There was a bitter wind blowing on my back as I took the photograph. Notice the rime ice on the fence posts and rocks. It is growing into the wind. Apparently the water droplets in the air become supercooled. In other words, they remain liquid even though they have been cooled below 0 degrees Celsius. This is because there is nothing to help ice crystals to nucleate. The wind blows them onto cold objects which then make the supercooled liquid freeze instantly - but on the side that the wind makes them hit. Hence the rime grows into the wind.

A moment on Foulney Island

 

I walked out onto Foulney Island near Barrow for the first time in nearly 40 years. The wind was unbelievable, nearly wrenching the car doors off. Here's a view of the car park barrier with the town in the background. If you enlarge the picture, you might be able to make out the Town Hall and the submarine sheds. The car park barrier is an example of a cantilever - a beam supported at only one end. In theory, the whole barrier should tip over to the right, rotating clockwise around a pivot point at the base of the support. So the concrete support must provide an equal and opposite moment to prevent that happening.

Under pressure

 

This is an aneroid barometer used to predict the weather. It's actual a pressure gauge. It's a bit like one of those party whistles that you blow into and they unwind. What happens inside is that the high pressure air pushes on a curved tube inside which is attached to a needle. This gives a reading for pressure on the scale shown - 1023 millibars on the inner scale. The recent stormy weather is associated with low pressure. Atmospheric conditions drive air away from an area. This causes lower level air to spiral in to fill the gap like water going down a plug hole. Hence the low pressure end of the scale is labelled with winds and rain. High pressure air brings settled conditions. So if you can measure the air pressure you can guess at the likely weather forecast.

Cooking my Sunday lunch in a bothy

 

Here's my Sunday lunch cooking in Kershopehead Bothy - vegetarian's nightmare I'm afraid. How does the thermal energy get from the stove to the food? First of all the combustion reaction between the gas and the air releases energy in the form of heat. If the flame is touching the pan then there will be direct conduction. If the flame is a little below the pan, the thermal energy will heat the air. The air will expand and float up to hit the bottom of the pan. Then there will be conduction from the air to the pan. The thermal energy will go through the pan itself by conduction. Conduction is much better in the metal because there are free electrons which can go ahead and hit ions further ahead in the atomic structure (the lattice). The bacon and sausages were touching the metal so thermal energy conducts through into the meat. A lot of energy is wasted heating the air above the pan. It expands, becomes less dense and floats away by convection. The efficiency is probably low because so much is wasted but I didn't mind because the useful energy cooked my lunch.

Hanging loose on the Scottish border

It's long time since I did my degree and I've forgotten a lot of the maths. I can remember that when a wire or chain hangs under its own weight, the shape is called a catenary. And I remembered that it involved hyperbolic functions. Like many things in my degree, I could do the questions but didn't really understand. Perhaps I'd better have a look at some of it. Most people have some idea about trigonometry. These are circular functions, based on a circle of radius 1. The equation of such a circle is xsquared + ysquared = 1. A hyperbola is a shape you get for xsquared - ysquared = 1. Instead of sin, you get sinh. Instead of cos you get cosh. Some work to be done here. Incidentally, the photograph is taken in the Kershope Forest and shows a bridge from England to Scotland. I was standing in England and the far side of the Kershope Burn is in Scotland.

Ice beard at Loch Ken

 

I have seen this twice this winter, both on cold days. I though that it was a fungus. It turns out that it is actually ice. It gets called "ice beard" because of the hair-like quality of the ice. Apparently the sap cools down towards freezing point and expands as it does so. This cracks the bark. Water then comes out through something like capillary action and freezes into these fine filaments. Wikipedia says that Alfred Wegener, the man responsible for Continental Drift theory, was interested in this phenomenon too.

The corona of the Moon

 

This photograph looks quite fuzzy but that's what I was after. It shows the Moon in the middle and the bright fuzzy patch around it. I've been meaning to look it up for a while now because I've noticed that it is always a restricted small area. It's called the corona of the Moon and is caused by the diffraction of light through water droplets. The suggestion is that different sized droplets can lead to different sizes of corona. This one was about 3 little fingers across so I'll remember to measure other ones. The effect called the halo of the Moon is due to refraction, which is a different bit of Physics.

The weather in chaos

 

We were ringing bells in Whitehaven in the middle of yet another storm. Here's a view from the church porch where I sat reading an article in Physics World about chaos theory. Weather is a chaotic system. It goes round and round but never quite repeating itself. It is cyclic in the sense that roughly the same sort of weather happens at roughly the same time each year. In Chaos Theory there are settled motions called Strange Attractors. Systems can flip between attractors. Maybe the awful spate of storms in the UK at the moment is one attractor. Something will need to dislodge the weather into another attractor, another pattern of weather.

Focusing on an iPad

 

Before you ask, no, this isn't mine. Being a Luddite I haven't succumbed. But I wanted to check out what I'd been reading about the short focal length of the camera. The optics seemed very good but the focal length looks to be about 1cm. Now focal power = 1/focal length. 1/0.01m is 100 Dioptres. That's a strong lens. I'll need to work out how strong my glasses are but they are diverging lenses so it won't be as easy to work out.

A new wind turbine

It looks like they are putting up a new wind turbine at Great Orton near the Watchtree Nature Reserve. The bottom picture was taken through the reserve's telescope. It takes energy to build any power station. You just hope that it generates more energy when it is working than is used making it. Although actually that's a problematic statement because it implies that turbines make energy. They don't. They harvest the wind's kinetic energy and transform it into useful electrical energy. I've heard people say that more carbon dioxide is released making the concrete base than is saved by using wind power but I've never seen any hard data to support this claim.

 
 
 

 

Cooling my computer

Here is the heat sink from my computer. It's made of aluminium and has a fan on the top. Notice that it is not solid. It is made of thin layers of metal to give it a big surface area. More on that later. Computers have miniature circuits which overheat easily. That can destroy delicate components so they need to lose thermal energy quickly and efficiently.

 

 

Notice that under the microprocessor mount there is white paste. This is conducting paste/ It means that the thermal energy from the microprocessor conducts easily into metal. The metal conducts thermal energy because it contains free electrons. These are able to go on ahead to hit other atoms and make them vibrate. Remember that conduction is when one atom hits the next and makes it wobble!

 

The large surface area is to enable the thermal energy to be passed on to the air by conduction. Then there would naturally be convection in the air. It would become less dense and rise. The fans speeds up this process. It removes the warm air quickly and replaces it with cooler air. If cooler air is touching the hot metal then the conduction process will go more quickly. If the metal and the air became the same temperature then there would be no further net conduction. The fact that the aluminium is silver means that heat radiation is not an important process. In fact, it could cause problems by being absorbed by other parts inside the computer and causing it to overheat.

A calmer sea at Silloth

We walked in lovely sunshine at Silloth today. The tide was coming in. I noticed a mismatch between the surface waves and the tidal current. The waves are coming top left to bottom right in the photograph. The tidal current moves left to right. I wonder if the waves are always in this direction? I will remember to look. The wind was blowing left to right so the waves were not lined up with the wind. In the photograph, the tidal current hit the groyne. It flowed over it in the same way that a river flows over a step in a weir. I think the water must have gone faster at this point because the wave seemed to stretch sideways - see the wedge of clearer water in the middle. Then there was an area of turbulence. Could this be a version of the aerofoil effect? And notice that because it is a wedge, my proposed speed change must be more pronounced further out.

Momentum and waves at Silloth

 

Look at the wave hitting the vertical end of the breakwater. The water has been thrown vertically upwards. This means that a force must have been acting on it in the vertical direction. That's odd if you think that a wave is coming in horizontally and hitting a vertical surface. The contact force between the wave and the surface should act at 90 degrees to the surface and thus act horizontally in the opposite direction to the direction of the wave. I think that the wave itself must have been moving vertically at the time of impact so that it did have some initial momentum in this direction. Also, the end of the breakwater probably isn't truly vertical but I didn't fancy going to find out at the time that I took the photograph. But with lots of news coverage of similar waves at places like Aberystwyth, something is causing the waves to go up vertically.

Newton's Law and Lifeboats

 

Silloth lifeboat was out on the very high tide this morning. The sea was very stormy. These two photographs show the boat launching itself off one of the waves. I think that some aspects can be explained by Newton's First Law. This says that if no other force acts on an object it carries on in a straight line at constant speed if it is already moving. Let's assume that the boat is not accelerating. When the wave falls away beneath it, the boat carries on through the air as shown. Now actually gravity acts on the boat pulling it down as well, so instead of a straight line we'll get a parabola. The boat must be moving faster than the waves for this to happen.