Why do aerials have direction?

The pictures come from the museum at Croome. I remember studying this for my degree but I've lost the detail now. So I was wondering why you get the lobes for electromagnetic waves and don't get equal intensity all the way round. It turns out that it is to do with interference. There are angles where there is destructive interference. I don't yet fully understand why. But notice that the smaller wavelength is more uni-directional. That means that the lobe doesn't touch the ground. In the top picture the radar can only detect planes in front that are as far horizontally as the plane is vertically above the ground, because the ground reflects waves and it detects the ground as well.

The Flame Probe

I suspended a foil covered football from the ceiling and charged it up to +1000V. I used a flame probe to measure the electrical potential in the space around the ball. The flame probe is a hypodermic needle attached to a gas tap with a tiny flame on top. The tip of the needle is attached by wire to the plate of a gold leaf electroscope.  The large + voltage on the ball pulls free electrons up the wire from the plate of the gold leaf electroscope onto the tip of the needle. That leaves the electroscope positive so the gold leaf is repelled upwards. The angle is a measure of potential energy because work has to be done by the electric field of the ball against the attraction of the electrons to the nucleus. Energy is stored when work is done against an attractive force.

 There has to be a flame on the tip because the flame creates ions which discharge the free electrons. If they built up on the tip, they would cause a field that would distort the field being measured by the probe.

The closer the probe is to the ball, the stronger the field and hence the bigger the angle. We projected the gold leaf so that we could take a more accurate measurement of the angle.

Keeping the milk fresh part 2

Last week I used ice to keep milk fresh but that was not an option when we spent 3 days away from electricity. This time we used a bucket of water. All we were doing was increasing the mass of liquid that would have to be heated. The water and the milk have to be in thermal equilibrium - ie they will settle at the same temperature. Thermal energy from the air will thus be spread through far more molecules of water than if we'd just left the milk. Each molecule gets a smaller share of the thermal energy so the internal energy of each molecule only goes up by a small amount. Temperature is a measure of the internal energy.

Estimating the walkie talkie frequency

On camp for the D of E Silver, we sat debating the frequency of the walkie-talkies. I estimated the aerial at perhaps 20cm. Aerials like this are half wavelength. To make the mental maths easier, I took the wavelength as 0.50m. Using the wave equation, frequency = speed of electromagnetic waves/wavelength = 300 000 000/0.50 = 600 MHz. Same make walkie-talkies on the Internet are claiming 400 - 480 MHz so that not a bad estimate!

Solar phone charger discharged my phone!

I borrowed a solar phone charger. I set it up in bright sunshine and all was going well. After sunset last night it was still connected for about an hour and nearly discharged the phone. The solar panel and the phone battery must act as emfs in parallel. When the sun in shining, the emf of the panel will be higher than that of the battery and so will send charge that way. However when the sun sets, the emf of the phone battery will be higher. At any point in time, charge will move in such a way as to try to equalise the emfs.The higher emf will always send energy to the lower. The difference is that the solar panel is constantly having its energy replaced by an external source.

More electric field patterns

The theory says that field lines leave and join surfaces at 90 degrees. I went on to have a point with a plane electrode, as shown in the top picture. The semolina lines are very close to the the theory. A uniform field has parallel field lines. Near the surface of the plane electrode the field approximates to uniform. The same could be said in the middle of the gap between the two point charges shown in the bottom picture,

Electric field lines with semolina and cooking oil

 I put cooking oil into a Petri dish and sprinkled on some semolina. I used some electrodes made from bent coat hanger and connected it up to 2000V. The pieces of semolina touch the electrodes and gain a charge. They are then pulled along the electric field lines. I suspect that they join in clear lines from one side to the other because each charged piece attracts the next. That probably means that one side of the piece of semolina becomes positive and the other side negative - charge separation. Notice that no pattern is shown outside the gap between the electrodes presumably because there is no possibility of a continuous chain of + and - all the way to the other plate.

Flux Lines and Faraday

This is how Michael Faraday came up with the concept of the magnetic field - iron filings sprinkled around a magnet. So a force field has SHAPE. We also used plotting compasses to show the same shape and that it has DIRECTION.

Somewhere along the line I have picked up the idea that they are called FLUX lines, which is Latin for flow, because he thought that there was a flow around a magnetic circuit. I was told that this isn't true. In my final year at university we used an equation for magnetic machines like motors that used flux as if it were current in a circuit. Not true but it certainly worked, I have been trying to check what I remember being told. I found this on the NASA site http://www-spof.gsfc.nasa.gov/Education/whfldlns.html It echoes what I have just described but not exactly. I had not known that he had called them Lines of Force. I need to read more on Faraday and reflect on how many half-truths I've picked up along the way.

Latent Heat on Great Dodd

I came up with a new strategy to keep the milk fresh for brewing up after a long walk from Dunmail Raise north over Helvellyn and beyond: pack the milk with ice. The milk has come from the fridge and will eventually reach the ambient air temperature whatever happens. Thermal energy will flow from the warmer air into the milk until the milk and the air are at the same temperature. There is so much air that it will not noticeably decrease in temperature. The ice adds one complication: after the thermal energy raises the temperature of the ice to 0 degrees Celsius, the ice then needs to melt. Thermal energy flows in but the temperature doesn't rise. Because the thermal energy seems to disappear, it is called LATENT HEAT where latent means "hidden". The energy is actually being used to break the bonds that hold the molecules together as a solid. This uses up rather a lot of energy that would otherwise warm the milk up to ambient air temperature. Once the ice has melted, this process continues, warming ice and water up to air temperature eventually. Crucially, this takes longer so there is less chance of bacteria making my milk go off.

Calibration at Long Meg Stone Circle

 We called in on this stone circle near Penrith. I knew that the idea was to line up the tall lone stone called Long Meg (the other stones are her Daughters) with the sun on Winter solstice.But was it sunrise or sunset? I got my compass out and stood in the middle of the ring. 220 degrees - nearly south-west so certainly sunset. Long Meg is the odd one out. She is red sandstone from nearby. The other stones are different - glacial erratics I believe. You don't need a circle for a once-a-year alignment. Only two stones would be needed. Was she a late addition?

The stone below even looks like Cross Fell above it. The oddity is that in the picture above, you can't quite see the Lakeland Fells above the stones because of the slope. If the circle had been 50m further it would have had a brilliant view in all directions. 

 So if the other stones mark calendar points marked by the Sun or stars, the stones would be placed by observation not calculation. Hence this is an early example of calibrating a scale.

Fahrenheit 451

Wigton library Book Club book this month is Ray Bradbury's Fahrenheit 451. I last read it 3 decades ago. Mrs B has enjoyed the book a lot. Big ideas about free speech. The temperature is said to be the autoignition temperature for book paper. At that temperature, the air will provide enough energy to reach the activation energy for the combustion reaction. Fahrenheit is an old and slightly bonkers temperature scale. The full story is here https://en.wikipedia.org/wiki/Fahrenheit I'd always understood that Fahrenheit had simply chosen a zero point as the coldest temperature he could find, and essentially that is true - with the caveat that it needed to be repeatable. He had to be able to recreate it to calibrate more thermometers. The other fixed points were the melting/freezing point of pure water and blood temperature. All good so far - but why the odd selection of numbers? It seems it was based on the work of an earlier scientist who had chosen 7.5 for freezing water and 22.5 for body temperature. I'll try to find out why. All Fahrenheit did was multiply these by 4 to get round numbers and then adjust from 30 and 90 to 32 F and 96 F so he could easily have a doubling scale.

Volta at Wray Castle

Another name on the door at Wray Castle. I knew that he invented a type of battery but that was pretty much all. But thinking about it, that's quite an awesome claim to fame. It just seems so obvious now. Why had it not been obvious before 1800?? Is there anything that will be invented soon that will seem so blindingly obvious in 200 years time?

Elastic collisions at Wray Castle?

I hadn't played snooker since I was in the Sixth Form. I still can't get the angles right. But this is such a brilliant example of the laws of mechanics that there should really be one in every lab. The idea is that momentum is preserved in each collision. The balls have equal mass. An elastic collision is one in which momentum is conserved AND kinetic energy is conserved. In this case kinetic energy cannot be conserved because you hear the click of one ball into another - some kinetic energy is transformed into sound. I shot the white ball with initial velocity u into a red ball that was initially at rest. After the collision both balls moved on. Say the white ball has v1 and the red ball v2. Here are the equations for conservation of momentum and kinetic energy:

Combining the equations you get

This means that kinetic energy can only be conserved if v1=0 and the white ball stops dead. So the fact that the white ball goes on a bit is evidence of an inelastic collision. I hadn't realised that before.

Abingdon bun throwing

Sadly we were unable to be there but friends who were said it was great. Here's the video of this weird old ceremony http://www.oxfordmail.co.uk/news/14551727.VIDEO__Cloudy_with_a_chance_of___buns__Crowds_in_Abingdon_covered_with_bread_for_Queen_s_Birthday_ceremony/?ref=arc Buns are thrown from the top of the old building onto the crowds below. I tried timing the fall. The motion is parabolic. Vertical fall is independent of horizontal movement. I think a time of about 2 seconds is quite close. Timing from individual hand on the roof to hitting the ground is difficult. The equation needed is height = 1/2 x g x time-squared = 1/2 x 10 x 4 = 20 metres. Not too bad.

Rayleigh at Wray Castle

The National Trust's Wray Castle by Windermere using to be a Merchant Navy college and the rooms are named after physicists who worked on related areas. I teach Rayleigh's criterion (see http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html) but reading about him, I notice that he won the Nobel Prize for discovering Argon. He used the idea of Rayleigh scattering to explain why the sky is blue. This is a brilliant explanation of what is going on if you carry on down through the articles  http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#c3 The actual equation for Rayleigh scattering is hideous but seems to be crying out for some spreadsheet analysis when I have time. I like the diagrams showing the difference with Mie scattering. The issue seems to be that Rayleigh scattering is fairly uniform in all directions whilst Mie scattering massively favours the forward direction.

Making a model of a lunar standstill

The lunar standstill involves some difficult 3D reasoning so I tried to build a model. You can see the Equator drawn in black on the tennis ball. I've added the axis of the Earth sticking out of the North Pole. Here the Earth is shown upright but actually it is tilted at 23 degrees to the plane that contains the Sun and the other planets. So I've added that plane in clear plastic and tilted it at 23 degrees to the Equator. The Sun appears to do a circle around the Earth. I've drawn it on. It is called the Ecliptic. The Moon takes about 4 weeks to go round the Earth. It appears as a blob of putty on a wire. It is not on the ecliptic. It's orbit is tilted by another 5 degrees.

This is the situation at a lunar standstill. Notice how far above the Equator the putty Moon is - the Moon will appear very high in the sky.

It takes 2 weeks for the Moon to reach the other side of its orbit. Now notice that you are having to look down through the ecliptic so the Moon will appear very low in the sky. This is essentially a lunar standstill - that in 2 weeks the Moon goes from its highest possible to lowest possible position (when viewed looking due south from us).

But the orbit itself doesn't stay still. In the same way that a spinning top goes round in an arc whilst continuing to spin, so the orbit twists - it's called precession. It takes 18.6 years to get back to the position shown in the earlier photographs.

Zodiac signs on the Balmoral sundial

This sundial was in the garden of Balmoral Castle. I was interested that it had the odd cross-hatch pattern on it and zodiac signs round the outside. Turns out that the curves going laterally across the sundial are the loci of the shadow of the tip of the gnomon. The shadow length will be different in different seasons. Thus the shadow length can be linked to a zodiac sign, which in this case is used to denote where the Earth has reached on its orbit around the Sun. I guess that you have to know whether you are before or after midsummer to select which of the two signs offered at the opposite ends of the curve.

Mental arithmetic in the hills part 1: Grasmoor

We climbed Grasmoor by the improbably steep Red Gill.It was a lot further than it looked from the bottom. I resorted to the little finger method to try to work out how far we'd gone. No calculator with me so this is how I did it in my head: My little finger is worth a 1 degree angle. There are 360 degrees in a circle which is 2 pi radians. So 360 degrees is the same as 6.28 radians. I degree is worth 6.28/360 radians. I said 628/360 is approximately 2 so the 1 degree is approximately 0.02 radians. If you enlarge the lower picture you can see our car park to the right of my finger. The car takes up about 1/10th of my finger so a car is worth about 0.002 radians. A car is about 2 metres long. Arc length = radius x angle in radians. Thus distance to the car (the radius) = arc length/angle. The car acts as the arc length in this sector so distance from car = 2/0.002. Dividing by 0.2 is the same as x5. So dividing by 0.002 is the same as x500. Distance to car = 1000m. By comparing with neighbouring hills I knew that our altitude was about 600m so distance is about right!

Lunar standstill at Tomnaverie Stone Circle

We visited this stone circle when we were staying in Tarland in Aberdeenshire. I wondered what the bit in the middle picture meant about the limit of the movement of the Moon. It turns out that it is called a lunar standstill and was not an unusual thing for a stone circle to mark (see https://en.wikipedia.org/wiki/Lunar_standstill) I'm finding it quite hard to understand. Try this video of the event at the Calanais stone circle on Lewis https://www.youtube.com/watch?v=e98oObp4nwM I don't think that the analysis is scientific and you may want to take some of the comments with a pinch of salt but it seems like a reasonable visual recording of the event. The film shows the Moon crawling along the horizon so I guess this is what they mean for Tomnaverie. I had never heard of this and will need to get back to my 3D rotational mechanics to understand what is actually going on!