Star magnitudes

The Greek astronomer Hipparchus looked at the heavens in antiquity and noticed that the stars were not equally bright to the naked eye. He reckoned that there were 6 levels of brightness, which turns out to the about right. He called the brightest stars magnitude 1 and the dimmest magnitude 6. On the picture of Cygnus shown, the two bigger dots are about magnitude 2 and the one at the bottom of the wing is magnitude 3. Deneb has been cut off this diagram and is magnitude 1. The modern system can use measuring instruments not eyes so is more precise and awards decimal places as well. Of course, these are apparent magnitudes because they show what it looks like. Some dim stars seem bright because they are close and some bright stars seem dim because they are distant. Scientists ahve been able to work out bright stars actually are and have calculated the absolute magnitude to compensate for this problem.

Hollow figures and inertia: not the centrifugal force again in Köln

So this is how they make Easter eggs! Put the hot liquid chocolate in a mold and spin it round. The chocolate tries to keep going in a straight line because it has inertia. The spinning forces act on the metal mold so they are pulled round in circles. The chocolate tries to keep going and hits the metal wall. The metal wall pushes back inwards on the chocolate: a centripetal force. The chocolate stays plastered on the edge, prevented from carrying on through the wall of the mold by this centripetal force. Many people say that the chocolate has been thrown to the outside by a centrifugal force. My Physics teacher argued otherwise but it was years before I understood why.

Tracking the American space program on Gran Canaria

Our coach went past the Maspalomas station at the southern end of Gran Canaria. We were told that it was used to track American space missions in the 1960s. A little research shows that it was built for the Mercury project, the first American human space flights. You can see the bases they used here https://en.wikipedia.org/wiki/Project_Mercury#Tracking_network. The orbits themselves are interesting. The mission illustrated did 6 orbits and only one went over Gran Canaria. The orbit is a wavy line on the map as a projection from 3D onto 2D and then that the Earth is tilted at 23 degrees. Orbits took 88 minutes so must have been low. Coming back to the start of the orbit after an hour and a half, the Earth had turned through about 20 degrees and the town on the ground underneath would not be the same, hence the lines don't repeat.

Learning to love constellations

I had always thought that constellations were a stupid idea. Humans seeing patterns that aren't really there. Linking together stars that are really massive distances apart in 3-D space. But I've recently spent time out at night learning my constellations. Delphinus is one that I've learned to identify in the last week. By learning the constellations I have begun to be able to find my way round the night sky. The patterns divide up the sky and make it possible for me to identify individual stars. I have found mu-Cephei in the constellation Cepheus. Herschel called it the Garnet Star. It is a deep red and is a huge red giant - they say one of the most luminous objects we can see though tiny because of how far away it is. Constellations have helped me to do this!

Monorail at Dusseldorf Airport

I was interested in this automatic monorail and how it managed to line itself up with the exit doors on arrival. There were two sets of doors - one on the carriage and one on the station. They had to be perfectly aligned. It looks like there are strong magnets exactly opposite the doors which must be sensed by the carriage.

Watts per square metre in Wuppertal

The Schwebebahn in Wuppertal is part powered by solar panels. 558 W over 74.53 square metres means 7.4 W per square metre when the photograph was taken. I looked at a solar insolation map for Germany http://www.solarserver.com/knowledge/lexicon/s/solar-radiation.html This seems to give Wuppertal as 950 kWh per year per square metre which would give an average of 0.108 kW or 108 kW per square metre. If that's the case, we were well below average. But then I first heard of the place in the phrase "Es regnet immer in Wuppertal"!

A smile in the sky

It's been a great summer for sundogs. These photographs were taken at Oswestry. What interested me most was the top picture. The arc was curving away from the Sun and was above my head almost at the zenith. I've seen almost complete circles of the Sun this year - there are traces above the sundog in the second picture - but they all curve concentric to the Sun.

Negative curvature of space-time: the col on Hesk Fell

In a most amazing bit of outdoor Physics, this col between Stainton Pike and Hesk Fell above Devoke Water was used to describe negatively curved space to me in a way that I'd not heard before. The col is like a saddle. In the picture, it goes down and then up away from us onto Hesk Fell. Left to right it curves the opposite way. Now imagine banging in a peg in the middle with a rope of a certain length attached to it. You are on the end of the rope and walk round in a circle. On the flat, the circumference comes out to be 2 x pi x radius. On this surface, it is bigger than 2 x pi x radius. That means that the surface has negative curvature. Why does it happen? Because the twisting of the land stretches the space that makes up the surface so there is more space to cover. I understood this forum post http://math.stackexchange.com/questions/619063/circumference-of-a-circle-in-hyperbolic-space but I'd like to get to grips with the maths. Apparently it is a hyperbolic space and Roger Penrose does write about that!

Ploughing boulder on Whit Fell

Thanks to Keith for pointing out to me these boulders that are gradually working their way down the side of Whit Fell above Devoke Water. The give-away is that earth is piling up on the downhill side and that a gap is opening up behind. The blocks moving like this were up to 2 metres long and maybe 1 cubic metre in volume, giving a mass of maybe 3 tonnes. I found a link to a much more impressive one in the Cairngorms http://www.landforms.eu/cairngorms/ploughing%20blocks.htm This article suggests that the stone is a good conductor of heat. That will conduct heat up from the ground, leaving the ground colder. The water there will be more likely to freeze. As this melts in the spring, the boulder is able to move downwards. At a few millimetres a year, this block will have been going for a couple of decades. It's nearer the sea than the Cairngorms and lower so perhaps does not freeze as often.

Was radar invented in Dusseldorf?

I found this plaque on a house round the corner from where we were staying in Dusseldorf. "Der Ur-Radar Erfinder" would be the original discoverer of radar. I'd never heard of Christian Hulsmeyer. You can read it for yourself but he was first to patent the idea of using Hertz's discovery that radio waves reflect from metal objects. It was to be applied to shipping to stop collisions. Sadly it never quite worked out. https://en.wikipedia.org/wiki/Christian_H%C3%BClsmeyer

Unconvinced in Electric Brae

 Electric Brae is the famous place where cars roll uphill if you take the brakes off. I've been wanting to go for years. I confess to being a little disappointed. The slopes are so gentle that when we were there it was hard to figure. Funnily enough, I'm more convinced in hindsight by the photographs.

 In the picture above, the road is actually going downhill.

In the picture above, the road is sloping uphill. It does look downhill! Take the handbrake off and the car rolls backwards towards where I stood the picture. What's happening? I've been asked about it by classes many times in the past. I always make this model. The folded paper represents a river valley with a stream where the fold is. You know that the stream is at the bottom of the valley so you expect the road to be going DOWN to meet it. If you play with the angle of the V fold and the tilt of the paper, you can see that it is possible to have the road slope the wrong way.

 Above would be the Electric Brae set up. Below is what you mind expects.

Schwebebahn in Wuppertal: centrifugal forces

 The Schwebebahn in Wuppertal is an amazing overhead monorail built about 100 years ago. It is nearly 10 miles long and really looks like Blade Runner from below. It's one of the wonders of Europe.

The carriages hang from a single suspension point.

This means that as you go round corners, the carriages lean outwards. It feels as though the carriages are being pushed outwards. My Physics teacher at school was quite clear: "There is no such thing as a centrifugal force." There are only centripetal forces pulling towards the middle. Here, the centripetal force is the contact force of the rail pushing on the wheel. The wheel goes round the corner. The carriage has inertial mass. Newton observed that inertial masses like to keep going in a straight line at constant speed. The wheel turns the corner but the carriage tries to keep going straight so it starts to lean out. No centrifugal force here, just inertia.

Induced magnetism rescued my key

I dropped the window key down a crack. I thought that a strong magnet would pull it out so I fetched one that I had salvaged from an old hard drive. It wouldn't fit into the crack because of the bits of hard drive arm still attached to it. So I found a screwdriver and attached the magnet to it. The screwdriver fitted into the crack and pulled up the key. The screwdriver is steel. It contains magnetic domains, areas of magnetism within the metal. The strong magnet was able to line these up temporarily so that they act together, turning the screwdriver into a temporary magnet. This is called induced magnetism.

Average speed on Pontcysyllte Aqueduct

This is an amazing feat of engineering. I timed this narrowboat crossing. We walked the 307 metres almost as fast. It took 6 minutes and 20 seconds or 380 seconds. So the average speed was a little over 1 metre per second. Student will be required to know the usual average speed of various modes of transport for the new Physics GCSE. I suspect narrowboats won't be required.

Isolation transformer: shaver socket in the bathroom

Today's big question has been about these shaver sockets. Why are you allowed to plug in shavers in the UK when nothing else is allowed to be plugged in? It turns out that there are two parts to the answer. The first is to say that the socket is a special type of transformer. It has a 1:1 turns ratio so it doesn't change the voltage or current. However, the secondary is electrically isolated from the primary - they are connected by a magnetic field not by wires. The primary circuit is earthed. You are also earthed because you are standing on the ground. So if you touch the live in the primary circuit there is a complete circuit from the live to your hand down through you to the earth and through the earth back to the live. Current flows around that loop and hurts you. But the secondary circuit is isolated from the primary. It is not earthed. Even if you touch the live, no complete loop circuit back exists so you don't get a shock. So this is a safety transformer. The second thing is that they are given 200mA fuse so the maximum nominal power rating = 0.2 x 230 = 46W. It limits the power so most devices couldn't be used without blowing the fuse.

Refractive index - an amazing fish tank

 I spotted this fish tank today - look how narrow it looks from the front.

 This is how wide it actually is end on.

 I measured its width as 30cm.

Then I used the ruler from the front to measure how narrow it looked to me. In this view you can see that the 0cm mark seems to be lined up with the back of the fish tank but that the width only seems to be 16.5cm. The reason for this illusion is that light travels slower in the water and glass than it does in the air. This means that the light bends as it goes through the tank, a phenomenon called refraction. Our brains cannot cope with the fact that the light is not going straight so our brains compute where a straight ray of light would appear to have come from. The result is this optical illusion. The bending power of the water and glass is called the refractive index. It can be calculated by doing real width divided by apparent width. So 30 divided by 16.5 = 1.8.

King of the Mountains: Tour of Britain does gradient on The Struggle

We watched the Tour of Britain bike race come up The Struggle from Ambleside onto Kirkstone. The gradient gets up to 20%. Physicists love gradient but we normally do up divided by across, in other words, how far up you go for every one you go along. It turns out that road gradient is not the same. The old 1 in 5 that I remember from childhood means 1 up for 4 along the slope of the road - in other words, along the hypotenuse. 1 divided by 5 is 0.2, or the new 20%.

Width of a rainbow at Brothers Water

I spotted this rainbow on the campsite at Brothers Water. It occurred to me to measure the width of the rainbow. It was roughly twice my little finger and therefore roughly 2 degrees. This article shows that there should be about 2 degrees between red and blue https://eo.ucar.edu/rainbows/

Fountain in Nordpark, Dusseldorf

I've been looking at fountains all my life but on this particular night it struck me that the water jets stay together in a coherent parabolic shape until they are almost at the top. Then the shape becomes far less defined as the water comes down. One explanation could be that the water contains sections that are fired at different speeds. This would mean that they wouldn't go quite as high and would come down slightly earlier, broadening the beam. Maybe the pump is a series of pulses rather than a continuous push.

Multiple sundial at Culzean Castle

This multiple sundial in the walled garden was fantastic. It looks like the gnomon in the middle picture is probably angled at the latitude angle usually used for the slope of a horizontally anchored gnomon. Technically they should all show the same time so it is easy to assess the relative accuracy. They come with very variable precisions. Notice how the width of each scale division decreases in the middle photograph although each represents an hour. The resolution decreases.

Sundial sunset at Culzean Castle

This sundial at Culzean Castle was almost on the correct time last week. My watch said 7.51pm BST and it said 6.52pm GMT. This is a very precise sundial, to the nearest 2 minutes. But of course, it might be precise but it is not always accurate. There is a fierce debate in UK science education about the definition of these terms.ACCURATE means correct and given the problems highlighted by the Dusseldorf correction graph, sundials are only accurate some of the time. PRECISE is often defined as "to more decimal places", though in the case of a scale like the sundial, the word RESOLUTION would now be used instead of PRECISION - how small the scale divisions are. There is a brilliant poster from the NPL exlaining precise and accurate http://www.npl.co.uk/educate-explore/posters/sport/accuracy