Total internal reflection at Blackpool Illuminations

This fountain at the Theatre d'Amour was interesting. As the water fires upwards, it also sprays out sideways. It is lit from below at the single point from which the water diverges. Yet the light follows the water as the water curves. This is particularly evident on the left hand side of the spray. Light goes in a straight line and yet it can curve by zig-zagging due to total internal reflection.

Wave equation from Blackpool Tower

I was looking down from Blackpool Tower and noticed that the wavelength seemed to be increasing as the waves reached the shore. But the opposite should be true. Since velocity = frequency x wavelength and waves slow down in shallow water, the wavelength should decrease if the frequency remains the same. Maybe the wavelengths really are bigger further out but perspective makes them look smaller by comparison. A quick search of the Internet came up with some interesting sources to look at further.

Concave mirror on Blackpool Pier

I loved the mirrors on Central Pier in Blackpool. This was the concave one. When you are reflected, the top of the mirror sends the rays from your head downwards. The bottom of the mirror sends the rays from your feet upwards. If you stand a long way off, the two rays cross over and the rays from your feet end up on top. You look upside down.

Closer in, the rays have not had a chance to cross over so you are still the right way up. What is more, given that your brain thinks the image is as far behind the mirror as you are in front, it computes where the rays that are converging must have been behind the mirror, working out that they must have been further apart back there. So your brain gives you an image that is bigger than the original.

A dislocating gate

The gate in the top pictures seems like an odd one. It is only actually attached to the gate by the top hinge. The bottom is merely leaning on the gate. I've drawn a force diagram at the bottom. Only the top hinge is needed to produce a normal reaction force N to hold up the gate. The bottom hinge pushes on the gate with a force R to create a moment that is equal and opposite to the moment created by the weight of the gate. The contraption at the bottom is there to keep the gate in place as it turns.

Angular width of a rainbow

If you look at this rainbow, its angular width is about 1 degree, the angle subtended by my little finger. Also note that it is about 90 degrees to the horizon. This happens later on in the day when the Sun is nearing the horizon. A rainbow is a full circle in theory. Its centre is diagonally opposite to the Sun, following a line down from the Sun through you. The centre is thus called the anti-solar point. The lower the Sun, the closer the anti-solar point is to the horizon and the more of the rainbow is above the horizon. I suppose that in theory half of a rainbow should be above the horizon at sunset over the sea and the angle to the horizon at that point would be exactly 90 degrees.

Gneiss at Crocodile Rock, Rosemarkie

I had always associated gneiss with Lewis so I was a bit confused to find it on the east coast at Rosemarkie. Lewisian gneiss is the oldest rock in the UK. The rocks are called Pre-Cambrian because they predate the first named geological era. That means they are over half a billion years old. Gneiss is a metamorphic rock that has recrystalised due to heat and pressure. I think the original rock here was granite, which would account for the pink colour. And how did it end up here? Well, it turns out that we were on a continuation of the Great Glen Fault - plenty of heat and pressure as the north of Scotland scraped against the Highlands but also the possibility of bringing deeper rocks to the surface. And the rock on the beach really does look like a crocodile!

A new type of filament bulb

This is an LED filament bulb. That's an oddity. A filament is normally a wire that gets hot and glows. The wire is said to be incandescent. Here, LEDs are produced in series along a stem to look like a filament. This is how it gets to be only 8Watts. see https://en.wikipedia.org/wiki/LED_filament

Resultant torque on the waterwheel at Acorn Bank

You'll notice that when you drop coins onto the wheel above, they fall off centre. This is so that they create a resultant torque around the centre. When the coin hits the wheel, the wheel applies a force to decelerate the coin, by Newton's Second Law. In turn, the coin applies an equal and opposite reaction force on the wheel, by Newton's Third Law. This reaction force is off centre, so there is a force x perpendicular distance from the middle - a TORQUE. In rotational terms, Newton's Second Law is written as resultant torque = moment of inertia x angular acceleration. So the wheel starts to turn.

And there was more than one way of having water flow onto the wheel to create a resultant torque. At Acorn Bank, the water came from above but on one wheel it fell down the back of the wheel and on the other wheel down the front. They would spin in opposite directions.

This blog is liking Monkman and Seagull

I can thoroughly recommend the first episode of Monkman and Seagull's Genius Guide to Britain https://www.bbc.co.uk/iplayer/episode/b0bl1vp2/monkman-seagulls-genius-guide-to-britain-series-1-1-england The bit about Emley transmitter is very much the sort of thing that this blog likes to do!

Cantilever stairs at Acorn Bank

The formula for the deflection of a cantilever beam can be found here https://en.wikipedia.org/wiki/Deflection_(engineering)#Uniformly-loaded_cantilever_beams The density of sandstone is 2000 kg per cubic metre. I'm estimating 150cm long, 10cm deep and 20cm wide. That gives volume 0.045 cubic metres and mass of 90kg. Weight is about 900N. Weight per unit length = 600 N per metre. Moment of inertia is width x height cubed/12 = 2.5 x 10^-5. I think it is this area moment of inertia that I need because the units work out correctly if done like this. The Young Modulus for sandstone is given as 1 - 20GPa so I'm going to choose mid-range as 10GPa. Putting the numbers into the deflection formula I get a deflection of 1.5mm. That sounds reassuringly sensible. I had wondered about the effect of the stair above pressing down but that must be cancelled out by the support offered by the stair below.

Baffle in the drying kiln at Acorn Bank mill

I was interested in the practical aspect of the design of this grain drying floor. It needs to have a big surface area so as much grain as possible can be dried at once. However, the heat source is narrow - it's a coal fire underneath. They clearly found that a narrow source wouldn't spread out naturally so they installed a baffle to spread the heat. It wasn't still there so it wasn't possible to see how it had been made.

Apple picking at Acorn Bank: stability

We were interested in the tripod design of this ladder for picking apples. The steps got narrower towards the top. An object is stable is the line of action of weight from the centre of mass lies within the base area. The triangular base gives a bigger than normal area and the design makes it hard to lean so far that the vertical line down from the centre of mass is outside the base area.

Polarised green sea

On Scilly, the sea was noticeably green in many places, mainly shallower bits. Here at Old Town on St Marys I realised that the water looked green when I was wearing my polarising filters but not so much without. The top picture shows without, the middle picture shows the greenish tint through the filter and the bottom is the filter through 90 degrees. This green colour is clearly plane polarised. I had come to the conclusion some time ago that the colour of the surface of the sea is usually a reflection of the sky colour. Polarisation by reflection is common above the Brewster Angle. However the sky wasn't green so I don't think that's happening here. NASA suggest that green sea is due to phytoplankton https://science.nasa.gov/earth-science/oceanography/living-ocean/ocean-color I don't know if that is likely so close to the shore.

Sixth Form estimation question 1 - How many grains of sand are there on this beach?

This is picture of a beach on the Isles of Scilly. Estimate how many grains of sand are on the beach giving reasons and showing calculations.

Drifting on the open sea off Scilly

We went out on a boat 10 miles off Scilly to look for Wilson's Storm Petrel. The engines were turned off for 2 hours and we just drifted. It took me a long time to realise that looking straight out for the back of the boat was not showing me where we have been. It seems that we were moving sideways with the swell. You might be able to spot the movement of the waves in the pictures above. I hadn't really thought much about drifting. Turns out it depends a lot on the design of a particular boat but is due to both wind and current. see http://www.ybw.com/forums/archive/index.php/t-91754.html I think that the swell is likely to give some information about the wind direction rather than the current, but the swell could have been set up by winds on the other side of the ocean some days ago.

Time Trial Wheels at Whinlatter

The riders had their special time trial bikes out yesterday. Most were riding with solid back wheels. The idea is that they have less drag. Drag must be caused by the air rushing around the spokes. There is the possibility of vortex shedding on a small scale, I suppose. The solid wheels don't have this problem. However you don't see them on ordinary days because if the wind it blowing from the side they present a bigger target and put sideways forces on the bike, making it hard to control.

Graphene in my tyres: Tour of Britain at Whinlatter

I was intrigued by this assertion on the side of a promo bus at Whinlatter. I didn't even know that it referred to tyres. Anyway, here's a link to an explanation https://www.cyclingweekly.com/reviews/tyres/vittoria-corsa-g-plus-tyres The claim is that the addition of a small amount of graphene increases grip and reduces rolling resistance. I can see it with the rolling resistance with what I know about graphene but grip? Anyway, the magazine did a proper scientific test on the rolling resistance. The details are at the bottom of this page https://www.cyclingweekly.com/group-tests/choosing-the-best-road-bike-tyres-20156 but it was done indoors on rollers under controlled conditions. This tyre came second so there seems to be some truth in the claims. But they aren't cheap! I couldn't afford to buy them...

Upside down: the Moine Thrust at Knockan Crag

I was so pleased to visit the Moine Thrust. More than 400 million years ago, two early continents crashed into each other due to plate tectonics and this pushed older rocks over younger ones. At least that was the first evidence to geologists that something very wrong had happened here. You usually expect the rocks at the top to be the youngest ones. The model at the top shows the rock layers - silvery Moine Schist above the younger Durness Limestone. And the last picture is the actual place on the hill!

Occulting every six seconds

The light stays on for 6 seconds and then turns off for about a second. They service the bulb once a year. It turns on when it gets dark. On average it will be on for say 12 hours a day - it clearly wasn't properly dark when I took the photograph. In one hour it would be on about 500 times so in a year that would be on over 2 million times. LED must be able to cope with a lot of switching without being damaged.

Range of lighthouse on Chanonry Point

Having noted that I could see lights on an oil rig that I worked out was 10 miles away, I wondered about the nominal range of this lighthouse as being 15 nautical miles. I've been trying to find out the power of an LED replacement bulb but that's hard because it is less electrical power for the same brightness as an old-fashioned bulb. I found a similar lighthouse that used to have a 250 Watt incandescent bulb. I was going to do an inverse square law calculation based on this power but the problem is that 250W of electrical energy in does not mean 250W of light energy out. It has taken me into territory about human perception of light that involves lumens. More research needed.

More measuring of distances at sea

I was wondering how far away the oil platform was moored off Cromaty when this cruise ship helpfully sailed in front of it. It was a Princess lines ship, most likely the Crown Princess, which claims to be 195 feet high. That is 63 metres high. It subtends about 0.25 of a degree as compared to my little finger or 0.0043 radians. Distance away = 63/0.0043 = 14.6km = 9 miles roughly. So maybe the best thing to say is that the rig was about 10 miles away. More on this later.