A curved lake in a mapping

 

I love the panoramic function on the camera. It must simehow be mapping from curved space onto a flat plane, like the way that the globe gets distorted when mapped onto a flat sheet. You can get away with it for small sections of the globe but trying to represent the whole globe on one flat sheet leaves it distorted. Here Wastwater was straight when I was looking at it but now looks distinctly curved.

Arch dam at Seathwaite Tarn

 

Seathwaite Tarn was turned into a reservoir for Barrow over a hundred years ago. The dam is actually curved - seen behind the spillway in the photo above. Most dams I've seen are straight. This one has its curve facing the water. It occurred to me that an arch is a strong shape because the weight of stone above an arched window pushes the arch blocks into each other, locking them. Here, it is the water pressure that does that job. Turns out this type of dam has a name: an arch dam. It is neatly summarised by The British Dam Society who say that this type is rare in the UK because it needs strong rock foundations, presumably to be able to push back on the blocks that make up the dam. That is the case here.

How long was the adit at Seathwaite Tarn Mine?

 

In his book Mining in the Lake Counties, W T Shaw explains that you can guess the length of a tunnel from the volume of rock that has been removed. There is an impressive spoil heap at the entrance to the now blocked up adit - Wainwright's chapter on Grey Friar has a picture of what it used to look like. I'm estimating the spoil heap to be 10m x 10m x 5m meaning 500 cubic metres of rock. If the tunnel was 1.5m high and 1m wide, that would mean a tunnel 300m long. I have been unable to find any information about this mine because it is not mentioned in Shaw's book.

Speed of water in the stream

 This small stream on the way down Buckbarrow had an interesting feature. As water hit a shallow, weed-infested section at A, bubbles formed. They stayed until B. I timed several. It took around 3 seconds to go from A to B. Closer inspection wit walking poles suggested about 3 metres long so the speed would be 1m/s through this section.

Deceleration at Swirls

 Deceleration is a word rarely seen on road signs. Acceleration, the rate of change of velocity, is a vector. That means it can have any direction. Since it is usually measured along a line like a road, it is given a positive value if the velocity is increasing or a negative value if the velocity is decreasing. This negative value for acceleration is called deceleration. Clearly if you were waiting in the lane next to the sign, you would have no rate of change of velocity so would not be decelerating and would have no business in that lane.

                                       

Is it possible to move 730kg?

I have been thinking about the result of my calculation yesterday that the mass of the roundabout was 730kg. I have translated into hundredweight and it is about 14cwt. That is the mass of a smallish tenor bell in a bell tower which is moved by a wheel about the size of the roundabout. It sounds feasible the calculation is in the right ball park.
 

Trying to find the mass of the roundabout

 I was back on the roundabout. I timed myself as 7 seconds per rotation near the centre (say 0.5m from axis) and 8 seconds when I was about 1.5m away.

The movement should involve conservation of angular momentum. I have added my point moment of inertia to that of the roundabout, which I have taken to ne a disc of radius 1.5m. The result is a mass of 730kg for the roundabout. It might be a bit high but is not totally unrealistic.

Vivid blue from polarised sunlight

 Through a polarising filter, the reflected sunlight from the shallow water at Fleswick Bay was a vivid blue - a sort of metallic indigo colour. It was very striking seen live and some evidence of it has come out in the photographs in the middle of each picture. I have seen it before but always associated with reflections from water through polarising filters. The colour is always this deep blue or indigo.

Even more evidence from the mirror

 It was a bit later in the morning today so the sun had moved round to a different angle. Light was hitting the other mirror door. The direct shadow of the blinds can be seen with the reflected image on the lower left. Again the spectrum is at a different angle to the reflections. There were also curved spectra in mid left.

More about the refraction from the bevelled mirror edge

 I posted last month about the prism effect from the bevelled edge of a mirror. This time I noticed that the spectrum cuts across the pattern of the reflected blind slats. In other words, the process of producing the spectrum is pulling the light through a bigger angle than the reflection is. I a suspecting that there is some refraction involved with reflection from the back of the mirror but will need to think further about a possible ray diagram.

Stress patterns in the ice

 I know that it is possible to see places of high stress in plastic using polarising filters, but it looks as though I have managed to see them in ice today. It only worked through my polarising sun glasses. 

A moment of inertia in Patterdale

 I timed 2 circuits of the roundabout as shown below.

Then moving towards the centre, I timed again. This time each rotation was 1 second faster.

The reason is that for circular motion, it is not just mass that affects motion but distance from the middle. The combination of the two is called moment of inertia. Angular momentum is conserved in the movement to the middle. Angular momentum = moment of inertia x angular velocity. Moving towards the centre reduces the moment of inertia because it is easier to accelerate a mass closer to you in a circular motion. If momentum is conserved but moment of inertia is reduced, angular velocity must increase thus each rotation takes less time.

Miners' Balcony Path at Glencoyne: another equipotential

 The miners who worked at the Greenside Lead Mine certainly ensured that they didn't waste energy traversing the hillside on their way to work. The path around Glencoyne follows the contour faithfully - a spectacular equipotential to walk.

It leads to the hole dug in the 1950s as a safety evacuation route from the mine.