Looking for the mile-long chimney on Raise

 There used to be a smelt mill at the Greenside Lead Mine. Smelting is the process of heating lead ore with a more reactive element. This would be the carbon in charcoal or coking coal. The metals bond ionically and reactivity is governed by the attraction between the electrons and the nucleus. The further the electrons are from the nucleus, the more "shielding" there is said to be and the easier it is for the metals to give away electrons. But carbon bonds covalently. I'd be interested to find out what governs reactivity in covalently bonding elements. 

The Smelt Mill had a long flue that ran up the hillside because the exhaust gases would contain vaporised lead that would be wasted. The longer the flue, the more likely the lead would be to be deposited out of the air. So the flue was a mile long. The photos start at the top and go down tot the bottom. We found bricks in the channel at the bottom. 

Calculating angles for the gradient

 1cm on a 1:25000 map represents 250m on the ground. I have used arctan to calculate the gradients, having explained why it is tan on the previous post

Now the angle for the number of contours could be +-1 degree depending on whether the contours are just inside the edge of the 1cm or whether the next contour is only just beyond the edge. Looks like the rule of thumb is roughly double the number of contours to get the angle. I tested the theory on this photograph of Catstycam.

Using a protractor, the angle of the steepest part of the ridge disappearing into the cloud in 25 degrees. On the map that section has 12 contours in 1cm which comes out at 25 degrees. 

Starting to think about gradient

 I recently read an article that gave a table converting the number of contours per cm on the 1:25000 maps with the actual angle of the slope. As I think the steepest slopes I climb as a walker are 45 degrees, I was interested. The first issue is how the slope is being measured. I offer two possible ways below. When the steepness of a road could be given as 1 in 4, I understood that it meant 1 up for every 4 along the slope of the road. That would be a).

But what about maps. I think maps have to be b) because the distance along the slope is further than that along the adjacent on the triangle. It would mean that when the landscape was projected onto a flat map, points in hilly areas would end up further apart. Here's a flat map representation below.

If I try adding relief to make it like it really is, the sides of the map end up 10cm closer. 

So to preserve true horizontal displacements when projecting a landscape onto a flat plane, it must be method b). Note that for small angles, either calculation will give the same answer to 2sf.

Swath turner at Mirehouse

 

This is a horse-drawn machine for turning rows of cut hay to help them dry. I was taken by the way that mechanical power is transmitted from the turning wheel to the rotating forks that turn the hay. There is a bevelled gear attached to the back axle that turns a shaft so that the turning direction has been rotated through 90 degrees in the horizontal plane. Then the bevelled gear at the top end rotates it in the vertical plane. In effect, we've gone from rotation around the x-axis to rotation around the y-axis and finally around the z-axis. It's opened up thinking about the efficiency of gears https://www.meadinfo.org/2008/11/gear-efficiency-spur-helical-bevel-worm.html

I hadn't come across the word "swath" but it means a row of cut hay. It will be linked to the word "swathe" that I do know. Photos of similar machines can be found here. I have been reading James Rebanks' English Pastoral which explains the hay system very well. 

Cathodic protection at Mirehouse

I posted about cathodic protection of pipelines last August http://wigtonphysics.blogspot.com/2020/09/cathodic-protection-anode.html I have now found this example closer to home at Mirehouse. As explained previously, the system needs a power supply and this must be one of the points where its working can be checked. The pipeline is steel so it could corrode.
 

Measuring the SHC of water

 I inserted a 12V heater through polystyrene into a beaker of water. I pushed a thermometer through as well.

I put bubble wrap round.

You'll be able to tell from the photo that I had first found the mass of the water. 

I took the temperature every minute for 12 minutes and plotted a graph of temperature against time. At first, the temperature stays constant and then goes up steadily. I drew a straight line through the section of steady heating. The water must be stirred whilst being heated. The equation is Delta E = m.c.Delta(theta). Delta E, the energy added = current x voltage x time in seconds. Delta(theta) is the temperature rise. Putting the two equations together, we get Delta(theta)/time = current x voltage /mc. But Delta(theta)/time = gradient of straight bit of the graph. So in the end, specific heat capacity              c = (current x voltage) / (mass x gradient).

Helgoland by Carlo Rovelli

 

Thanks to Jack for lending me the book. The relational interpretation of quantum mechanics was new to me. What I picked up from the book was that the view of distinct separate objects is out, along with the privileged position of an observer. This is because the Schrodinger's Cat story links merely me and the cat, but I must be observed too and so on in an infinite web of relations. Rovelli's idea is to get away from the split into Copenhagen versus many-worlds. I was interested to learn much more about Ernst Mach's philosophy and also to find out about Aleksandr Bogdanov. Not a book to read when you're feeling tired, though!