Garden sprinkler

These systems are ingenious. The flow of the water pushes against a lever and the moment from that impulse force is greater than the moment from the spring so the lever is pushed out of the way and water escapes. There is then no impulse force so the spring provides the resultant moment and the lever springs back cutting off the water supply. I didn't get close enough to work out how the system gives angular momentum to spin the spray.

Human wind speed measurer on Sheffield Pike

I've tried this one before but last time I made the mistake of leaning forwards into the wind. Balancing on my toes made it harder to determine the exact pivot point. This is a refinement of the method as the heels make a clear pivot point. The red arrow is my weight which we'll say is 630N. Distance from red arrow to heels is roughly the length of my boot so let's say 0.3m. The clockwise moment is 630 x 0.3 = 189Nm. The blue arrow is the force of the wind on me. Newton's Second Law says that resultant force = rate of change of momentum. F=d(mv)/dt. Here we can write F=vdm/dt. We will assume that the air is stopped dead. The rate of change of mass is basically the mass of air that hits me and stops dead in one second. This is the mass of air contained in a volume as area Av as velocity tells you the distance for 1 second. My area = 1.8 x 0.3 = 0.54 square metres. The density of air is 1.2 kg per cubic metre so dm/dt = 1.2 x 0.54 x v = 0.65v kg per second. I will assume that the wind force acts half way up me so anticlockwise moment = 0.9 x 0.65 x v^2. Equating the moments, we get 0.9 x 0.65 x v^2 = 189. Wind speed v = 18 m/s. This is 65 km/h which is roughly 40 mph. It was a very windy day so that is not inconceivable.

Resolution of longitude and latitude on Slight Side

We visited the memorial to a WW2 plane crash site on Slight Side. I know that at least one old book gives the grid reference as being on the wrong side of the mountain so we used Paul's phone to get latitude and longitude. Putting this into an Internet converter gives NY 20864 05193. The precision of +-0.0001 degrees corresponds to 1.7 x 10^-6 radians. The radius of the Earth is 6400km so it gives the place on the surface of the Earth to the nearest 10m using the arc length small angle formula.

The air crash was a terrible tragedy. The pilots were flying from Sunderland on a training flight. There is more information at http://www.yorkshire-aircraft.co.uk/aircraft/lakes/v6565.html which implies the other aircraft crashed in a different location, which might explain the grid reference confusion. You can find pictures of the second site here https://www.peakdistrictaircrashes.co.uk/crash_sites/lake-district/hawker-hurricane-v6565-v7742-slight-side/

 The views were so beautiful on the day that we visited. A sad location.

You can tell which parts were aluminium and which parts were steel.

The Wain Stones: Gritstone Tors

Ronald Turnbull's book called Granite and Grit is one of my very favourite books. It's about the rocks found in the mountainous areas of the UK. He writes so well and it's actually witty; not the dry academic tome you might expect. He notes that whilst we usually associate tors with granite, there are other rock types that also produce tors. We visited the Wain Stones on Bleaklow, which are famous for looking like kissing heads. 

 Gritstone tors are cracked horizontally first. This is along the boundaries between different depositions because they are sedimentary. He says that they crack vertically underground when water is expelled under high pressure.

 Gritstone is very coarse sharp sand. It occurred to me that this would have been made by erosion millions of years ago - ie it was on the surface of the Earth. Then it spent millions of years below the surface and here it is again up on the surface in time for me to see it.

Jodrell Bank: It's a sign!

Not quite the usual advertising in the gents'.

Bleaklow: low flying jets

I have been used to low flying military aircraft but under the flight path to Ringway you get passenger planes low over the hills. I think the wingspan of this one is 80m. If my finger subtends 1 degree, the 80m is worth about 2 degrees. In radians that is 0.035 radians. Small angle in radians = arc length/radius. Here radius means height of plane so 0.035 = 80/height. Height above me = 2285 metres. That sounds far too big. I thought it seemed quite low. Even if my finger was only 50cm from the camera the height stubbornly refuses to come much below 2km.

Hayfield Campsite: moving shadows

The Sun covers 360 degrees in 24 hours so it moves at 15 degrees an hour. The shadow of the trees was like that of a giant sundial gnomon and the question was how far to move to get another hour of sunshine. How far is 15 degrees on the ground?

Angular resolution at Jodrell Bank

The cafe at Jodrell Bank is a good place to stop for refreshments on a long journey. You don't have to pay for the exhibition just to use the cafe and you get views like this! The dish has a diameter of 76.2 metres. Angular resolution is given by Rayleigh's Criterion and is wavelength/diameter. Frequencies are between 408 MHz and 6GHz. The respective wavelengths are 0.73 metres and 0.05 metres. This gives the respective angular resolutions as 0.00958 radians and 0.000656 radians, These are 0.55 degrees and 0.0376 degrees. This latter is 2.3 minutes of arc. Smaller is better for resolution: the smaller the angle the closer the two objects can be and still be distinguished.

The speed of sound in Wasdale

The usual problem with military planes in the mountains is not seeing them because I end up looking at the sound. Light is so fast that we assume that it arrives instantly. But sound takes about 3 seconds to travel 1km. That must have been the distance to this Hercules. We were able to find it because it travels a shorter distance during the 3 second delay than fighter jets would. Thanks to Paul for the photo!

Counting people on Scafell Pike

These two posts are on the main path up to Scafell Pike used by 3 Peaks walkers. From the panels facing the path, I'm guessing that an infrared beam must cross the path. When the beam is broken, it must click a counter circuit on by one.

Efficient hand drier at Pagham Harbour

A hand drier with a heating element uses about 5 times the energy as one without. Suppose a 1000W heating element. That must mean that the fan for the air blower must be 200W.

Fourier Analysis on the sea at Scarborough

During a walk along the marine drive at Scarborough I noticed two distinct sets of plane wavelengths as well as a lot of other bits. the main swell had a wavelength of maybe 10 metres but there were other waves that seemed to be nearer 50cm. The swell was clearly reflecting intact. It reminded me that the sea must be a superposition of many frequencies of disturbance. If it were a sound, it wouldn't be very harmonious. The deconstruction of such a mess into component frequencies is done by Fourier Analysis. I felt as though I'd caught a glimpse of what this actually means.

A visit to the centre of the UK: Dunsop Bridge

Last November I posted about how we found the centre of mass of the UK with a cardboard cut out http://wigtonphysics.blogspot.co.uk/2016/11/centre-of-mass-of-uk.html The method finished like this:

Now I had thought that Haltwhistle was the centre of the UK. But the method given for Dunsop Bridge is the same method I used. See https://en.wikipedia.org/wiki/Centre_points_of_the_United_Kingdom And here's what they say in Dunsop Bridge...

Dunsop Bridge: catching water for Blackburn

We went to Dunsop Bridge in the Forest of Bowland to see the Pallid Harrier. Turns out that the whole valley supplies Blackburn with water. The valley was not suitable for a reservoir so water is taken straight out of the rivers. I was taken aback by the claim of 34 million litres per day. A litre is 1000 cubic centrimetres but 1 cubic metre is 1 million cubic centimetres. So there are 1000 litres in a cubic metre. Blackburn is taking 34000 cubic metres a day. I looked on a map to assess the catchment area of the river. It fills less than a 5km by 5km square on the map. So let's estimate 10 square km. 1 square km is 1 million square metres so we have a catchment of 10 million square metres. 34000/10million = about 3mm depth of water. Now that doesn't sound too bad.

Light sabre in the Solway sky

I spotted an interesting feature last night. It hasn't photographed as well as I'd hoped but just above the bottom corner of the garage roof there is a vertical line. It remained steady until the Sun had gone completely over the horizon. It was clearly caused by the Sun illuminating cloud. I think it was probably a transparent layer of cloud and that the way that the Sun was shining from behind the lower clouds lit up a column through it but I couldn't easily detect the rest of the cloud. It could just have been a fluke that sunlight was lining up with a single cloud column but it didn't move at all whereas the strip of cloud above and right moved across to the left over time. It looks like it was probably a sun pillar caused by tiny ice crystals http://earthsky.org/earth/what-is-a-sun-pillar

Lord's Rake - decomposing rock layer

I'd read about it for years but I've finally been to inspect Lord's Rake on Scafell. I was amazed by how weak and fractured the rock is. Bits look like they are about to fall from the walls and some bits come off in your hand. Then there are the solid retaining walls. I haven't been able to find anything out about the geology but it is volcanic and will be part of the Scafell caldera. So my guess is going to be that we might have ash layers that have been upended and sit vertically. In one layer the ash particles are less cohesive and that accounts for the weakness. There have been earth movements before in this area - I posted about the fractured rock on Scafell Pike last time I went.

Evaporation: Beckhead Tarn has disappeared

Beckhead Tarn between Kirk Fell and Great Gable has completely gone. I've never seen anything like it. Perhaps it has trickled through into the ground due to lowering water table in the dry weather. But let's calculate how much energy would be needed to make it evaporate. Let's assume it is circular and of diameter 40 metres. It is only ankle deep so volume of water = pi x 20squared x 0.1 = 125 cubic metres. That's a mass of 125 tonnes of water. Latent heat of vaporisation of water is 2260 kJ per kg. That means 280 million kJ of energy. But we need also to remember that the water needed to be heated up to make it evaporate. It would be extreme to have it heated to boiling point but let's do it: mcdeltatheta for a temperature rise of 90 degrees Celsius needs 125000 x 4200 x 90 = 47 million kJ. Say the Sun was a 1000W per square metre heater, that gives 1.25 million Watts.Total Joules divide Watts gives 261600 seconds = 72 hours of sunshine. It might be feasible since it last rained.