This pair of #Swans and their juvenile #Cygnets have set up a resting spot on the banks of the #Canal and on the edge of the shared #Cyclepath and #Footpath. I'd passed them before but didn't have a camera with me at the time. As you can see, they have no concerns with people being quite close by but someone told me that they've been quite aggressive, no doubt if someone has been perceived to be a threat.
Yesterday, we went on a trip to #Penzance in #Cornwall. There is a direct #RailwayLine running from here to #London #Paddington. My local station is about half way along this 6-hour route and I've been on the London leg many time and so I thought it would be nice to go to the end of the line in the other direction. There are lots of #RailwayStations with strange names, like #Lostwithiel and #StErth and so it was nice to pass through them on our way.
Looking east along the beach, you can see #StMichaelsMount, which is built on a part-time island, in that it is an island when the tide is in but otherwise you can walk to it over a #causeway. We did that a decade ago. Here are a couple of views with a #ZoomLens (I didn't have space to pack my telephoto lens).
The #town of #Penzance can be seen in the opposite direction.
Parts of the #beach have #grey compacted sand. It's firm and yet soft and when wet it forms a shimmering mirror for the sky.
From the next #headland, you can get a really good view of St Michael's Mount. I think the light conditions here were better too in the early afternoon.
Off the shore, there were several #vessels including this #ship. I'm not sure what its function is but it's certainly for some special purpose.
The #sea appeared #blue or #green depending on the underlying geology.
Here. it even has patches of gold colour looking a bit like those pools into which people drop coins.
The boundary of #Devon and #Cornwall is marked in the south by the #RiverTamar. Across it, there is an old and historic #RailwayBridge called the #RoyalAlbertBridge, which was built in the mid 1800s by #Engineer #IsambardKingdomBrunel, Here, you can see it on the approach on the #train. This was taken using my #Android phone.
Right next to it is the much more modern #RoadBridge, which is a #SuspensionBridge.
Following on from yesterday's posting of flow around a #ZhukovskyAerofoil, I've added #equipotential lines (blue) in addition to #streamlines (black). The two families are #contours of the #real and #imaginary parts of an #AnalyticFunction and therefore have the property of intersecting #orthogonally. The plots aren't ideal as there is some anomalous features where the equipotential lines are very close to the #aerofoil but it's still not bad.
Here, each frame is a different #wing profile, obtained this time by keeping the imaginary eccentricity of the generating #circle constant and varying only the real part.
#MyWork #CCBYSA #AppliedMathematics #Aeronautics #Aerodynamics
The #Zhukovsky #Aerofoil (sometimes transliterated as #Joukowsky from #Russian), is a 2D model of #streamlined #Airflow past a #wing. It uses #ComplexVariable and is an #AnalyticFunction (i.e. #Differentiable everywhere, save at isolated #Singularities). Take a circle in the #ComplexPlane which is not quite centred at the #origin but passes through the #coordinate (1,0) or (z=1+0i). Using the mapping w -> z+1/z, you get something that looks remarkably like an #aerofoil.
It is a #ConformalMapping meaning that angles are preserved during the mapping. In this animation, I've varied the imaginary part of the the eccentricity, while keeping the real part the same. With a zero #AngleOfAttack, you can see the change in the airflow around the #wing as its shape changes.
#MyWork #CCBYSA #AppliedMathematics #WxMaxima #FreeSoftware #Aeronautics #Aerodynamics #LaminarFlow
J'ai un milliard de truc à vous montrer en retard ...
Pour commencer deux #illustrations à l'occasion de la sortie de #VenC 3.2.2 dont l'annonce a été mise en ligne sur LinuxFR. On se revoit vite pour la suite !
Bisous & data love
#linux #venc #web #python #sitestatique #logiciellibre #freesoftware #floss #art #freeart #artlibre #gimp #artwork #digitalpainting #ccbysa #creativecommons
I like the #flowers of this #plant but it is growing out of a gap in #concrete by the porch and garage. I think it must have propagated from a neighbour's #garden many years ago. I tried to take a cutting and plant it in some soil in the back garden but it withered away. Evidently, it only likes rocky conditions. Can anybody tell me the species?
One of the disadvantages of a fine day is that the #HighPressure keeps #dust and #pollution trapped at lower levels of the #atmosphere. This makes #visibility poor. Not far off sunset and you can see a layering effect in the mid and #background with the #horizon barely visible in the #haze.
A high-speed road or railway track that is poorly designed. The vehicle moves at constant speed from the straight segment of road or track directly onto a CircularArc and thereby encounters an instantaneous application of centripetal acceleration. This is neither good for the driver and passengers who will feel a sudden force outwards, nor for the vehicle which my skid and impose large stress changes in the axles and bearings.
This is why #Engineers use #TransitionCurves in the form of #CornuSpirals or #Clothoids to connect from the straight segment onto a circular arc. It has the property that it starts with zero #curvature at the beginning and then the curvature increases linearly with distance travelled along the curve. At the appropriate curvature, it is connected to a circular arc with the same curvature. The people in the vehicle and the vehicle itself are much less stressed by this solution.
#MyWork #WxMaxima #CivilEngineering #HighwayEngineering #CCBYSA
Forgive the recent apparent obsession (I'd call it a fascination) with the #cycloid but I've just discovered something I'd not heard of before. It is also called a #TautochroneCurve or #Isochrone curve, which means that a particle starting from any location on the curve will get to the #MinimumPoint at precisely the same time as a particle starting at any other point.
Here's an #animation I wrote today in #Maxima which illustrates the property.
#Dynamics #Kinematics #Mathematics #AppliedMathematics #Mechanics #ClassicalMecanics #WxMaxima #FreeSoftware #MyWork #CCBYSA
After lunch yesterday, we went to the #HistoryOfScienceMuseum in #Oxford. It's not very big but contains some really fascinating exhibits. It is right next to the #SheldonianTheatre and well worth a visit.
Here are wooden models of the #FivePlatonicSolids.
This is a beautiful example of #HandWriting in a book. #Writing like this is certainly a lost art these days.
Here I am explaining to my spouse the similarities and differences between #Octants, #Sextants and #Quadrants.
This wooden box contains some immaculate #brass #DrawingInstruments. Another rarity these days but I do remember learning how to use similar #instruments while studying at university.
A brass #sundial.
Without anything but manual #SurveyingEquipment, humans were able accurately to map out the entire globe. It's amazing what can be achieved when humanity works together. But also, this model is absolutely gorgeous.
Not to be outdone, the #astronomers mapped the #sky and here it appears on a companion globe.
No computers were around then but the ingenuity of humans to develop calculating instruments to allow them to crunch numbers meant the creation of some devices of stupendous cunning.
To this day, trainee pilots have to master the #CircularSlideRule in order to do calculations for various tasks. Before flying was ever developed, such #SlideRules were in common use.
This #camera is another fine example of hand-made instruments. The craft and skill of whoever made it is a marvel.
Yesterday, we went on a day trip to #Oxford by #train. No other means of powered transport was used as we #cycled to and from our local #RailwayStation.
Here is the #countryside zooming past the train window.
It was a nice day to be out and the city has its own distinctive #architecture, much dominated by the UniversityOfOxford.
Some of the centre is a zero-emission zone or #ZEZ, aimed at curbing the use of polluting vehicles. Such vehicle owners need to pay to use roads in that area.
Here I am walking up a street with some nice buildings in the background.
The view of a church from across some botanical gardens.
The entrance to those gardens.
The #SheldonianTheatre. This is where the degree ceremonies take place.
Oxford #TownHall is in a similar style to other buildings in the city.
I'm not sure what this building is but I don't think it's part of the university.
A couple of weeks ago, I posted an #animation of a point on a circle generating a #cycloid.
If you turn the curve "upside down", you get the #BrachistochroneCurve. This curve provides the shortest travel time starting from one cusp to any other point on the curve for a ball rolling under uniform #gravity. It is always faster than the straight-line travel time. This is an interesting problem in #ClassicalMechanics and exercised luminaries like #Newton and #Euler. I think the latter's use of the #CalculusOfVariations is a stroke of genius.
Anyway, the #animation took a bit of thought as it requires a bit of #Mechanics, some #Integration and is made a bit more tricky as the curve is multi-valued and so you need to treat different branches separately. The #AnimatedGif was produce with #WxMaxima.
For some reason that I can't fathom, I'm not finding it possible to upload the graphic and so if you want to see it, please use the link below.
https://drive.google.com/file/d/1edcZnZ_uiaQOQrFB03XHslNUVCmxcSut/view?usp=drive_link
#MyWork #CCBYSA #Mathematics #Maths #AppliedMathematics #Physics #Calculus
Nothing too remarkable about tonight's #sunset. I just happen to like the three parallel #contrails. We live under two orthogonal #airways here, one running north-south and the other east-west. The latter is usually busier as it includes transatlantic air traffic.
Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic #curve over a length equivalent to the #circle's circumference and has #cusps whenever the point is in contact with the surface (i.e. the two sides of the curve are tangentially vertical at that point).
Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.
#Mathematics #Geometry #Maths #AppliedMathematics #Mechanics #Kinematics #Dynamics #Physics #MyWork #CCBYSA #WxMaxima
Today we travelled to the #CityOfBath, which is just over an hour away by train, making it suitable for a day trip. We cycled to our #RailwayStation and left our #bikes there. In #Bath, we only used pubic #buses and walked everywhere; we were lucky that although today had been planned well in advance, the weather was wonderful.
After a quick visit in the morning to the #UniversityOfBath, we spent most of our time wandering around the centre of the #city. The #RoyalCrescent has houses on its perimeter, curved in a #CircularArc, overlooking a park on the lower slopes.
The #RiverAvon flows through the city and here, you can see it and also one of the famous #bridges, called #PulteneyBridge, which has shops over the span.
There's a nice walk along a stretch of the #river and here you can see the bridge from which the last #photograph was taken. I like the reflection of the river on the underside of the #arch.
#BathAbbey is made of the same stone that most of the #city is made and it gives a uniformity and harmony giving #Bath a unique character.
Some abandonned offices nearby #Nantes. To bad there was nothing left to loot !
#photographies #urbex #offices #art #artwork #free #libre #artlibre #freeart #diaspoart #ccbysa #creative-commons #mywork #picture
