The Fortifications Of Wissembourg

First time in the Channel Tunnel!

Hard to believe, given that I have family on both sides of the Channel, that this month was the first time I used the Tunnel! For a long time, I've lived on the Western side of France and travelled in a car, so going to Calais to catch the shortest ferry links or LeShuttle never made sense compared to a relaxing six-hour crossing from a port in Normandy. Now I live in Eastern France and don't use a car, so the train is a no-brainer, and finally, I took the Eurostar from Lille to London.

On paper, the trip is amazing: just 90 minutes, roughly 30 on the French high-speed line, 30 in the tunnel, and 30 on High Speed 1 in England. Buuuuut... you need to get to the departure station around 60 minutes early for security and border checks, there's not a lot to do in the densely populated waiting area, and once on the train, I found it quite hard to relax in the hard, narrow seats under rather harsh lighting. While the ride was quick and operations felt reliable, the comfort of some regional trains has won me over more swiftly. That said, I've also been underwhelmed by the German ICE 3 (BR 407), which is the same Siemens Velaro D model as the Eurostar e320.

The Channel Tunnel turned 30 this year, with the French high-speed line connected to it upon opening and TGV-derived stock at the ready (now called the Eurostar e300, left), while the UK finished their high-speed line to London in 2007 (plaque at St. Pancras, right). Since then, it's been possible to go from London to Paris or Brussels in under two and a half hours (not counting security before boarding).

And there I was, starting to think I'd be riding the Seikan Tunnel before the Channel Tunnel!

Success for Aston Martin at the Spa 24 Hours courtesy of Comtoyou Racing! The British marque hadn't won the Belgian classic since 1948, and hadn't won a 24-hour race outright since 1959, which was the year the legendary Carroll Shelby won Le Mans with Roy Salvadori in a DBR1 (pictured above at Le Mans Classic in 2018).

Aston Martin have had success at Le Mans since, winning the GT class four times with the Prodrive-built DBR9 and Vantage GTE (pictured above at Le Mans in 2013, a tragic event for the team as Aston driver Allan Simonsen driver died in an accident early in the race). But in the races where GT3 cars are the headline, they have typically struggled to beat the powerhouse brands from Germany and Italy. Seen below is a predecessor of the new Spa winner: the 2013 V12 Vantage GT3, raced at the Nürburgring 24 Hours (pictured at Le Mans Classic in 2018).

Steep stuff: climbing the Hohentwiel

The altitude difference between Singen town centre and Hohentwiel fortress is only around 200 m... but a view of the mountain shows that it's going to be covered in a rather short distance.

To be clear, 18% is the steepest incline on the road, if you're driving a car, and even then, you'll only get to the Hohentwiel Domäne intermediate stop. The footpath starts climbing further around the mountain, and it's more of an 18% average!

The Domäne has a hotel-restaurant, at which I had lunch, providing shelter during a heavy shower! This made me hesitate to push further, and the previous post showed that there were more hovering around. I took a chance, the rain stayed away. Pick up a ticket to the castle and go through the little museum, and it's back to the climb, for pedestrians and cyclists only... still with over 20% in places!

Views from Ôwakudani

As the volcano's activity isn't explosive, and there's a whole hot spring business around it, humans have been trying to tame Mount Hakone, as evidenced by the many consolidation structures seen at Ôwakudani.

These continue down the valley to contain landslides which could happen if things get more intense. Nonetheless, occasionally, a gas vent juts out, placing a distinctly natural form amongst the organised, man-made network of walls.

The yellow deposits are typically sulphur from a very pungent gas. Depending on the direction of the wind, the smell in some locations on the summit can be quite literally breathtaking.

The views, meanwhile, are figuratively breathtaking, from the striking contrasts in vegetation in the foreground to Lake Ashi and the outer mountain range of the Hakone caldera in the background.

And, of course, it is possible to see Mount Fuji from Ôwakudani. Terms and conditions apply, as always, but what little I could see on that morning gives a sense of scale to the great mountain. However, later that day, we would be treated to a much clearer view of Fuji-san.

Sangaku Sunday #7

We're back with a new problem from Miminashi-yamaguchi-jinja! This is going to be more ambitious than the first one, though it won't be much harder from a geometry standpoint - the main tool will still be Pythagoras's theorem. But we really need to set the stage for this one.

Consider an isosceles triangle, with two circles whose diameters are on the height from the apex, tangent to each other, and so that the top circle passes through the apex and the bottom circle is tangent to the base. We seek to draw one more circle on either side, which is tangent to the first two, and tangent to two sides of the triangle.

Details and first questions below the cut.

The triangle is given: it is an isosceles triangle SNN'. For the sake of simplicity, let's shrink or blow up the figure so that the height SO is equal to 1 (for a configuration with height h, we will just need to multiply all the lengths by h). The length of the base NN' is therefore the fixed parameter of the problem, and, as the figure is symmetric with respect to SO, we only need to set the length ON as our parameter: set ON = b. Hence, we are working in the right triangle SON.

The problem involves finding the three circles that fit the configuration in SON. Let these circles have respective centres A, B and C, and respective radii p, q and r. The radii are the unknowns of our problem, and we need to find three independent relations between them to solve. From the sketch, it looks like there should be only one solution.

The first relation is obvious: 2*(p+q) = 1, as the diameters of the first two circles form the height SO. This is also very easy to solve: if we have p, then q = 1/2 - p.

A second relation must start to involve r. For this, project the centre of the third circle onto SO and ON, calling these projections P and Q respectively. Now we get to two questions for you to munch on.

1: Prove that

2: Get the lengths AC and PA. Deduce another expression for PC, and prove that

With that, we just need another equation to find p, and we'll be done.

I sighted this Vectron at Karlsruhe: a Dual Mode, which can move either with its Diesel engine or getting its energy from the overhead wires (German 15 kV AC only for now). However, it only delivers a third of the power of a standard all-electric Vectron, and is therefore not designed for main line hauling, and is expected to be more at home near sorting yards. Deutsche Bahn have also bought some of these as ICE rescue locomotives, serving when a train breaks down.

For Vectron!

Produced since 2010 by Siemens, the Vectron is a modular locomotive platform with various engine options - AC electric, quad-voltage for use across Europe, "last-mile Diesel" option for parking, Diesel motors, dual mode/hybrid... It hauls both freight and passenger trains. But the main reason I've wanted to mention the Vectron is...

this Mitchell and Webb sketch!

This is from series 3 of That Mitchell and Webb Look, which was aired in 2009. The Siemens Vectron was officially launched in 2010, so it's fair to say that the name appearing in both is a coincidence. However, when I see a Vectron, it reminds me of this sketch, so it's harder for me to take this train seriously!

But it is serious business, as it is one of the most common locos in continental Europe. Only Iberia (due to using a different gauge) and France (because if it ain't Alstom, they'll oust 'em) don't see much of them. The examples shown here are from Germany, Switzerland and Slovakia, and were all pictured in the same area of Germany. The quad-voltage version in particular allows companies to carry freight all over Europe, they're virtually borderless.

Yet here I am, still snickering at the name, by Vectron's beard!

Towers and trains at Oberwesel

Downstream from Bacharach and Kaub seen in the most recent posts, Oberwesel is a gorgeous town on the left-hand side of the Rhine, with many of its medieval walls and towers still standing. The railway was built alongside these walls near the river, and even goes between two towers, the Katzenturm (left) and Ochsenturm (right). Add the hills in the background, and it is certainly a spectacular train spot.

Here is another tower, the Haagsturm, in a view from the station platforms. (I just got off that train and failed to position myself in time to get the sign out of the way bottom left.) The two trains shown were the only types visible that day, as the intercity traffic was diverted to the other side of the river via Wiesbaden.

Further from the river, another section of town walls and towers runs through the hills. In the centre of the picture above, taken from the short but steep Elfenlay trail, is the Kuhhirtenturm (with raised drawbridge), with St Martin's Church rising behind it.

Oh alright, have a wider view from the Elfenlay.

What to do at Ôwakudani

... or what to do on the summit of an active volcano. As inauspicious as that sounds, as long as Mount Hakone's activity can be described as moderate (localised fumaroles and hot springs) and a full-blown eruption doesn't happen, and that hasn't happened in thousands of years, it's possible to settle some permanent attractions. The Ropeway is undoubtedly one of them, and the Geomuseum, housing explanations about the mountain's history and geological peculiarities, was a very pertinent addition 10 years ago.

However, the summit's biggest draw has to be its black eggs. No, black eggs aren't what you get when you raise chickens at the top of an active volcano, but it's what you get when you boil eggs in the natural volcanic spring water on Mount Hakone.

So a few restaurants have popped up in Ôwakudani to serve these curious delicacies. To be clear, it's just the shells that turn black due to the minerals in the hot spring water; they still protect the inside from those minerals, and the egg cooks perfectly normally, and the edible parts are still white and yellow. Apparently, I don't eat hard-boiled eggs.

The eggs are cooked in the steaming plant next to this fumarole further up the hill. It can be visited via a trail through some less stable ground. If I remember correctly, this trail is only open at certain times for a limited number of people at a time. Although it's only 300 metres from the main part of Ôwakudani, half a dozen shelters have been installed in case of emergency (one such concrete structure can be seen behind the steaming plant).

But how do the eggs get up there if the trail isn't always open? With their own lovely little ropeway! White eggs go up, black eggs come down, ready to be served in the restaurants!

Some life in the rock pools of Hashigui-iwa! The crabs in the first picture were very small, but the one hiding in the second picture was more sizeable. I forget how big, but it was big enough to observe scuttling for shelter as I approached. Closest match on iNaturalist appears to be the Striped Shore Crab, which grows up to 5 cm.

The local birds of prey, likely kites, were also out, surveying the area.

Latest ambiance from Strasbourg, with love from our end-of-year mascot: Chris Moose!