Rheinfall: Up Close, Personal And Wet

The CFTR's steam train

In a serious rain shower, the Chemin de Fer Touristique du Rhin's train stops at Volgelsheim station, where the association that maintains the line has its museum. The train itself is made up of former Austrian carriages built in the 1920s with what I suspect were 2nd and 3rd class seating.

The locomotive is a T3 tender built around 1900 at Graffenstaden, just South of Strasbourg, for the Alsace-Lorraine Railways. At the time, the region was under Imperial German control, hence the Eagle logo and German inscription "Elsaß-Lothringen" above the number. The association has two of these, nicknamed Berthold and Theodor. These are supported by small Diesel engines; on our trip, one of these hauled the train to the depot, where the extent of the association's work is on display. The active engines are maintained here, while others are being restored.

Peut-être un jour? - To run again one day?

The town of Breisach, on the other side of the Rhine and therefore in Germany, is visible, and a boat carries passengers across the river from near the depot.

To end the "Canal Contraptions" mini-series, here's a brief look at the Keage Incline on the Lake Biwa canal in Kyoto. Located near Nanzen-ji and its famous aqueducts, it's apparently a popular sakura spot, not that I'd know visiting in July...

Boats were loaded onto wagons at one end of the slope, and hauled by an electric engine up or down before being unloaded back into the water at the other end. Thinking about it just now it sounded rather ludicrous to me, but I was picturing long European-style barges, but the boats of Meiji period Japan were probably not that big, as a picture of the surviving wagon shows.

We didn't go down to the incline, it was just something the friends I was travelling with that day brought up between Nanzen-ji and our next destination. Something to go back for...

Sangaku Saturday #12

Having mentioned previously how mathematical schools were organised during the Edo period in Japan, we can briefly talk about how mathematicians of the time worked. This was a time of near-perfect isolation, but some information from the outside did reach Japanese scholars via the Dutch outpost near Nagasaki. In fact, a whole field of work became known as "Dutch studies" or rangaku.

One such example was Fujioka Yûichi (藤岡雄市, a.k.a. Arisada), a surveyor from Matsue. I have only been able to find extra information on him on Kotobank: lived 1820-1850, described first as a wasanka (practitioner of Japanese mathematics), who also worked in astronomy, geography and "Dutch studies". The Matsue City History Museum displays some of the tools he would have used in his day: ruler, compass and chain, and counting sticks to perform calculations on the fly.

No doubt that those who had access to European knowledge would have seen the calculus revolution that was going on at the time. Some instances of differential and integral calculus can be found in Japan, but the theory was never formalised, owing to the secretive and clannish culture of the day.

That said, let's have a look at where our "three circles in a triangle" problem stands.

The crucial step is to solve this equation,

and I suggested that we start with a test case, setting the sizes of the triangle SON as SO = h = 4 and ON = k = 3. Therefore, simply, the square root of h is 2, and h²+k² = 16+9 = 25 = 5², and our equation is

x = 1 is an obvious solution, because 32+64 = 96 = 48+48. This means we can deduce a solution to our problem:

Hooray! We did it!

What do you mean, "six"? The triangle is 4x3, that last radius makes the third circle way larger...

Okay, looking back at how the problem was formulated, one has to admit that this is a solution: the third circle is tangent to the first two, and to two sides of the triangle SNN' - you just need to extend the side NN' to see it.

But evidently, we're not done.

"Stick an aircraft engine in it" part 1 - Boeing Jetfoil

In the late 60s and early 70s, all branches of transport were hoping for an increase in performance similar to what the jet airliner brought to aviation, and the solution was invariably to use similar gas turbine technology, with invariably identical career trajectories when the oil crises hit, as, apart from in aviation, far more economical engine options were available. So I was very surprised to see this still active in Japan last summer:

This is a hydrofoil which uses gas turbines to power a pump-jet. Once it is going fast enough, it takes off and runs on foils, greatly reducing water resistance and achieving speeds up to 45 knots, over 80 km/h (which, on water, is very fast). I remember seeing exactly this type of vessel in ferry brochures when I was a child; Oostende Lines operated some between England and Belgium. The advent of the SeaCat, a class of huge Diesel-powered car-carrying catamarans, got the better of the hydrofoils and the hovercraft, which was incidentally another case of "stick an aircraft engine in it".

This specific class of hydrofoil takes the mantra to another level, as it was designed by Boeing, which named it the 929 Jetfoil. Production was licensed to Kawasaki Heavy Industries in Japan, which made boats for the domestic market. The Rainbow Jet is one of these, running between Sakaiminato on the San'in coast and the Oki Islands. I saw more of them at Atami in Eastern Shizuoka, providing transport to the Izu Islands. So, despite the astronomical 2150 L/h consumption (though to be fair, I can't find consumption numbers for equivalent foot passenger-only catamarans), Japan still runs them...

When I have the inspiration, I stage an Easter Bunny Massacre. Also it's April Fools' Day, so I wanted to post something funny. Lacking inspiration at the moment, I looked back at a previous Easter weekend.

Summer highlight reel: Île de la Table Ronde

To the South of Lyon, the "Island of the Round Table" in the middle of the Rhône offers a fantastic escape from the city. While the East side is exposed to a lot of noise from motorway traffic, the inside and West shore are gorgeous, and the southernmost end is a nature preserve.

The river flows by at a steady pace, making it a good spot for a reaction ferry similar to the ones in Basel. Fair play to the locals, they thought that too!

Bridges now do the job - though the suspension bridge from Vernaison isn't doing too well. Built in 1959, it needs replacing and until then, traffic is limited on it so as not to overload it. This hasn't been helped by the North side of the island being an industrial estate.

In the centre of the island, one finds a ruined farm, the Ferme aux Loups. One thing @teamroquette likes to do is geocaching, and so we looked for some, but the most elusive geocache of all was the namesake of the island. There are pictures of a round table associated with the island on Google Maps, but we missed it. That said, one Google review also mentions that they couldn't find it, so who knows.

We did find these interesting and somewhat imposing water level meters though. Lay on them to measure yourself... and get the wrong answer!

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!

A last, albeit light, taste of winter for this season in the hills of Southern Schwarzwald. There should have been a lot more snow in this area in February, but still saw some, both on-site at Titisee, and in the distance, on the Alps visible from the village of Saig. With my sister, we walked through a snow shower on the way back down!

Not the first time we've been to this area. A train goes from one lake at Titisee to another at Schluchsee, with this cheeky station on the way:

"Taaaaaaake the train!"

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.

Saint Servan and the Solidor Tower

On the right-hand side of the Rance river, just before the fortified city of Saint Malo on the estuary, is the smaller town of Saint Servan. In fact, it technically isn't a town anymore, it was absorbed by Saint Malo in the 1960s. But for most of history, there was a stark contrast between the two, as Saint Malo fiercely proclaimed its autonomy several times. Hence the Solidor Tower.

Consisting of three tightly-bunched round towers and their connections, the Solidor was built in the 14th century by the Dukes of Brittany as a means to control the Rance estuary, against the rebellious Saint Malo if needed.

Like other fortresses, such as the Bastille in Paris or the towers at La Rochelle (another time maybe), its strategic value soon dwindled, and it seemed best-suited to serve as a prison or as storage during the late 18th-early 19th centuries. It has been an officially classified monument since 1886, and had housed a maritime-themed museum since 1970, though this appears to be in limbo and I can't find the tower's current function.

A walk along the coast on the West side of Saint Servan will reveal a bit more history: an old lifeboat station, a small tower in the sea that serves as a tide gauge... further up, a WWII memorial with the remains of concrete bunkers, and further along, a view of Saint Malo. It's a worthwhile detour for people visiting Saint Malo, especially if you're concerned that the city centre will be too crowded. But I think I remember parking here wasn't easy either; on a nice day, the locals who don't want the hassle of "intra-muros" would come here.