Two Crossings Of The Rhine

Strasbourg's tramway's 30th anniversary!

On this day in 1994, Strasbourg inaugurated - or rather, resurrected - its tramway network. Like many cities in France, Strasbourg had a streetcar system until the late 1950s, when it was decided that cars would take over. 30 years of worsening congestion and pollution later, the town chose a tramway, which had made a successful return in the mid 1980s in Nantes and Grenoble, over an automatic metro to revitalise its transit service.

Unlike Nantes and Grenoble, Strasbourg looked to foreign streetcar manufacturers Socimi and ABB, who designed a fully low-floor tram with generous windows. The Eurotram was at first a 33-metre vehicle (original form seen above), which quickly proved insufficient. A lengthened version, with an extra motor module and carriage, appeared in the following years.

Personally, I quite like this tram for the massive windows, the very mechanical sounds as it runs, and the fact that the warning bell is a real bell (later models have an electronic bell which... just sounds worse). A downside I have noticed, though not for me specifically, is that it has a low ceiling.

After losing out in the 90s, national constructor Alstom won the next round of contracts for Strasbourg's trams in the 2000s. The Citadis model, fully low-floor and taller than the Eurotrams, entered service in 2005. More Citadis trams arrived in 2016, with a new design that I really like, and with special adaptations to allow it to run in Germany, as the network crossed the border to Kehl in 2017, a first for a French tram operator.

Today, the network consists of 6 lines, crisscrossing the city centre and heading out into the suburbs. A 7th line is in the planning stages, due to head North towards Bischheim and Schiltigheim. Despite refurbishment, the Eurotrams won't be around forever, and new trams are on order - more from Alstom.

To build or not to rebuild? The case of Heijô-kyô

In 710, the Imperial court moved from Kashihara to Nara. Just over 80 years later, the capital once again changed location, settling in Kyôto where it would stay for a millennium. The palace in Nara was abandoned, and in the 1000 years that followed, the grounds were used for menial things. However, a few structures have been rebuilt in recent years, such as the main audience hall in the background, which was completed in time for Heijô-kyô's 1300th anniversary.

Besides a museum housing artefacts from its 8th-century heyday, the palace is seen here hosting some art exhibits, and a play is underway, just visible in the above photo. Of course, I didn't understand a word of it...

This view of the Suzaku South gate shows how recently interest was given to the site: by the time excavations had begun, a railway was already running through it! This is the Kintetsu line, opened in 1914. As such, trains between Ôsaka and Nara pass directly through this historic site.

Sangaku Sunday #11

We're almost there! We have three relations between our unknowns, the radii p, q and r. Actually, let's write them in the general setting, with any height.

Set SO = h and ON = k (so the number b in the problem so far has been equal to k/h). Repeating what we've done in previous steps, and substituting q and r in the final equation so that we get an equation with just p (I've done it so you don't have to), this is what we're solving:

The plan is simple: get p with the last equation, deduce q then r with the first two. The execution of the plan... not so simple. That last equation is messy. Let's tidy it up a bit by noting that it is actually a polynomial equation of the variable x=squareroot(2p):

There are formulas for the solutions to an equation like this, but if we can avoid using them, we'll be happy.

Here's what I did - and you can do too: a numerical test. Let's take the simplest dimensions for a right triangle, h = 4 and k = 3. Replace in the last equation and notice an obvious solution. Deduce p, then q, then r. Jubilate - until you realise something is very, very wrong...

Out of service: the Trieste-Opicina tramway

While the reopening of Notre-Dame cathedral in Paris is making big news, and while I'm in a bit of a tram phase on the blogs, spare a thought for the tram line between Trieste and Opicina, closed following an accident in 2016. And it's a real pity, because it was a wacky one.

Trieste is a city by the Adriatic Sea, surrounded by steep hills - and I mean steep. Opicina is 300 m higher, and the tram line features gradients as steep as 26% - link to the Hohentwiel hike for scale. Steel wheels on rails weren't going to be enough...

Initially, the steepest section was built as a rack-and-pinion railway, but in the late 1920s, it was replaced by a funicular system. Cable tractors would be coupled to the streetcars to push them up the hill, and control their descent on the way down - that's the curious boat-like vehicle in the photos (at least I'm getting boat vibes from it). The picture below shows just how steep the climb is.

In the later years of operation, these cable tractors were remotely controlled from the tram. The streetcars themselves date back to 1935, with wooden doors and fittings, making the Trieste-Opicina tramway a charming and technically unique heritage system.

Sadly, the line is not running. Two streetcars collided in 2016, they were repaired, but service has not resumed. One vehicle, coupled to the cable tractor, remains stationary at the foot of the climb, near where the second photo was taken. A look on Google Street View shows that cars are now habitually parked on the disused tracks. The number 2 tram route between Trieste and Opicina is currently served by the number 2/ bus.

Hello! I just saw your post about the conference. I know it's very niche, but I'd love to hear / read more about your sangaku presentation. I actually went back to Konnō Hachiman-gū this afternoon, hoping to see more examples, but no such luck. (I cannot decipher them, of course, but I taught English at a faculty of engineering, and my students could. Sometimes. )

I'll put together something about the shrine, but どうぞお先に。Nudge nudge hint hint.

Hi, thanks for the message!

The presentation was in two main parts: first the historical context of the Edo period and function of sangaku in developing mathematics during that time, and second a closer look at Kashihara Miminashi Yamaguchi-jinja's example with a modern solution. I can't read the sangaku in full, but I have been able to pick out the parts with numbers and compare some of their results with the formulas.

I can probably put together a mini-series at some point. Which parts would you want to hear more about? (That's a general question btw: anyone can reply and add the conversation of course.)

The conference went well, as far as I can tell, so here are a couple of low-sun views of Kashihara's preserved Edo-period area, Imai-chô, as an outro. The first building seems to be operating as an art gallery (maybe?), while the other is a neat little temple. Both are on the same street, 大工町筋, which Google Translate says could be Daiku-chô suji or Daiku-machi suji... or it could be something else, I don't remember reading the name myself on site.

Different place next.

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).

The Fog on the Rhine (is all mine, all mine)

After three weeks of marking, I finally managed to get out of my hole in late January. I was beckoned out by dense fog, seizing the chance to enjoy the misty atmosphere. When I reached the park that straddles the French-German border, I found it on the edge of a fog bank, with haze on one side of the footbridge and perfectly clear skies on the other.

While not among the most outstandingly beautiful parks, the Jardin des Deux Rives has things to offer on both sides of the border, and, just for that ability to hop over to another country, it ranks very high on the cool factor.

Not that the birds would know. They were just taking in the winter sunlight while they could.

The Montech water slope

At around the same time as the "Inclined Plane" of Saint-Louis-Arzviller, other types of boat lifts were being engineered in other places. One of these was the Montech water slope, situated in Southern France on the Canal Parallel to the Garonne (Canal Latéral à la Garonne), the canal from Toulouse to Bordeaux which most people would probably refer to as the Canal du Midi - a better-known term though strictly speaking, the Canal du Midi is only the section from Toulouse to the Mediterranean.

From what I can garner, the two-headed vehicle used on this slope is a conjoining of two Diesel railcars built by Soulé in the early 70s, running on tyres and featuring a daunting-looking shield. This shield would be lowered behind a boat, and the machine would travel up and down the slope, carrying along the boat and the water it bathed in!

However, the performance of this system is less impressive than the Inclined Plane. It bypasses 5 locks, and saves 45 minutes of travel time. That's not nothing, but if you arrived at an end and just missed the train, then going straight to the locks wasn't going to be much longer than waiting for the next one. Also, far more power is required to make this work (I'm reading 1000 hp motors, versus 125 hp for the Inclined Plane), and it's Diesel.

These photos were taken in late 2017, 8 years after the water slope closed. It was only serving leisure boats by then, and, as I've insinuated, it wasn't very economical to run. As far as I can tell, the 5 locks beside it never closed, and are in use today.

The slope and its tractor have since been renovated, and the site's current state can be seen in a Tim Traveller video published in 2021.

"Take the aircraft engine out!" - the AP1-88 hovercraft

The Tim Traveller has just dropped a video about the massive SR.N4 car-carrying cross-channel hovercraft (which got a mention here) on display at Portsmouth, and he notes that there is still an active hovercraft service between Portsmouth and the Isle of Wight. That reminded me that I had a couple of pictures of that, and I thought I was primed for part 3 of "stick an aircraft engine in it". Two problems though.

First problem, the pictures aren't great. Taken in 2012 from the Mont Saint Michel ferry exiting Portsmouth harbour with my previous camera, which had a less powerful zoom and a lower resolution than my current one. It's still enough, in conjunction with the Wikipedia page on Hovertravel, the company that operates these vehicles, to narrow it down. The hovercraft can only be one of two vessels, the Freedom 90 or the Island Express (squinting at the bow it might be former), but the exact identity matters little. Both are of the same type: an AP1-88 built by the British Hovercraft Corporation, successor to Saunders-Roe who built the big cross-channel model.

And that's where the second problem arises: the AP1-88 is not powered by aircraft engines! It is powered by 4 Diesel engines, making it much quieter and more economical to run, while still capable of reaching 50 knots. It shows that passenger hovercraft transport is possible without gas turbines, and Hovertravel's current fleet consists of two Diesel hovercraft built in 2016 by Griffon.

Nonetheless, chalk up the hovercraft as something I have seen in action!