"Stick An Aircraft Engine In It" Part 2a - SNCF Turbotrains

The first race car I supported: the McLaren MP4/13-Mercedes

Aidan Millward, a YouTuber who talks a lot about racing history and current affairs, recently went to an exhibit at Silverstone and came face to face with the first Formula 1 car he supported, Damon Hill's 1996 championship-winning Williams FW18-Renault. Which reminded me: I've met my first F1 hero too.

The Formula 1 season I remember paying attention to more or less in full was 1998, and the driver I supported - as you usually start in sport by supporting someone before growing more neutral when they leave - was Mika Häkkinen. Like Hill two years earlier, Häkkinen was in a car designed by Adrian Newey, who had changed teams in 1997, and he won the championship with it. The McLaren MP4/13 has a wonderful shape, and the black, silver and white with red accents is an unmistakable turn-of-the-millennium livery.

This car can be found at the Mercedes-Benz Museum in Stuttgart, courtesy of McLaren's engine partner of the time. On the racing floor of this very complete museum, well worth the visit, the MP4/13 is in fine company: Mercedes's other F1 champions from the 1950s with Fangio and since 2008 with Hamilton, Sauber Group C sportscars, the CLK-GTR, DTM touring cars, race trucks (yes that's a thing), and many more...

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.

Wow, I basically forgot the Nishi-Kyushu Shinkansen in my run-down at the end! But yes, it is a complicated situation, with a stretch of line isolated from the rest of the network (there's that gauge difference explained above), and Saga-ken disagreeing on how to build the connection to the main Kyushu line. No clear plan yet apparently. :(

60 Years of the Tokaido Shinkansen!

On 1 October 1964, a railway line like no other opened. Connecting Tôkyô and Ôsaka, paralleling an existing main line, the Tôkaidô New Trunk Line had minimal curves, lots of bridges, zero level crossings. Striking white and blue electric multiple units, with noses shaped like bullets some would say, started zooming between the two cities as at the unheard-of speed of 210 km/h.

This was the start of the Shinkansen, inaugurating the age of high-speed rail.

The trains, with noses actually inspired by the aircraft of the time, originally didn't have a name, they were just "Shinkansen trains", as they couldn't mingle with other types anyway due to the difference in gauge between the Shinkansen (standard gauge, 1435 mm between rails) and the rest of the network (3'6" gauge, or 1067 mm between rails). The class would officially become the "0 Series" when new trains appeared in the 1980s, first the very similar 200 Series for the second new line, the Tôhoku Shinkansen, then the jet-age 100 Series. Yes, the 200 came first, as it was decided that trains heading North-East from Tôkyô would be given even first numbers, and trains heading West would have odd first numbers (0 is even, but never mind).

Hence the next new type to appear on the Tôkaidô Shinkansen was the 300 Series (second from left), designed by the privatised JR Tôkai to overcome some shortcomings of the line. Indeed, the curves on the Tôkaidô were still too pronounced to allow speeds to be increased, while all other new lines had been built ready for 300 km/h operations. But a revolution in train design allowed speeds to be raised from 220 km/h in the 80s to 285 km/h today, with lightweight construction (on the 300), active suspension (introduced on the 700 Series, left) and slight tilting (standard on the current N700 types).

Examples of five generations of train used on the Tôkaidô Shinkansen are preserved at JR Tôkai's museum, the SCMaglev & Railway Park, in Nagoya, with the N700 prototype lead car outdoors. It's striking to see how far high-speed train technology has come in Japan in 60 years. The network itself covers the country almost end-to-end, with a nearly continuous line from Kyûshû to Hokkaidô along the Pacific coast (no through trains at Tôkyô), and four branch lines inland and to the North coast, one of which recently got extended.

東海道新幹線、お誕生日おめでおう！

Something you don't see every year down South: ice! And not just a little, some proper icicles on this fountain on Place de la Trinité in Toulouse.

Plus a bit of snow sticking to the ground in the parks, as seen from the Natural History Museum.

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.

Feeling rather non-committal today, so here are some flowers from the Expo '70 Commemoration Park near Osaka. This is probably going to start a mini-series because the place is huge, so more information will come later.

Sangaku Saturday #13

Last week, we uncovered this configuration which is also a solution to our "three circles in a triangle" problem, just not the one we were hoping for.

This is something that happens in all isosceles triangles. Draw the inscribed circle, with centre B, and the circle with centre C, tangent to the extended base (ON) and the side [SN] at the same point as the first circle is. Then it can be proved that the circle with centre A, whose diameter completes the height [SO] as our problem demands, is tangent to the circle with centre C.

But that's not what I'm going to concentrate on. Despite this plot twist, we are actually very close to getting what we want. What the above configuration means is that, returning to the initial scaled situation with SO = h = 1 and ON = b, we get

Knowing a solution to a degree 3 equation is extremely powerful, as we can factor the polynomial and leave a degree 2 equation, which has simple formulas for solutions. So, to finish off, can you:

1: prove that

2: solve the equation 2x²-(s-b)x-1 = 0, and deduce the general formulas for p, q and r that fit the configuration we are aiming for;

3: test the formulas for an equilateral triangle, in which s = 2b.

This last question is the one the sangaku tablet claims to solve.

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!

Sangaku Saturday #3

Another problem this week, adding to the configuration we looked at previously.

Specifically, given two circles tangent to each other and tangent to a same line - these circles have respective centres A and B, and respective radii p and q -, we want to construct the circle tangent to both of the original circles, and tangent to the line beneath them.

Can you prove that the radius of this third circle, denoted r, satisfies

and deduce a formula for r as a function of p and q?

Help below the cut, answers next week.

Hint. Name K, L and M the intersections of the circles with the line below, and use the previous result on each pair of circles to get the lengths KL, KM and LM. One of these lengths is the sum of the two others.

Schirmeck castle

Overseeing the valley of Schirmeck, the castle, built for the Bishop of Strasbourg in the 13th century, is a short walk and climb from the town centre. As it was designed to protect a corner of the territory, that's apparently where we get the term: Schirm'eck. It was defeated by the Swedish during the Thirty-Years War, with some of the stone from the ruins being used to build other structures, such as the church.

Today, there's obviously not much of it left, though a square tower was restored and houses a small museum (closed when I visited). The Yoshi art was probably not part of the original episcopal aesthetic...