Up The Monumental Stairs At Auch

"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...

Some amusing art in Matsumoto

In my previous post, I mentioned I was taking the train from Nagano to Tokyo, but my destination for the day was actually Matsumoto. There's quite a lot to see there, mainly the castle, but I'll get to that another time. For now, I'd just like to share some lighter, more amusing details.

This awesome statue depicts two samurai frogs riding on toadback - the poor thing seems to be overwhelmed! That would be because the street by this river has adopted the frog as a mascot. According to local history, the river used to have loads of frogs, making it a rather noisy place (I bet, if my memories of Futami, Mie, are anything to go by!). But after a typhoon caused a flood, the frogs left for higher ground and didn't go back to the river, so loads of frog statues were erected instead.

On the bridge near the entrance to this street and near the castle, other creatures could be found: "Y-cats", created by Yamazaki Takashi. I think this was a temporary exhibit.

Oh alright, I'll tease the castle...

Nagahama Castle Ruins

Like Hikone Sawayama, Nagahama Castle is not on the list of Japan's 100 Famous Castles, nor on the list of Japan's Next 100 Famous Castles. Like Hikone Sawayama, it was a pre-Edo period fort which was owned by clans which at some point landed on the wrong side of the unifiers of Japan. Little is left, and short posts mark where buildings would have been. It's a short climb from the base, and the view of Uchiura from this location is pretty good.

This part of Numazu, and the island in the middle of this shot, Awashima, is most famous for being featured in the anime Love Live! Sunshine!!, which I know nothing about but saw some hints of (train for another day). It's possible to see Mount Fuji from here on a good day. And... well, I could see some it...

It's a considerable distance from a train station, though there appears to be a bus stop at the base, but I was driven there by a friend so I don't know how frequent the buses are. We were also lucky to get on a quick boat tour out to Awashima and back, with the chance to see the castle from a the sea, against the hilly backdrop of Izu Peninsula.

Sangaku Saturday #4

In the previous info post, we went over the debate on the religious aspect of sangaku, and the fact that the absence of prayers on these tablets was more puzzling to some than the mathematics. As such, the tablets are not ema prayer tablets, but donations, which usually don't feature prayers on them. Case in point, some consecrated sake and French wine seen at Meiji-jingû in 2016.

Beyond wishing for good fortune and health, such donations serve two very worldly purposes: to contribute to the life and prestige of the shrine or temple (having a famous contributor makes the shrine famous by association), and to advertise the donor in return, as their name is on display. See this large torii at Fushimi Inari Taisha paid for by TV Asahi (テレビ朝日).

With that in mind, Meijizen's cynical comment from 1673 that sangaku aim "to celebrate the mathematical genius of their authors" may not far from the truth. The authors of sangaku are looking to gain notoriety through the publicity that the shrine or temple provides. But was the bemused Meijizen the target audience?

More on that in a couple of weeks. Below the cut is the solution to last week's problem.

The solution to the first problem (below the cut in this post) is the key. Name K, L and M the intersections of the three circles with the horizontal line. Then, by using that previous result,

Indeed, as in that problem, we can construct three right triangles, ABH, ACI and BCJ and apply Pythagoras's theorem in each.

Now, it suffices to note that KL = KM + LM, so

or, dividing by 2*squareroot(pqr), we get the desired result:

Inverting and squaring this yields the formula for r:

This gives us the means to construct this figure on paper using a compass and a marked ruler. Having chosen two radii p and q and constructed the two large circles (remember that AB=p+q) and a line tangent to both, placing M and C is done after calculating the lengths IK=CM=r and IC=KM=2*sqrt(pr).

Gimont

During my only winter down South, way back when I'd do road trips (solo of course), I set out from Toulouse for a day to visit Auch, with a break in the countryside each way, partly to admire the snow on the Pyrenees. This first picture was taken on the outbound leg, and I forget where it was.

On the return leg, I stopped at Gimont, possibly drawn in by the distinctive church. There is also a Cahuzac Chapel next to the town, which gets a laugh because it has the same name as a former budget minister who was convicted for tax evasion. The shameless git even tried to run for Parliament again once his ineligibility sentence was served. Same name, but no relation, I should stress.

Like a lot of places in this corner of France, there are a lot of brick buildings in Gimont, and some peculiar traditional structures, like the Halle covered market. Inexplicably, a road runs through it.

The town also boasted a world-class motocross track, which hosted rounds of the 250cc World Championship in 1985 and 1990. But in 2019, so not long after my visit, the land owner wanted their turf back, and the Gimont Moto Club has since been looking for another location to open a new circuit. Here's how it rode:

Ichibata Dentetsu

The only train to Izumo Taisha is operated by private company Ichibata Dentetsu, or Bataden. Twas not always thus, as the JNR had a short 7 km branch line from Izumo-shi to Taisha until 1990. It was served by direct expresses from Nagoya and Kanazawa (11-hour day express Taisha) and night expresses from Ôsaka (Daisen).

But Bataden is no upstart, they've been around for a long time. They've been connecting Matsue Shinjiko-Onsen, Dentetsu Izumo-shi (neighbour to JR Izumo-shi) to Izumo Taisha-mae since the 1920s. On of their trains of the time was the DeHaNi 50, left in its refurbished DeHa 50 form. On the right is the 7000 Series, the company's newest model... and their first new train since the DeHaNi 50!

In the 90-year interim, Ichibata has relied on second-hand trains (yes, that's a thing in Japan), mostly from Tokyo-based Keiô. A rather nice retreat for these vehicles, from the crowded suburban lines around the capital, to scenic moseys around Lake Shinji... There are some special liveries and trains, such as Shimane-no-ki below, with some nice wooden decking inside, and single-seat semi-compartments! "Wait, is this First class?", I remember thinking to myself.

Hormone is apparently short for ホルモン焼き, horumon-yaki, a dish that originated in Ôsaka. It is made from miscellaneous organs, but the organs aren't where the hormones come from... It is marketed as a meal that can improve stamina, but ホルモン is also close to 放る物, read hôrumon in the local dialect ôsaka-ben, which means "discarded things", which is what horumon-yaki is made of. Maybe the latter came first, and was construed in to ホルモン as a kind of joke.

With thanks to @felvass for the hint.

Friendly faces on Dôtonbori

Dôtonbori is the street to go restaurant crawling in Ôsaka (if you have the stomach). As there's a lot of venues, there's a lot of competition, so a lot of wacky stuff to draw the passer-by's attention.

If anyone knows why this restaurant is called Shôwa Hormone, please let me know. Shôwa, I can guess, is nostalgia for the post-war Shôwa era; but Hormone needs a good story behind it!

Is this guy mad at people double-dipping their fried skewers?

By the way, that's two fronts featuring another monument of Ôsaka, Tsutenkaku tower, just in case you forgot where you were.

Finally, we have this guy, a true local hero: Kuidaore Tarô. This animatronic was introduced in 1950 as a mascot for the Cuidaore restaurant, which has since closed, but Tarô and his drumming were such a stable of Dôtonbori, that people clamoured to have him back.

I dunno. I think he looks like Brains from Thunderbirds under the influence of the Mysterons. A figure of his time though.

"Kuidaore" by the way, is from the proverb:

京都の着倒れ、大阪の食い倒れ Kyôto no ki-daore, Ôsaka no kui-daore Spend all your money on clothes in Kyôto, and on food in Ôsaka

Today, "kuidaore" is colloquially translated as "eat until you drop" - so go restaurant crawling if you can!

"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!

Sangaku Sunday #6

We are about to solve our first sangaku problem, as seen on the tablet shown above from Miminashi-yamaguchi-jinja in Kashihara.

First, we should conclude our discussion: what are sangaku for? There's the religious function, as an offering, and this offering was put on display for all to see, though not all fully understood the problems and their solutions. But a few people would understand, and these would have been the mathematicians of the time. When they visited a new town, they would typically stop at a temple or shrine for some prayers, and they would see the sangaku, a sample of what the local mathematicians were capable of. Whether the problems were solved or open, the visitor could take up the challenges and find the authors to discuss.

And this is where everything lined up: the local school of mathematics would have someone new to talk to, possibly to impress or be impressed by, and maybe even recruit. With the Japanese-style mathematics of the time, called wasan, being considered something of an art form, there would be masters and apprentices, and the sangaku was therefore a means to perpetuate the art.

Now, what about that configuration of circles, second from right on the tablet?

Recall that we had a formula for the radii of three circles which are pairwise tangent and all tangent to the same line. Calling the radii p, q, r, s and t for the circles of centres A, B, C, D and E respectively, we have

for the circles with centres A, B and C (our previous problem), and adapting this formula to two other systems of three circles, we get

for the circles with centres A, C and D, and

for the circles with centres B, C and E. Add these together, and use the first relation on the right-hand side, we get a rather elegant relation between all five radii:

Of course, we can get formulas for s and t,

r having been calculated previously using just p and q, which were our starting radii.

For example, setting p=4 and q=3, we get, approximately, r=0.86, s=0.4 and t=0.37 (this is the configuration shown in the figure, not necessarily the one on the tablet - I will be able to make remarks about that on another example).

ICE 3 (Gen.1)

After visiting Karlsruhe Palace, I had a bit of time while waiting for a (packed) regional train South to wander around the station. There was quite a lot going on, as on top of the local traffic from S-Bahns to REs, busy intercity lines to Freiburg and Basel, Stuttgart and Munich, Mannheim and Frankfurt meet here. A chance to see my favourite German high-speed train: the Baureihe 403 ICE 3.

Entering service in 2000, over 10 years after the first InterCity Expresses, the ICE 3 was a revolution in European high-speed rail. These were the first 300 km/h-capable trains that weren't of a "power car & carriages" layout, using distributed traction (motors all along the unit) like Shinkansen trains. And a sleek shape to boot! They were designed by Alexander Neumeister, who also penned the 500 Series Shinkansen. Hmm, maybe that's why.

The ICE 3 would be the first example of Siemens's Velaro series, which would be an export hit: the Netherlands, Spain, China and Russia purchased this model. The type received a redesign in the late 2000s that I could only describe as "more beefy": the Velaro D was taken up by Germany, Turkey and Eurostar.