"Stick An Aircraft Engine In It" Part 1 - Boeing Jetfoil

Schauinsland

Since it's been mentioned in the comments on the previous post, we might as well have a look at the Schauinsland, a 1284 m peak on the outskirts of Freiburg im Breisgau. Only 7 km from the Schwabentor, the base is accessible by bus, before boarding a 3.6 km gondola lift ot the summit.

Opened in 1930, the Schauinslandbahn was the first gondola lift built for continuous operation, with the cabins running through each end station at slow speed to turn around while letting passengers off and on. The cable car takes the riders up the hill, offering panoramic views of the Black Forest. And then there's the view from the tower at the summit... I visited in summer, but it must be fantastic in winter too.

The cable car is not the only transport infrastructure to be found on the mountain, as mines operated there until the mid-20th century, so some mining railways with preserved vehicles can be found. Some of the tunnels can be visited (though writing this post reminds me, I haven't been inside yet).

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.

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.

Rheinfall: up close, personal and wet

Let's start by crunching the numbers: the Rhine falls in Switzerland are 23 m tall and 150 m wide (boat for scale). On average, in summer, 600 cubic metres of water pass through every second. That's 600 000 Litres - assuming you need 2 L of water per day and will live to 80 years old, that's easily 10 times more water than you will drink in your entire lifetime, past your eyes in one second. Every second. Of every day. They don't turn this off at night!

Obviously, this is quite the unstoppable force, and the people at Rheinfall have figured out several ways to allow visitors to witness this force up close. A trail down from Schloss Laufen to the river side includes several platforms right next to the rushing water. It's noisy, it's impressive, and definitely humbling to be almost in the path of a wall of water.

But several steps further are available: boat rides that go against the current, right into the stream of the waterfall, and, not to be outdone, a boat that goes to the jagged rock smack in the middle of the falls, and drops you off for 20 minutes. I didn't do those because I was wet enough just from the rain, but it was tempting. So was a zip line in the hills, but man, if there was a zip line crossing the Rhine in view of the falls - not over them directly because that would spoil it for everyone else, but around where one of the boat crossings is -, that would be incredible!

Speaking of that rock in the middle, I love it. It's a masterpiece of erosion, and still taking the full force of the Rhine... for now. In a few thousand years I guess we won't be sending so many people there.

Rheinfall: a second look

The weather improved greatly throughout my day at Schaffhausen, and I'd read that the falls are lit up at night, so I decided to give it a second look. And this was the view from the scenic Neuhausen Rheinfall station when I got back:

The falls roughly face West, so the evening is actually the best time to photograph them as the sunlight hits them directly.

Also, the boats stop at 6:30 in the summer, so we get a clearer view of the pool below, and no-one standing on the rock in the middle.

The trail on the Laufen side remains open though, so people can still see the falls up close, as described in the previous post.

The bridge on the far left of the top picture and at the back of the second picture is a rail bridge carrying the line from Neuhausen (central) to Schloss Laufen. It's no doubt one of the most spectacular in Europe, and it doubles up as a footbridge, allowing people to walk alongside some Swiss Dostos.

Oh, and they do light up the falls at night.

Hikone Sawayama: summit & castle

It's not about what is there today, as much as it's about what was there. Sawayama was the original location of Hikone Castle, and it is quite possibly the most important castle in Japan to have been completely lost, as it was the castle of Ishida Mitsunari, the leader of the Western Army which lost the battle to unite Japan following the death of Toyotomi Hideyoshi. There are so few traces of the castle, no obvious tell-tale structures... This small altar may trace its roots back to the days of the castle, or maybe not, but this is just about it.

Sawayama Castle was thoroughly dismanted after 1600 following the defeat of Ishida, as the new lord of the area, Ii Naomasa, appointed by the victorious Tokugawa clan, relocated the castle to a smaller hill closer to Lake Biwa. Hikone Castle, which still stands today, basically recycled the materials from Sawayama, and the view of the "new" castle complex and the lake is the main draw for hikers today.

The summit offers good views of the mountains on the other side too, with the industrial complexes near Maibara, most noticeably Fujitec and their 170 m-tall elevator test tower, in the foreground.

First Christmas Market of 2024

Not as early as Ebisu, but still, just over a month before Christmas, I got to my first market on 23 November. On our way to Thann with two fellow hikers, our train was delayed and we had half an hour to kill in Mulhouse. I know the city centre is quite nice, so we went there, and found the Christmas market!

Place de la Réunion is gorgeous with its trompe-l'oeil facades (walls that have bricks, columns and other ornaments drawn on them) and church, which, unusually for a major French town, is a Protestant temple. It's extra-special with Christmas decorations, such as the town hall seen above. The water mill wheel is the emblem of Mulhouse, referencing the name's origin, Mülhausen, "mill house".

The abandoned Arzviller-Henridorff "lock ladder"

On my return to the Plan Incliné (previous post) in 2021, I added a walk along some of the section that the boat lift bypassed. The canal behind this door (lock n°17) has been closed and emptied, the tranquil flow replaced by an overgrown stream, but the paths along it have been maintained, and some sections added to improve the walking or cycling experience.

The lock houses, homes to the workers, are still standing, some used by artists as galleries and workshops.

The boat lift was created to bypass a system of 17 consecutive locks which took a whole day to traverse. I didn't go along the whole route to lock n°1 (I probably would have if Arzviller train station was still open), but beyond the "lock ladder" on the Western side is a 2 km canal tunnel, still in service today and a bit of a traffic jam, as it isn't wide enough for two boats to pass.

I probably should walk the whole route one day. As it's along a canal, it should be easy gradients, it's just the distance between Réding and Lutzelbourg train stations that needs to be covered. I think it'll be worth it, and a chance to see the entrances to the tunnels too.

Hohentwiel fortress

We've seen the stunning volcanic surroundings of Hohentwiel, and managed the climb - now we're at the gates of the fortress. Or the... tunnels of the fortress?

The entrance tunnels are a recent addition to the fortress, in the sense that the 18th century is more recent than the 10th, when the castle was first mentioned. For around 900 years, Hohentwiel Castle stood, seemingly and effectively invincible, receiving updates in line with the battle tactics of the times, as this entrance tunnel leading to a forward bastion, shows.

Now we are at the actual gates, exceptionally wide open to allow traffic in to set up or take away festival equipment. I thought they were setting up, but I can't find a trace of what was due early August. The largest festival the castle hosts is late July, so maybe they were taking away... but wait a minute. This place hosts festivals. It's huge.

Hohentwiel Castle is on two levels. So let's assume you and your army have made the climb, survived the open trench in the middle of the tunnels, got through the gates - and your objective is still up there. A 15% incline and the upper fortress drawbridge and gates are yet to be passed.

Perhaps unsurprisingly at this stage, one understands how the castle went undefeated. Owned by Swabian then Württemberg dukes, it stood in the crossfire of French and Austrian troops during the Thirty-Years' War between 1618 and 1648 - and survived five sieges.

It was another major conflict, nearly two centuries later, that would claim the Hohentwiel. And even then, it wasn't taken over in battle. The territories Napoleon conquered included Württemberg, and the French Emperor ordered that the castle be decommissioned and ruined in 1803.

Undefended and stripped of meaningful material, the castle was open to the public, who quickly took a liking to the astounding views of the Hegau area and the Bodensee (Lake Constance) in the distance. It became a tourist destination as early as the 1840s. And, as mentioned before, today it hosts festivals.

Hohentwiel Castle is a fantastic visit. It is an enormous complex, with a lot of structure left. The history and stunning views make the effort to get there well worthwhile. I recommend hiking from Singen city centre if you can for the fuller sense of reward!

Shionomisaki: Honshu's southernmost point

Southern Kansai is probably best known for the Kumano Kodô, the pilgrimage routes related to the Nachi shrine and temple complex with one of Japan's most famous waterfalls. But Southern Kansai is also Southernmost Kansai, and the Shionomisaki peninsula, part of the town of Kushimoto is as South as it gets for the main island of Japan.

Beyond this lawn and those rocks is the Pacific Ocean: just water for thousands of kilometres in this direction! The nearest substantial landmass due South from here is Papua New Guinea, 35° latitude lower, or 10% of the Earth's circumference!

That's a nice lawn by the way, it would be a shame if someone...

Shionomisaki is basically Honshu's version of "Land's End" or "Finistere", and there is a little leisure complex to mark it. The recent Geopark Centre is good, but the blue buildings in the previous shot, the shop and restaurant and the observation tower, are from a different time and showing their age - case in point, the children's cups in the restaurant with the mascot of the 1998 World Cup in France!