A Pendulum Day

“I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth.”
― Umberto Eco, Foucault’s Pendulum

But if fell later as they tried to move another piece. Note the rare “suspended section” of blocks. I’m not sure of the physics of leaving a few behind for a handful of microseconds.

Along with my Difficult Reading Book Club I’m plowing ahead through Umberto Eco’s Foucault’s Pendulum – ten pages or so a day. It’s enjoyable, though truly difficult. I feel I should be looking up every odd word – searching out details on every unique concept – but there are pages to get through so I soldier on. Have to come back later. I’d take notes – but they would be longer than the tome itself.

One concept that haunts my dreams is the eponymous swinging orb. I knew about the Foucault Pendulum, of course. I have even seen one – a big, famous one – at the Smithsonian in Washington (though it looks like it isn’t there any more). I knew the theory, that the pendulum is actually always going in the same plane, but the earth moves under it. The more I thought about it the more I realized it isn’t that simple.

What follows is some boring, technical crap. If that doesn’t interest you, here’s some cute cat photos.

Ok, I can imagine a Foucault Pendulum at the North Pole. I can see it moving around in 24 hours.

But, I thought, what about one at the equator? Wouldn’t it be stationary?

So I looked it up online and I was right. It would not move.

But what threw me off were the latitudes in between. Because there is an angle between the string of the pendulum and the rotation of the earth – it rotates, but slower. The closer to the equator, the longer it takes to go around. The precession period for an ideal pendulum and support system is 23.93 hours (a sidereal day) divided by the sine of the latitude. In the middle of the US, this is about 32 hours. This period of time is called a pendulum day.

sidereal day(23.93 hours)<solar day(24 hours)<pendulum day(varies by latitude) (though I guess there is a latitude near the north pole where the pendulum day is the same as the solar day….)

The problem that I have is this: imagine the pendulum at our latitude… it goes through a 24-hr. cycle… now the pendulum is in exactly (more or less) the same spot that it was at the beginning… yet the pendulum, because the pendulum day is longer than 24 hours, is not at the same spot.

If the pendulum is truly staying the same… and the earth moving beneath it… why doesn’t it return to the same relative spot in 24 hours?

I spent way too much time thinking about it. I kept thinking about cones.

I’m not sure I’ve completely worked it out – but this site helps. Here is the meat of the text:

The ‘plane’ of the pendulum’s swing is not fixed in space

It is worthwhile correcting a common misunderstanding about Foucault’s Pendulum. It is sometimes said (perhaps poetically) that the pendulum swings in a plane fixed with respect to the distant stars while the Earth rotates beneath it. This is true at the poles. (It is also true for a pendulum swinging East-West at the equator.) At all other latitudes, however, it is not true. At all other latitudes, the plane of the pendulum’s motion rotates with respect to an inertial frame.

It is easy to deal with this misunderstanding. Consider a pendulum at the equator, swinging in a North South plane. It’s obvious from symmetry that the plane of this pendulum doesn’t rotate with respect to the earth and that, relative to an inertial frame, it rotates once every 24 hours.

Alternatively, consider the motion of a point on the earth at a place that is neither at the poles or the equator. During a day, a vertical line at that place traces out a cone, as shown in the sketch at right. (If the earth were not turning, the half angle of the cone would be 90° minus the latitude.) During each cycle of the pendulum, when it reaches its lowest point its supporting wire passes very close to the vertical. So, at each lowest point of the pendulum, its wire is a different line in this cone. This cone is not a plane, so those lines do not all lie in the same plane!

For yet another argument, consider the motion of the pendulum after one rotation of the earth. With respect to the earth, the period of precession of the pendulum is 23.9 hours divided by the sine of the latitude. For most latitudes, this is considerably longer than a day. So, after the earth has turned once, the pendulum has not returned to its original plane with respect to the earth. For example, our pendulum in Sydney precesses at a rate of one degree every seven minutes, or one complete circle in 43 hours.

(I apologize for emphasizing this rather obvious point. I only do so because a correspondent has pointed out to me that many web pages about the Foucault pendulum – and even, allegedly, a few old text books! – make the mistake of stating that the pendulum swings in a fixed plane while the earth rotates beneath it.)

So, what is the path of motion of the pendulum? Remember that the point of suspension of the pendulum is accelerating around Earth’s axis. So the forces acting on the pendulum are a little complicated, and to describe its motion requires some mathematics. (Indeed, even talking of a ‘plane’ of motion on a short time scale is an approximation because even in half a cycle the supporting wire actually sweeps out a very slightly curved surface.)

Now my head hurts. Unfortunately I can’t relax. I have my reading to do.

Sweet dreams.

Solar Impulse

I had a very busy day planned for today – work in the morning, appointments in Richardson at two, Frisco at three, and Plano at six. Still, there was a gap in there and I found out that there was a chance to go see the Solar Impulse out at DFW Airport before it flies to St. Louis.

Solar Impulse is a Swiss solar-powered aircraft, now on a tour of the US. I had eagerly watched it on the news as it flew from San Francisco to Phoenix and then on to Dallas/Forth Worth. I really wanted to see it in the air, but that requires timing and time I don’t possess, so I had to settle for a visit to the hanger.

I carefully plotted my driving around the city and arrived at the airport early. We took a shuttle bus from the designated parking area to a large temporary hanger where the aircraft was displayed.

Even grounded inside a tent-like hanger it was an amazing sight. It is a huge monster of an aircraft, especially when you consider it only holds one person. With its incredible wingspan and delicate construction it has a look of gentle grace and efficiency that is obvious even when it isn’t moving. I wandered among the onlookers, snapping photos, talking to the crew that was hanging around, and then simply looking, trying to soak up as much of the uniqueness and innovative spirit that I could.

It is something that, under idea conditions, can fly forever – charging its batteries by day. It’s only limits are the weather conditions and how long the pilot can go without sleep. There is no beauty more sublime and powerful than that of something that works so well and so perfectly.

I’m wondering when it will be able to leave. Obviously, it requires still air conditions to take off and the southern gale force winds that have been rocking the area show no signs of abating. It was a strange contrast – the delicate plane, resting peacefully, while a constant howling and snapping din slammed around it – caused by the terrific wind whipping the fabric of the temporary hanger into a frenzy. The sound was so loud that it almost drowned out the thundering roar of the jets taking off from the runway next to the hanger.

Solar Impulse

Solar Impulse

Solar Impulse

Solar Impulse

Little guy hanging out in the cockpit of the Solar Impulse

Little guy hanging out in the cockpit of the Solar Impulse

Demonstrating the construction techniques of the Solar Impulse

Demonstrating the construction techniques of the Solar Impulse

It's impossible to photograph and difficult to describe how long and slender that wing is.

It’s impossible to photograph and difficult to describe how long and slender that wing is.

The Shuttle, then and now

NASA Photo

Today I walked down to the break area at work to get some ice and I saw a small clot of folks gathered around the television, holding their coffee and watching the screen. I glanced to see what had their attention and saw footage of the Space Shuttle Discovery strapped to the top of a Boeing 747 on its way to Dulles airport and the Smithsonian.

That scene brought back a long-ago memory for me.

It was… maybe 1980 or so. I was working for a salt company in Hutchinson, Kansas. We had bought a small solar salt company in Utah. The production method was to pump saline water from the lake into a series of crystallization ponds and let the sun evaporate the water over the summer, leaving a layer of salt on the bottom of the shallow ponds. This would be picked up by a loader, screened and packed into bags, and then shipped out for animal feed or de-icing.

The company offices and warehouse were in Ogden, but the production ponds were located on the Great Salt Lake in a very isolated location – a little ways around the tip of Promontory Pont.

There are several large, successful evaporation operations on the lake… this was not one of those. It was a small company that made some salt from a few acres of ponds. It was called the Lake Crystal Salt company and its location on the remote arm of the lake (sealed off, more or less, from the rest of the lake by a railroad causeway) gave it access to some concentrated brine, and it did produce a lot of salt in its tiny ponds.

It’s long out of business, but looking at google maps, the ponds are still there (I’ll remember the shape of those ponds ‘til the day I die).

At any rate, part of my job was to fly up to Utah at the end of the summer to do an inventory of the salt that had been produced in the evaporation ponds during the warm season. We had designed and built a core drilling machine out of a gasoline powered post hole digger and would don rubber boots and walk around the ponds in a grid pattern, drilling holes down through the salt to the hardpan beneath. I would reach down the hole with a tape measure and determine the depth of the salt. I still have small scars on my hands from where the rough salt crystals and harsh concentrated brine would scrape at my skin. I would then take all these measurements and use them to calculate how many thousands of tons of salt we would have for sale after it was harversted (harvested… it was surprisingly like farming).

It was a two – man job, so I would hire a laborer in Ogden and the two of us would drive out every morning to the site. It was a long drive through some very desolate country. A handful of workers lived in a dormitory out there, only coming back on weekends – but I didn’t want a part of that, so I stayed in a hotel.

It was quite a drive and to have time to get any work done we would leave Ogden well before dawn. From Ogden north to Brigham City and then west, out across the mountains and desert until we could curve south down the length of the Promontory Point peninsula. The sun would rise behind us and light the beautiful, rugged, isolated mountains in a golden fire.

One morning, as we were driving, not another car or soul in sight for miles, I spotted, way up ahead, something odd. It was an aircraft of some type. It looked like a biplane, though something was off. Distances are hard to judge in the desert, but it looked a long way away. That would mean it was huge. It was flying very low, however, so I wasn’t sure about that. As I watched, it flew behind a large mesa and I lost sight of it.

“What was that? Did you see that?” I asked my worker.

“I think I saw something, but I don’t know what it was,” he said.

We drove on, scouring the sky until we reached the opposite end of the mesa. Suddenly a huge, ungainly aircraft lumbered out from behind the rock and crossed the highway directly in front of us. It was no more than a hundred yards off the ground and no more than two hundred in front of us. I slammed the brakes and skidded to a stop on the shoulder. My worker and I tumbled out of the car and stood in the desert, our mouths hanging open as the plane slowly curved around us. We were gobsmacked. It looked so close we could reach out and touch it.

It was the Space Shuttle attached to the top of a 747. Keep in mind this was 1980 and the shuttle wouldn’t make its first powered flight for another year. My memory is a little hazy but I think we saw the Colombia on its way to Florida for its first launch. We had seen pictures of the shuttle and its transportation 747, but on the tiny television screens of the day. To see the thing live, so close, coursing through the crystal clear high desert air at dawn, unexpected in the middle of nowhere, was an astounding sight.

It flew past us and then disappeared behind another mountain. We climbed back in the car, drove on out to the evaporation ponds and put in a full day of work.

That night I watched the Salt Lake City news on my hotel television and they covered the landing of the shuttle at a nearby air base. They said that they had flown the shuttle past the Morton Thiokol plant out in the Utah desert mountains where they were building the solid rocket boosters to give the workers a view of what they were working on. On my next drive out to the ponds I looked closely and could pick out burned spots on the mountains where the engines had been tested.

I saw the Colombia once more, over Dallas, one morning twenty three years later. It was a nice day and we had the front door open to get some fresh air in the house and I was shaken by a loud boom from the sky. We rushed out to see the smoke trails in the heavens.The Colombia was breaking up over the metroplex to die and fall in a million pieces on in the East Texas Piney Woods.