Sunday, January 09, 2005

everything from the last two weeks

I've been off the blog for a while. We were spending a lot of time in the office, and not out in the field on the projects. I like field work, it gets me thinking.

New Year's was great. I never wrote about it before, but we've had three guests on and off, and on again, here at our place in Patan. Before Christmas, a friend from Stanford, Rosie, and two friends of hers from back home in Wyoming came through Kathmandu. They'd been in India since October, and stayed with us a few days before their trek to Everest Base Camp for Christmas. Did you know there's a wrecked Russian helicopter up there? It just stays. No one can bring it down. There are surprisingly few pictures of us with Rosie, Christina, and Jesse. Here's the best one:

Which is not good photography, like this:

The girls said the trek was incredible, and they got some amazing photos up there. Rosie put a lot of these Everest Trek photos up at rosieinnepal.

For New Year's, we spent the night in Thamel, the tourist hub of Kathmandu. If you look hard, the party in Thamel goes until 4 in the morning.

The girls left a lot of weight that they didn't want to pack onward to Thailand. I've started to read the 10 kg of books. I just got done with 'The Snow Leopard' - it's an account written by a guy who accompanied 'an eminent field biologist' to Inner Dolpo in 1971. Dolpo is usually grouped with Mustang as the two areas of Nepal that are the last vestiges of traditional Tibetan life on earth, where Tibetan Buddhism and the older religion B'on are practiced as they were hundreds of years ago, lamas live in remote monasteries overlooking lakes that no boat has ever been in, and life is largely spent on surviving at high altitude. The author writes a great deal about his calm introspections up there, on life and consciousness. Bill Murray said in Groundhog's Day that he saw himself, in five years, 'living at high altitude, where he can really think clearly'. That was a line to impress Andy McDowell.

Thinking about what I'm doing here in Nepal, I'm not living out Bill Murray's line, as Kathmandu is only at 1000 meters - and I'm not given to the introspections on consciousness that Peter Mattiesson was, as I'm not removed from all aspects of 20th/21st century life, living in an ancient society of eastern thought. I'm also not an eminent modern writer who's devoted the last ten years of my life to Buddhism. The point is, while the topic is not deep introspection on consciousness, I am given to thought here - much more than I was at home. The thoughts are on my own life and the things that interest me. I've been reading a lot, and have drawn up plans for ideas that come to me. I have more ideas here than I do at home, probably because of the distance from the usual distractions of my life.

Two of the things I've been thinking about are limits of linear analysis, and the implication of geometry on optimizing mechanical design. There are a lot of things structural engineeers learn in school that ME's don't, even though ME's need to optimize geometries too. ME's designs see more non-ideal loading I think, but I think there are common principles. The Tar Pul carriage supports, in the nominal case, two point loads of passengers, so why not make the nominal carraige frame a two-segment furnicular arch, then go from there. I should put up some pictures to make more sense about the carriage thing.

The furnicular curve is the line of zero bending moment - that sounds good to design a structure around, doesn't it? ME's have the advantage over structural engineers that we don't have to be as afraid of tensile and complex shear forces - it's steel tubes, not concrete. Furnicular lines got me thinking more about the Tar Pul wire, a suspended cable under its own weight with a few additonal point loads:

Looks easy, but the more you think about it, it isn't. What's the departing angle of the wire just on either side of the loads. Leibniz, Huygens, and Bernoulli's solved the math problem of the shape of a hanging wire in 1669 - it's a catenary curve. But, if you use that equation, do you get the unloaded Tar Pul wire's shape, really? The Tar Pul, like most suspended-cable systems, have rigid horizontal end conditions for the wires. With those end conditions, the wires have a finite 'tangency section' at the ends. How long is the horizontal section? That depends upon the preload and the the modulus of elasticity, I think. The point is, it gets complicated quickly. Now let's add some point loads. Math says if you add a point load, there's a discontinuity in the cable. A discontinuity in applied force is the same thing as a discontinuity of the curve, since the curve's derived from a force balance. But a wire can't have a discontinuity, or it would break. But no loads are point loads. So, the loads must be distributed per Hertzian contact stresses, the wire must be continuous, and each wire segment between loads must form a furnicular curve of zero bending moment. I think we're beyond the limits of linear analysis.

But then, there's another way to look at things, the way Roark's Formulas for Stress and Strain looks at beam problems. That book has formulas for cases like this:

It may even have formulas for tangent end conditions and non-central loading, I need to look. Their fomulas make up for the point-load discontinuity problem by considering the beam as having a modulus of elasticity, and able to take bending moments - so then it's non-fernicular. Maybe we should constrain the Tar Pul wire kinematically and use this method. Fernicular or beam analysis - that's the question. Either way, it proves to be a tough problem. Maybe someone's written a book about this kind of thing. Someone built all those ski lifts, right?

In other news, some friends of mine have put together a blog site on liberal politics and the environment - I like it a lot, if only because I know these people aren't wacko leftists with wacko leftist agendas, acting to counter the outrageous statements of wacko conservatives with equally outrageous wacko liberalism. They're 'thinking'. It's


At 9:02 PM, Anonymous said...

Beecher, you're a NERD! I'm glad to see that you're still kickin' and doing well. Next time I'm sitting on a chairlift I'll take notes -- maybe there's something tricky about the shape of the mount where the chair sits on the cable...a taper to a weak edge assures a continuous derivative, doesn't it?
Picture a three way circular teeter totter with robots driving around on it, and be glad we're not taking 218 this year. Except they get a module with PID control. But I bet Tar Puls are more rewarding...


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