Comments on: The Two Towers XIV: Heavy Lifting http://docisinblog.com/index.php/2006/09/17/two-towers-part-14/ a physician looks at medicine, religion, politics, pets, & passion in life Sun, 15 Apr 2012 21:54:50 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: karrde http://docisinblog.com/index.php/2006/09/17/two-towers-part-14/comment-page-1/#comment-3888 karrde Fri, 22 Sep 2006 00:50:50 +0000 http://docisinblog.com/archives/2006/09/17/two-towers-part-14/#comment-3888 Say, I was told that cables hanging freely in the way you described would follow a curve called a "hyperbolic cosine". (At least, called that by mathematicians.) However, the description I was given matches the description of a catenary. If you know what the natural number <i>e</i> is, you get the hyperbolic cosine by calculating the following: (1/2)(<i>ex+e-x</i>) Of course, I think the hyperbolic cosine is cool...it's got an elegance to it that not many math functions have. Say, I was told that cables hanging freely in the way you described would follow a curve called a “hyperbolic cosine”. (At least, called that by mathematicians.)

However, the description I was given matches the description of a catenary.

If you know what the natural number e is, you get the hyperbolic cosine by calculating the following:

(1/2)(ex+e-x)

Of course, I think the hyperbolic cosine is cool…it’s got an elegance to it that not many math functions have.

]]> By: Barry Pike http://docisinblog.com/index.php/2006/09/17/two-towers-part-14/comment-page-1/#comment-3886 Barry Pike Tue, 19 Sep 2006 19:46:41 +0000 http://docisinblog.com/archives/2006/09/17/two-towers-part-14/#comment-3886 Fascinating story. And your pictures are marvelous. Fascinating story. And your pictures are marvelous.

]]> By: Maggie's Farm http://docisinblog.com/index.php/2006/09/17/two-towers-part-14/comment-page-1/#comment-3883 Maggie's Farm Mon, 18 Sep 2006 21:38:49 +0000 http://docisinblog.com/archives/2006/09/17/two-towers-part-14/#comment-3883 <strong>Monday Evening Links: Employees Only...</strong> (h/t, No Pasaran, and Cox and Forkum)Terror fund-raising in Boston. Solomonia.Hey, Carl. We love your books, but what is this baloney? BabaluA quote from a predictably intelligent Oxblog piece:A bit ham-handed perhaps, but one might even have argued t... Monday Evening Links: Employees Only…

(h/t, No Pasaran, and Cox and Forkum)Terror fund-raising in Boston. Solomonia.Hey, Carl. We love your books, but what is this baloney? BabaluA quote from a predictably intelligent Oxblog piece:A bit ham-handed perhaps, but one might even have argued t…

]]> By: Dr Bob http://docisinblog.com/index.php/2006/09/17/two-towers-part-14/comment-page-1/#comment-3882 Dr Bob Mon, 18 Sep 2006 03:40:33 +0000 http://docisinblog.com/archives/2006/09/17/two-towers-part-14/#comment-3882 See, I just <em>knew </em>my readers could figure this stuff out in their heads... thanks for the clarification, Durb. See, I just knew my readers could figure this stuff out in their heads… thanks for the clarification, Durb.

]]> By: B. Durbin http://docisinblog.com/index.php/2006/09/17/two-towers-part-14/comment-page-1/#comment-3881 B. Durbin Sun, 17 Sep 2006 23:46:49 +0000 http://docisinblog.com/archives/2006/09/17/two-towers-part-14/#comment-3881 Incidentally, the shape of cables before the decking is lifted into place is a bit sharper than that of a parabola. That is because the weight of the cabling changes how the whole length hangs, and that form is called <a href="http://mathworld.wolfram.com/Catenary.html" rel="nofollow">a catenary</a>. (Once all of the decking is in place, the cables will once again form something close to a catenary, but it will probably be slightly different due to some of the decking weight being taken by the towers.) The reason I mention this is because an inverted catenary (aka catenary arch) is the strongest arch you can build, literally. The pressure is equally distributed along all points. When I took ceramics, our teacher showed us pictures of a kiln they had built that was a catenary kiln; they'd laid the bricks over the form and removed the form, then had someone sit on it to demonstrate its strength— before they'd put any kind of mortar in it. In other words, loose bricks. Very cool. *cough* I just think that catenaries are cool... Incidentally, the shape of cables before the decking is lifted into place is a bit sharper than that of a parabola. That is because the weight of the cabling changes how the whole length hangs, and that form is called a catenary. (Once all of the decking is in place, the cables will once again form something close to a catenary, but it will probably be slightly different due to some of the decking weight being taken by the towers.)

The reason I mention this is because an inverted catenary (aka catenary arch) is the strongest arch you can build, literally. The pressure is equally distributed along all points. When I took ceramics, our teacher showed us pictures of a kiln they had built that was a catenary kiln; they’d laid the bricks over the form and removed the form, then had someone sit on it to demonstrate its strength— before they’d put any kind of mortar in it. In other words, loose bricks. Very cool.

*cough*

I just think that catenaries are cool…

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