3 ms·

Hold a chain at its ends, and let it hang down naturally. What is that shape called? A catenary and its equation is y = a cosh(x/a). Maybe you all knew that f

by jpmattia 10mo ago

Hold a chain at its ends, and let it hang down naturally. What is that shape called? A catenary and its equation is y = a cosh(x/a). Maybe you all knew that factoid already, but I learned the name of shape only recently.

vasco 10mo ago
And efficiency of the line depends on the curvature so for a given target efficiency you can calculate how far apart the poles can be. For electrical lines I mean.
staplung 10mo ago
I actually did already know that factoid but was struggling (am still) to see how it relates to a wooden trough that merely holds cables. Another interesting factoid about the catenary: Robert Hooke proved that it takes on the shape (though inverted) of the ideal arch, in terms of supporting loads above it. La Sagrada Familia in Barcelona is filled with them.
- ninju 10mo ago
  The Gateway Arch is an inverted catenary structure https://www.nps.gov/jeff/planyourvisit/materials-and-techniques.htm#:~:text=The%20stainless%2Dsteel%2Dfaced%20Arch,hanging%20freely%20between%20two%20supports. https://www.nps.gov/jeff/planyourvisit/materials-and-techniq...
- SECProto 10mo ago
  > but was struggling (am still) to see how it relates to a wooden trough that merely holds cables. Overhead Catenary [1] is a standard term, for a system that has two wires overhead - one suspended from the posts (forming a series of catenary curve), the other suspended from that cable at regular intervals (and held level relative to the track). The wood in Boston's system seems to replace the catenary cable. [1] https://en.wikipedia.org/wiki/Overhead_line#Overhead_catenary https://en.wikipedia.org/wiki/Overhead_line#Overhead_catenar...
- IAmBroom 10mo ago
  In a nutshell, the overhead power lines hang from their support points as catenary curves. This is important to the design of trains, because you have to calculate the variance in height over the caternary length (highest at attachment point; lowest at somewhere near the middle, but depending on incline).

vasco 10mo ago

And efficiency of the line depends on the curvature so for a given target efficiency you can calculate how far apart the poles can be. For electrical lines I mean.

staplung 10mo ago

I actually did already know that factoid but was struggling (am still) to see how it relates to a wooden trough that merely holds cables. Another interesting factoid about the catenary: Robert Hooke proved that it takes on the shape (though inverted) of the ideal arch, in terms of supporting loads above it. La Sagrada Familia in Barcelona is filled with them.

ninju 10mo ago
The Gateway Arch is an inverted catenary structure https://www.nps.gov/jeff/planyourvisit/materials-and-techniques.htm#:~:text=The%20stainless%2Dsteel%2Dfaced%20Arch,hanging%20freely%20between%20two%20supports. https://www.nps.gov/jeff/planyourvisit/materials-and-techniq...
SECProto 10mo ago
> but was struggling (am still) to see how it relates to a wooden trough that merely holds cables. Overhead Catenary [1] is a standard term, for a system that has two wires overhead - one suspended from the posts (forming a series of catenary curve), the other suspended from that cable at regular intervals (and held level relative to the track). The wood in Boston's system seems to replace the catenary cable. [1] https://en.wikipedia.org/wiki/Overhead_line#Overhead_catenary https://en.wikipedia.org/wiki/Overhead_line#Overhead_catenar...
IAmBroom 10mo ago
In a nutshell, the overhead power lines hang from their support points as catenary curves. This is important to the design of trains, because you have to calculate the variance in height over the caternary length (highest at attachment point; lowest at somewhere near the middle, but depending on incline).