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.
Maybe you all knew that factoid already, but I learned the name of shape only recently.
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.
https://www.nps.gov/jeff/planyourvisit/materials-and-techniq...
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_catenar...
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).