Suspension bridges
You must have seen the Golden Gate bridge or one of the other suspension bridges during your travels. What curve do the cables follow?
Admittedly, this is a bit mathematical. Hence, I shall abstain from giving points if someone complains. Otherwise, 1 point!
ps: Check out Manoj's angle trisection comments at http://xyfactor.blogspot.com/2006/05/trisect-angle.html
Admittedly, this is a bit mathematical. Hence, I shall abstain from giving points if someone complains. Otherwise, 1 point!
It gets somewhat interesting after you solve the problem. Shown below is a stolen picture of the chelsea bridge. In red diamond symbols are second order polynomial fits to the main cable. I simply digitized the middle cable and fitted it in matlab. While the good fit makes it very tempting to conclude that its a proof for a parabolic curve, the catenoid can also be series expanded to a parabola accurate to 4th order! Any small error in curve fit could push it this way or that. So, I guess the fitting does not say anything useful other than the fact that the cable is roughly a parabola.
ps: Check out Manoj's angle trisection comments at http://xyfactor.blogspot.com/2006/05/trisect-angle.html
posted by littlecow at 9/23/2006 09:05:00 PM
2 Comments:
A very fine answer indeed, Manoj. Welcome to the points table!
Grenade: To add to what you have said, I have noticed some bridges are slightly curved up (convex upwards). Perhaps a trick to keep the concrete in compression? (concrete is very weak in tension but is considerably stronger in compression).
Isn't that cure a cosh(x) curve if its hanging by its own weight??
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