What Shape Does a Catenary Shadow Form on a Cylinder?

Click For Summary

Discussion Overview

The discussion revolves around the shape formed by the shadow of a catenary on a cylindrical object, specifically a grain bin. Participants explore the geometric implications of the shadow cast by a powerline, which is assumed to be a catenary, under a specific sun angle. The inquiry touches on theoretical aspects of catenaries and their projections onto cylindrical surfaces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant observed a shadow of a powerline, which they assume is a catenary, on a cylindrical grain bin and questioned the nature of the shadow's shape.
  • Another participant suggested that the shadow is likely a conic shape, noting that catenaries involve hyperbolic cosines and that the projection could be a parabola or hyperbola.
  • A participant expressed curiosity about the conditions under which a catenary is formed, asking for clarification on the definitions related to the weight per unit distance of the wire versus the weight distribution along its length.

Areas of Agreement / Disagreement

Participants generally agree that the shadow is an interesting shape, but there is no consensus on the exact nature of the shadow or the conditions that define a catenary.

Contextual Notes

The discussion includes assumptions about the alignment of the powerline and grain bin, as well as the sun angle, which may affect the perceived shape of the shadow. There are also unresolved distinctions regarding the definitions of catenary formation.

tasp77
Messages
74
Reaction score
0
I saw a shadow of a catenary (or close enough) on a cylinder and wondered about the shape.

Specifically, it was a powerline strung between 2 utility poles, and the sun angle would have been around 45 degrees or so, and the cylindrical grain bin was between and north (I am in northern hemisphere) of the poles. The powerline I assume is a catenary, although it would be close to a parabola, right?, and the grain bin would be a vertically oriented cylinder to pretty high precision (neglecting corrugations).

The shadow of the powerline appeared to define a plane on the grain bin, but that is just to me and my bifocals. And the shadow also looked from a distance to be a segment of a circle, but I find that difficult to fathom, as how would a circular cylinder (so to speak) cancel out (so to speak) the catenariness of the shadow?

Anyhow, is this an interesting (and previously identified) shape?
 
Physics news on Phys.org
It's definitely an interesting shape and very likely to be a conic - catenaries have hyperbolic cosines in their equation & the projection is likely to be a parabola/hyperbola.
 
Hey thanks!

I don't think the powerline guys or the farmer oriented their items to amuse me, the alignment is just accidental, and it is clearly visible from the adjoining highway I travel on frequently, on sunny days.
 
BTW, is a catenary formed when the wire weighs the same per unit if distance, or is it when the weight per unit of distance the wire crosses the same?

Which is which, and what do we call the other one?

Examples would be for the first, just a wire hanging between 2 poles, for the second, it would be closer to a suspension bridge with the deck being of uniform weight all along its length.
 

Similar threads

Graduate Quantum Interest Conjecture and negative energy-density
  • · Replies 3 ·
Replies
3
Views
5K
Is my fictional Solar System stable and realistic?
  • · Replies 21 ·
Replies
21
Views
6K