What Shape Does a Catenary Shadow Form on a Cylinder?

Click For Summary
SUMMARY

The discussion centers on the shape of a shadow cast by a catenary powerline on a cylindrical grain bin. The powerline, assumed to be a catenary, appears to project a shadow that resembles a segment of a circle on the grain bin, which is oriented vertically. The user questions whether this shape is a known conic section, suggesting that the projection may involve hyperbolic cosines and could be a parabola or hyperbola. Additionally, the user seeks clarification on the conditions that define a catenary, specifically regarding weight distribution along the wire.

PREREQUISITES
  • Understanding of catenary curves and their mathematical properties
  • Familiarity with conic sections, particularly parabolas and hyperbolas
  • Basic knowledge of geometry related to cylindrical shapes
  • Awareness of the principles of shadow projection in geometry
NEXT STEPS
  • Research the mathematical equations governing catenary curves and their applications
  • Explore the properties of conic sections, focusing on parabolas and hyperbolas
  • Study the geometric principles of shadow projection on cylindrical surfaces
  • Investigate the physics of tension and weight distribution in cables and suspension systems
USEFUL FOR

Mathematicians, physicists, engineers, and anyone interested in the geometric properties of shadows and catenary curves.

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
4K
Is my fictional Solar System stable and realistic?
  • · Replies 21 ·
Replies
21
Views
5K