What Shape Does a Catenary Shadow Form on a Cylinder?

[tasp77]

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?

 

[Eynstone]

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.

 

[tasp77]

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.

 

[tasp77]

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.