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# Is there any man-made object so long that it won't lie flat?October 17, 2013 8:23 AM   Subscribe

In other words, something, like a pipe, that is so long and straight that it can't be laid flat on the earth because of the latter's curvature?
posted by gnossie to science & nature (26 answers total) 5 users marked this as a favorite

This is a questions that gets down to the definition of what "straight" means. People have discussed this topic before.
posted by jessamyn at 8:29 AM on October 17 [1 favorite]

...but SLAC is probably a good bet.
posted by katrielalex at 8:32 AM on October 17

The curvature of the earth is eight inches per mile -- natural variation in ground elevation is going to be much more significant.
posted by ook at 8:34 AM on October 17 [15 favorites]

I believe that the beamline at the Stanford Linear Collider is straight (in the sense that a light beam follows a straight line.) If the Earth was a perfect sphere, the center of the beamline would be about a foot closer to the center of the Earth than its ends would be.
posted by Johnny Assay at 8:35 AM on October 17 [3 favorites]

(And if you assume for the purposes of the question that the earth is a perfect sphere, then a straight object of any length will not lie flat on the curved surface, because geometry.)
posted by ook at 8:36 AM on October 17 [13 favorites]

Yeah, really depends on what you mean.

Take, for example, particle accelerators. The LHC is a ring some 17m in circumference, call it 5.4mi across. It's so big, and the experiments being conducted therein so sensitive, that it's affected by the gravity of the moon. They actually have to make adjustments to the geometry to account for that.

As noted, the curvature of the Earth is about eight inches per mile. So if it were perfectly "straight," each end of the ring would be about two feet further/closer /from/to the center of the Earth than the center would. Of course, they had to take that into account when they built the thing, as that would have a minute but non-zero effect on the magnitude of gravity. The fact that you could shoot a laser the whole way around the center does not, in fact, require that the actual shape be perfectly flat.

Extrapolate from there, and yes, definitely. Any plumbing system that is a mile long will need to account for an eight-inch change in elevation over the course of its length.
posted by valkyryn at 8:38 AM on October 17

Also, in discussions about "the curvature of the earth", not only is the earth an oblate spheroid (distance from pole to pole through the center is less than a similar measurement between two equatorial points), but density differences mean that if you measure "the center" by taking measurements of "down" from different places on the earth, you don't necessarily end up at the same center point.
posted by straw at 8:47 AM on October 17

Of course, finding a material that is lightweight and rigid enough not to bend / sag by eight inches over the course of a mile is a trick in and of itself.
posted by KathrynT at 8:48 AM on October 17 [14 favorites]

Let's accept the implied premise of the question, i.e. that you could find a place on the surface of the earth, on land, that was perfectly smooth, so that the curvature of the earth was the only geometric deviation from a flat plane. Then, I believe the answer is "No", simply because we don't have any materials that are rigid enough to avoid sagging or breaking under their own weight.

Imagine a steel I-beam, say a mile long. If you laid it down on the assumed perfect surface, it would bend to conform to the curvature. Anyone who has seen plate glass flex in a wind storm knows that crystalline structures would do the same thing. If something could be made so rigid that it wouldn't bend, I believe it would break.
posted by dinger at 8:56 AM on October 17 [1 favorite]

Tip o' the hat, KathrynT. You beat me to it.
posted by dinger at 8:58 AM on October 17 [2 favorites]

Any big bridge isn't "straight" in the Cartesian sense. Wikipedia claims the Verrazano Narrows Bridge is angled such that the tops of the towers are 1 5/8 inches (4 cm) further apart at the top.
posted by wnissen at 8:58 AM on October 17

A laser beam won't follow the curvature of the earth. It will bend somewhat, but not by much. I don't know if you count that as an object, but nonetheless.
posted by MuffinMan at 8:59 AM on October 17 [1 favorite]

We know that bridges and other large structures are designed with the earth's curvature in mind, but the question seems to imply a straight, rigid, moveable man-made object, being laid on a perfectly flat surface that conforms to the curving surface of the earth. As indicated in previous answers, such a surface would have a deviation of eight inches per mile, or two inches per quarter mile.

The longest man-made straight, rigid, moveable object that comes to mind would be the longest ship afloat, the oil tanker Jahre Viking, which is 1504 feet long. Presumably, it's keel is intended to be perfectly straight for most of that length, which is about a quarter of a mile. If we placed this ship on a perfectly "flat" surface that conformed to the curvature of the earth, we would expect it to balance in the middle and for the ends to be raised one inch off the surface, because of the two-inch per quarter mile deviation described above.

In reality, however, that ship, nor any other object so large, would follow whatever curvature is built into the surface and lay flat on it, because it is not rigid — in fact flexibility is built into it on purpose to allow it to flex with the waves. Similarly flexibility is built into skyscrapers to sway a little in the wind. Without this flexibility, ships and skyscrapers would break under high stresses.

So, the answer is: a theoretical rigid, straight object a quarter mile long, laid on a theoretical flat surface following the earth's curvature, would theoretically not lay flat but be up an inch at each end. But no such object exists, or could be made, and no such surface exists (though it probably could be made). (Come to think of it, a perfectly frozen lake probably comes pretty close.)
posted by beagle at 9:24 AM on October 17 [1 favorite]

Come to think of it, a perfectly frozen lake probably comes pretty close.

Nah, the water follows the curvature of the earth, too.
posted by Specklet at 9:37 AM on October 17

Specklet: Nah, the water follows the curvature of the earth, too.

Yes, that's what I'm saying. The lake comes pretty close to being the perfectly flat surface that follows the curvature. Now we need the rigid object to lay down on it, without breaking the ice.
posted by beagle at 9:39 AM on October 17 [1 favorite]

This was discovered in the 19th century when they started extruding longer steel rail. A rail can be made to come out of the die perfectly straight - but once they started reaching 500' or so, they found that they'd rock slightly when laid on the (curved...) ground. Shorter rails were found to actually be better at fitting the globe.

(And wow, I wish I had a source for this factoid, but I learned it by osmosis, hanging around engineering school.)
posted by AsYouKnow Bob at 9:41 AM on October 17 [7 favorites]

a perfectly frozen lake probably comes pretty close.

Ice is flexible.
posted by KokuRyu at 9:45 AM on October 17 [1 favorite]

Yeah...not even a beam of laser light will stay (perfectly) straight when tangent to the earth's surface. "Mass tells space-time how to curve, and space-time tells mass how to move."--John Wheeler
Even though the light itself is massless, it is still curved because the space it moves through is bent by the earth's gravity.
posted by sexyrobot at 9:46 AM on October 17 [1 favorite]

Carbyne might be strong enough to do what you are suggesting, gnossie, if it can eventually be made into anything. It is twice as stiff as any known substance.
posted by MuffinMan at 9:49 AM on October 17

But wait...

A pipeline could be laid on pylons that themselves account for the earth's curvature and terrain fluctuations, I guess. Is there anything like that?
posted by MrMoonPie at 9:52 AM on October 17

It's not quite the same, but the reflecting pool at the Christian Science Mother Church in Boston had to account for the curvature of the earth, or water would have only flowed over the edges in the middle. Other reflecting pools probably have the same calculations added.

Also not the same, but beams of light from beacons such as lighthouses are positioned so that they are visible further over the curvature of the earth in places where the light needs to be visible further out.
posted by ldthomps at 10:23 AM on October 17 [2 favorites]

Yeah...not even a beam of laser light will stay (perfectly) straight when tangent to the earth's surface.

It will stay straight by definition, no? If not, then what is straighter than light? It is following a geodesic.
posted by vacapinta at 10:49 AM on October 17

A frozen lake wouldn't be flat, unless it's flash frozen in an environment with no wind and even heat. Anyone that has shoveled off a spot on a lake to skate on could probably tell you there are often lumps and bumps depending on how/when/where it was frozen.
posted by blue_beetle at 10:51 AM on October 17 [1 favorite]

It will stay straight by definition, no? If not, then what is straighter than light? It is following a geodesic.

It's only straight in that it's following the local gravitational curvature of space/time. It's only "relatively" straight.
posted by blue_beetle at 10:52 AM on October 17 [1 favorite]

The curvature of a beam of light due to gravitational lensing is a couple orders of magnitude smaller than the curvature of the earth. For purposes of this question, I think it's reasonable to say a beam of light is straight. But it's not really an "object" in the sense of the question.
posted by miyabo at 11:19 AM on October 17

This was discovered in the 19th century when they started extruding longer steel rail. A rail can be made to come out of the die perfectly straight - but once they started reaching 500' or so, they found that they'd rock slightly when laid on the (curved...) ground. Shorter rails were found to actually be better at fitting the globe.

Rails are actually pretty flexible and bend easily. Continuous welded rail today comes out of the factory in 1320-foot lengths moving directly onto a train of flat cars. The trainload of 1320-foot rails has no problem bending around curves and over hills as you can see in this video. The rails bend just as easily when laid on the ground to accommodate hills and curves as you can see in this video.
posted by JackFlash at 11:56 AM on October 17 [5 favorites]

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