Does the design of a very large building have to account for the curvature of the Earth?

Factual Questions
21

Agree it doesn’t much matter when grading the construction site flat prior to erecting a structure; dirt is just not that precise. But when you want to install the floor, it may make a difference if you use a laser level or a water level. One of these methods will get you a floor that is laser flat, but is only truly level (with respect to gravity) at a single point. The other method will get you a floor that actually follows the curvature of the earth and is level at all points.

Having said that, the difference doesn’t matter much. 1 degree of circumference around the earth is about 69 miles. Taking an extreme example the Lockheed-Martin facility in Fort Worth, TX where F-16s are built, this building is about a mile long. If they used a laser level sited at one end of the building and poured the floor with reference to that beam, at the other end of the building the floor would be off-level by only about 0.0144 degrees. For most purposes, that’s not a big deal.

22

Here’s a (somewhat tedious) video on Earth curvature and the construction of LIGO from a flat-earth debunking channel:

23

Isn’t a poured concrete floor leveled by gravity? Seems to me it would conform to the curvature of the earth before drying.

24

Nah. Concrete is much too stiff to slump enough to level itself. The slump test for concrete quality has it form a quite significant mound when dumped from a cone form. Concrete is a non-Newtonian fluid, so behaves weirdly at best. This is one reason why they use vibrators to consolidate it. I guess if you were able to vibrate the entire pour as a single mass for long enough it might settle enough, but it would probably have long since set.

25

When required, by pouring (liquid) ‘leveling compound’ on top of the concrete.

Around here, done if they are laying floorboards on top.

26

Most suburban homes have a driveway that slopes downward toward the street, so if concrete were leveled by gravity, then most suburban homeowners wouldn’t be able to have a concrete driveway. There are limits, of course - you can’t sculpt wet concrete into a 20-foot tall wall and expect it to stay vertical - but it definitely doesn’t flow like water.

Wikipedia says the earth’s curvature was “taken in to account”, but it doesn’t say how, and there’s no cite, so I’m dubious. Assuming each of the two main support towers were independently constructed to local level, then the earth’s curvature wasn’t “taken into account” any more than it was for two unrelated buildings on the opposite sides of Manhattan. While the earth’s curvature definitely manifests in the extra distance between the tops of the towers, the only way I could think of that could actually matter WRT the design of the bridge would be the length of the main support cables, but we’re talking about an extra 1.625 inches on a main span of 51,120 inches. The seasonal thermal expansion/contraction of the cables is far greater than that.

The OP’s question was about whether there are actual cases for which it’s not negligible, i.e. do real-world architects and civil engineers have to consider the earth’s curvature when designing large structures. Respondents have shown that there are esoteric physics projects (e.g. SLAC, LIGO) with straightness requirements over long distances that can’t be met by following the earth’s curvature, but for even the largest conventional civil engineering projects - that is, structures on the order of 1000 feet tall and a mile long - I don’t think we can point to a project where it matters.

Part of the issue is that civil structures are generally made of individual components (e.g. steel beams) that are much smaller than the large dimensions under consideration here, and each component comes with its own shape tolerance, size tolerance, and installation tolerance. Taking the OP’s example, the Tesla factory probably will be made with steel columns on the order of 50 feet tall and maybe 100 feet apart. At that distance and size, the deviation from parallel between any two adjacent locally-vertical columns is 0.00027 degrees. According to this site on standard erection tolerances (hold your jokes), a 50’ tall column would be allowed to be off-plumb by 1 inch at its top, a deviation from local vertical of 0.191 degrees. Steel beams and trusses are imperfectly shaped/sized, bolt holes are imperfectly positioned, and all are imperfectly installed at the construction site. The allowed imperfections are hundreds of times greater than the deviations from rectilinear imposed by the earth’s curvature and are compensated for with oversized holes, shims, and lots of pounding and pulling by steelworkers to get it all put together. If you’re building a shopping mall or a battery factory, the errors introduced by the earth’s curvature get lost in the noise.

Edit: and now that I’ve said all that, here’s a case where the earth’s curvature did matter:

27

Damn, next you’re going to tell me pilots don’t have to make constant micro adjustments to counteract the Coriolis Effect or keep dropping the nose of the plane to avoid flying off into space!
All flat Earther tropes.

28

As seen in this Gish galloping thread

that at one point inadvertently ‘proves’ that the Moon doesn’t exist

29

Flerf is my guilty pleasure.
It was quite amusing to see the above YouTube link. 'Hey! Blue! “Light this dumpster fire”!

30

On my reading, the curvature that actually mattered was the East/West/North/South projection, not the vertical error. If you lay down straight railway rails on a sphere, not only will the ends rise off the surface, the corners won’t meet.

And on my reading, the curvature mattered for the reference plane, not for the design/construction.

31

Hello opiewan,
I made the Verrazzanno-Narrows Bridge calculation on my website
1728.org
(Scroll down to Puzzle #15)

32

Arguably this is also an interesting problem that gets things off rectilinear. How big does a building need to be before the walls are no longer straight or the corners no longer 90 degrees enough to matter?

I would expect that most surveying of buildings would use great circles to define lines, so less likely to be an issue. It is going to be a very big building before anyone notices that the angles don’t add up.

33

Turns out this is about projected coordinate systems (like UTM) — local flat planes that intersect the curving earth — vs. latitude/longitude (global system that follows the curves). To make sure the tunnels were located accurately (important to avoid all the stuff under central London), they had to make new maps with a new prime meridian.

34

Yeah, although it is even more horrendous than that. There are all manner of evil problems at play. The models used for the Earth have changed over the years (we now mostly use WGS84) but what rally screws around with mapping is the datum chosen for a UTM projection, and how large the individual projection is. When you project the spheroid onto a plane you choose where the plane touches the spheroid, and this defines the exact projection. One trouble is that no matter what you do, the scale changes across the map, with distances further from the centre being stretched more. Typically, rather than have the map plane touch the spheroid at point on the surface, the centre plane of the map is under the surface and the plane intersects the surface in a circle. Even then there isn’t a proper 1:1 scale, and a scale factor has to be included. Next you still suffer from the problem that when maps with different projections intersect, straight lines on the surface that cross map boundaries are kinked at the boundary.
So it appears that the rail system design had to create a new map set based upon a local datum, one that allowed them to minimise all the above issues.

In terms of the OP, this is still the original problem. It stems from issues with using a flat surface (the map) over the spheroid of the Earth. But rather than seeing height issues, we see it distort the geometry of the plan view.

This brings back mixed memories. Recently I had the job of creating dynamic map overlays for the entire Earth that could use a range of coordinate systems, and do so with enough precision that at the highest resolution accuracy was of the order of a metre. Getting things like UTM regions at the anti-meridian to work properly does one’s head in. Making it work properly at the poles similarly evil. Quaterions are your friend.

35

I believe that the runway for the Space Shuttle takes into account the curvature of the Earth.

I can’t find anything directly from NASA, but a couple of other places cite this.

"In the 1970s, NASA built its Shuttle Landing Facility (SLF) here to support its space missions. A 2.8-mile-long runway was constructed of concrete poured to compensate for the earth’s curvature. "

https://www.researchgate.net/publication/319380666_Atmospheric_characterization_on_the_Kennedy_Space_Center_Shuttle_Landing_Facility#pf9

" Experiments were conducted at the Kennedy Space Center (KSC) Shuttle Landing Facility (SLF) at multiple field deployments. The SLF (shown below in Figure 8) contains a 5 km long and 91 m grooved concrete runway that is corrected for the curvature of the Earth. This wide open and easily accessible location is conducive for long term optical testing over long ranges."

I’m taking a tiny grain of salt here, as I can’t find a specific cite from anything directly from NASA though.

36

Maybe a GPS controlled precision landing would demand that the surface be defined relative to the WGS84 geoid rather than a UTM based plane.

37

The issue with the London maps is a bit different from the issue with straight lines not staying level, though. If, instead of a spherical Earth, we instead had a planet shaped like a cylinder, then the arms of LIGO (or at least, one of them) would still be higher off the ground at the ends than in the middle, but there would be no problem at all with making flat maps of even a very large region.

38

Hard to say just what this might actually mean.

Is the runway constructed to be a single plane (thus, slightly lower in the center than at the ends)? That would add considerably to the cost, while providing no benefit to a landing Shuttle.

More likely, the site was graded level and the runway was constructed of multiple poured sections (as all concrete runways are). It thus naturally follows the curvature of the Earth, which involves no special planning or expense - and is optimal for the purpose.

39

I had a vague recollection of having heard that the Shuttle runway was flat and was higher at the end because the Earth curved away, so I went looking for a cite before making such a claim. I didn’t find exactly what I was looking for, but I think that the second cite, where they are using it for optical experiments because it is corrected for the curve of the Earth leads me to believe that it is in fact flat, not level.

It doesn’t seem as though it would cost much more to build, it’s only about a foot difference from level, and would be easy enough to grade with a laser.

Exactly what benefit that gives to a landing Shuttle, I’m not sure, but given the extreme tolerances and precision required to land it, maybe some NASA engineers at the time thought it would be useful.

40

I wouldn’t be surprised if the reasoning didn’t go any further than “Hey, gee whiz, someone just invented this nifty laser level! It’s a cool high-tech tool; let’s use it for our new cool high-tech project.”.

Even on a multi-mile scale, the differences between flat and level are small enough that, for any practical purpose, it would matter only trivially which one was chosen.