This question is inspired by a facility being built by Tesla in southeast Austin. I drive by it from time to time and I am struck by how large it is. The building is not very tall, but it is going to cover a very large area.
Do the architects and engineers for this car factory have to account for the fact that the Earth is round when designing a building of such a large linear dimension? Is the floor of the factory designed to be truly flat even though the Earth below the foundation is not? Is the difference in size between the actual planet and the building so great that it is irrelevant? How big does a structure need to be before the fact that the Earth is round becomes important?
In 1962, in the rolling hills west of Stanford University, construction began on what was then the longest and straightest structure in the world, the Stanford Linear Accelerator, or linac. It took four years to build and was affectionately known as “the Monster” to the scientists who conjured it. Building the 2-mile-long structure was an engineering challenge that required taking the Earth’s curvature into account (a 20-inch shift in the vertical axis). Electrons fired from one end of the gallery reached 99.999% of the speed of light in the first meter of their flight down the accelerator and collided with a target or particle beam at the other end.
Also the Verrazzano-Narrows Bridge in NYC was built taking the earth’s curvature into account. According to Wikipedia, the towers are not parallel to each other, but are 1 5/8" farther apart at the top than at the base to account for the earth’s curvature.
Specific to the Gigafactory in Austin, it’s supposedly going to be about 5 million square feet. That’s less than half a mile on a side, assuming it’s square. So the curcature of the earth over that distance would be about 4 inches, or 2" from the center to the edges of the building.
Four inches is a trivial elevation difference compared to the highs and lows of the area. The site will simply be graded flat as it would be no matter what size the building is.
The examples others gave involve more specialized issues, such as a very long bridge anchored to bedrock and needing supports perpendicular to the bedrock that are very high. In that case, the distance between the tops of the supports and the bottom will be different because of curvature of the Earth. But for a flat building, they just survey and grade, and having the center be 2" higher than the edges is easy to take out. Hell, in some places they have to remove elevation differences of many feet to build. A few inches is nothing.
Some people, flat Earthers in particular, can’t get it in their heads that flat and level are not the same thing.
If the site is large enough then grading it flat means it won’t be level and grading it level means it ain’t exactly flat.
For a very large building, I don’t think it’s true that there’s no distinction between local topology and the curvature of the Earth. If the walls are built perpendicular to a foundation that is a very large flat plane surface, then they will not be vertical, as in the example of the Verrazzano Narrows bridge cited above. It seems to me that you want the foundation to follow a surface of equal gravitational potential.
It might be negligible at the scale of this example, but for a large enough building it can matter.
They are farther apart at the top because of the earth’s curvature. They are both built to be vertical, but diverge because “vertical” at one tower is not parallel to “vertical” at the other.
In the case of the Tesla building, assume a big concrete slab floor. If you build it flat (i.e., in one plane), things will tend to roll towards the center of the building. If you build it level, then the building will be slightly wider at the roof line than along the slab (assuming vertical walls at each end) - just like the bridge towers.
I would imagine the elasticity of the building materials would negate any need to adjust for the Earth’s curvature for things like the gigafactory. For very large and also very tall structures (suspension bridge pylons) it sort of matters, but since these are joined by cables, it seems like that would provide the necessary capacity for adjustment.
The floor is an interesting one, but wouldn’t these buildings be constructed as a series of modules anyway? The floor isn’t going to be poured in one big slab.
I’m not sure there really are such things as materials that are rigid and inelastic at the sort of scale of the Earth’s curve.
8 inches per mile is only 2 inches per half-mile. It’s quadratic.
And I imagine that it’s more important for a building’s floor to be level than for it to be flat, unless for some reason you have straight beams traversing the entire building (as you do for SLAC, and also for LIGO, the example I was going to cite).
Here is an example of the opposite problem. At the model basin they had to curve the rails to match the curvature of the earth since that is what the water does. https://mht.maryland.gov/nr/NRDetail.aspx?NRID=938
I’ve always thought it would be great for an excavation company to advertise: “Some of you may believe the earth is flat, but we have the tools to make it so.”
On this scale, it’s approximately linear. 4 inches per half-mile. 80 inches per 10 mile.
The difference between straight and true may be greater on a plan, because the corners of the map may be referenced to something even more than a mile away.
It is approximately linear, but the linear portion is 0 inches per mile. The lowest nonzero order is quadratic.
Think of it this way: If it were linear, and dropped 8 inches for every mile in front of you, then it’d have to rise 8 inches for every mile behind you. Which it clearly doesn’t.
Yeah. Somewhere I read about a rectangular pool that was long enough and flat enough that when full, water flowed over the long sides, but not the short sides.
