Nope, it’s only locally flat. The surface of a lake follows the curvature of the earth.
Like the Mad Hatter’s tea party… 
https://www.maa.org/external_archive/devlin/devlin_03_10.html
The surface of a lake follows the current, which is, I think, a greater slope than curvature.
How does the current affect the curvature of the water surface?
I’m not sure why it would. The world is full of runways large enough for the shuttle. My home airport where I learned to fly had a 15,000 ft runway (same as the Space Shuttle Landing Facility), and was a designated space shuttle alternate. There are 18 runways in the world longer than the SSLF.
I’ve never heard of any of them being corrected for the curvature of the Earth… I don’t see why they would - airplanes/shuttle generally touch down in the first couple of thousand feet, then tye runway might as well be a highway. But maybe I’m missing some nuance of construction, Or they had to corrected for curvature when surveying or somethjng.
One place I have found significant discrepancies is in altitudes. GPS uses the WGS84 geoid to define the surface of the Earth, and its altitude determinations are provided relative to that. However maps are usually defined relative to a local datum, and that datum may define a significantly different altitude. Which seems odd to say the least, but I have seen a discrepancy of the order of a hundred metres. This hit me when working with mining data, which was done with UTM based maps referenced to the local datum and aerial survey data that was georeferenced with GPS. We just could not get our results to line up until I twigged that the datum offset could be so bad.
So, it isn’t impossible that the defined altitude of a runway could get you into trouble if you attempt a fully automatic landing under GPS guidance. This doesn’t change the building of the airstrip, but may mean that explicit care over the exact surface altitude needs to be taken.
Usually, even full IFR landings use instruments that are physically referenced to the actual runway, so they self align. But GPS isn’t locally referenced. For something like the Shuttle the precision needed is going to quite high. Landing a gliding brick isn’t forgiving. There is no go around and the stresses on the craft are on the margins.
Shuttles didn’t have fully automatic landing, humans took over miles from touchdown and landed them by hand. They also landed shuttles at Edwards AFB 54 times, 19 of which were on a dry lakebed, and once at White Sands on a dry lakebed. It doesn’t seem like taking the curvature of the earth into account during construction was really important to landing.
Nevertheless, some sites to say it was taken into account. This page mentions a height tolerance of 1/4 inch end to end.
And yet… this paper on the history of the shuttle landing site says nothing about curvature, but it does say “The landing strip is not perfectly flat due to a slope of 24 inches from the center-line to the edge. This helps to facilitate drainage…” One of the links posted earlier also mentioned a crown in the middle of the runway. This is what it it was referring to.
So, why were they worried about how flat it was over 15,000ft while intentionally making it very not flat side to side?
I think that there are enough cites to make the case that it is in fact flat, not level.
As to why, I think @Chronos has the answer. They could, and it wouldn’t really be all that much harder to do so. With all the unknowns involved in the space shuttle program, no one wanted to find that a shuttle crashed a landing because the runway wasn’t flat. Some engineer probably made a case that it would eliminate a slight possibility of complication on landing, and they decided to go with it rather than take the chance.
The shuttle doesn’t need all that length for the rollout. It normally lands about 2,200 feet from the beginning of the runway, then stops about the same distance from the end. There is considerable leeway in where it can land, and since it is not able to do a go around, if it is a couple thousand feet short or far, it can still safely land. That couple thousand feet translates to a couple of inches of height, which may have been enough to be concerned about a hard landing if that is not taken into account.
As to why it slopes to the sides, but not along it, that’d be because it does need to for drainage, and the shuttle doesn’t land side to side, so it wouldn’t make a difference. It’s much easier to land in the center of the runway than it is to land precisely a certain distance along it.
I can’t see anyone making that argument. Assuming the landing gear is 20 feet apart on a shuttle, veering off the centerline by ten feet, which is really easy to do when you’re steering with your feet, would put one side an inch lower than the other. That’s in real time, the shuttle would actually be unlevel by an inch. It doesn’t hurt anything at all, but it’s hard to argue that’s fine but an inch or two along the length of the rollout should be avoided.
The Shuttles did have a fully autonomous autoland capability that could get the shuttle onto the runway. It didn’t have the capability to handle rollout or braking. However it was never used to its full extent, although STS-3 let the autoland system take the shuttle to 125 feet above the runway before handing over control to the pilot.
It seems that in general pilots preferred to take those last few miles by hand. The STS-3 experience suggested that late handover to the pilot was harder to make smooth, so if the pilot was landing the craft, earlier was better. But, if needed, the shuttle was always capable of landing automatically.
The current affects the surface of the lake. Where it’s curved, it’s not following the earth, and It’s not flat either. A few lakes don’t have outlets: if they’re big enough, they aren’t flat either, and don’t “follow” the curvature of the earth.
“How” does the current affect the curvature of the water surface? That’s fluid dynamics, an interesting subject in it’s own right, but not one I could explain, even if I had more space than the margin of this page …
Cool! 10-15 years ago, I worked a lot with maps Mexican government surveyors had prepared for almost every ejido (rural village originating in land reform land grants) in the country, as part of the partial or complete (varied among ejidos) privatization process of these social properties. It was absurdly, unnecessarily precise from an engineering perspective, each vertex of each parcel polygon given x and y coordinates to the nearest millimeter (ridiculous — a total station infrared prism doesn’t have that kind of meaningful precision across a corn field or forest patch!)…and each ejido had its own prime meridian and origin point (0,0 x y location), so instead of UTM, it was “TME” (Spanish acronym for “ejidal transverse Mercator”).
Gods. You have my deepest sympathy. 
But a geoid doesn’t define the surface of the Earth. The geoid is the equipotential surface that most closely approximates the surface of the ocean (what’s colloquially referred to as “sea level”), and a specific geoid like WGS84 is a mathematical model that closely approximates that very complicated shape-- The actual surface can be thousands of meters higher, or hundreds of meters lower. And a datum will always be at or very close to the surface, so of course there could be discrepancies of hundreds of meters, or much more, between a datum and the geoid.
As for the Shuttle runway, I didn’t say that they made it flat for the sake of eliminating a slight possibility of complication. I said they probably made it flat because that’s what a laser level gives you, and they probably used a laser level because it was a shiny high-tech tool.
It seems someone made an argument to make it flat, as that is the result that we have.
I’ve watched a bunch of shuttle landings, and they are pretty good at setting it down right on the centerline. That’s going to be much easier than landing on a precise mark along the runway, given unpowered flight from orbit, and no chance for a go-around.
And laterally, it’s a crown, curved, rather than a straight slope. The difference between the wheels at 10 feet off the centerline would not be as much as if it were such a slope.
As I said, there would be a desire to eliminate any variables that they could. They were pushing the very limits of technology and human capability.
Having drainage on the runway is necessary, it’s Florida after all, and it rains a bunch there. The cost of not having drainage would be substantial. OTOH, the cost of following a laser level to lay out the runway along the length would be pretty minimal.
When I mentioned you, I meant only to agree with you that they did so because they could. I then went on to speculate as to why they may have thought they should. Sorry if I did not make that clear.
Anyway, this would actually be an interesting topic for Cecil to tackle, if he was still around. As is, I’m a patreon of Frasier Cain, so I may go ahead and shoot this question at him when he restarts his Q&A’s.
One thing I’ve noticed looking at maps of my local city is that rectangular street grids eventually have to be compromised because the grid can’t be extended indefinitely, presumably due to the Earth’s curvature. Typically a street or avenue will have to discontinue at some point. The effect is pronounced here because of our reasonably high latitude (45°N) and that the majority of grids are compass point N-S, E-W.
That’s not generally because the city itself is large enough for the curvature to be relevant. But cities are usually laid out based on statewide coordinate systems, and over the area of a whole state, the curvature is relevant, and so those coordinate systems usually have small corrections on some regular basis.
If, at the time you created the state coordinate system, you already knew where the cities would be, you could design your coordinate system around them, with no corrections within the cities themselves and large corrections outside of them. But this isn’t generally known at that time.
Yes - but it’s thoroughly unclear what variables are eliminated by making the runway flat, rather than level. One effect would be that the Shuttle is touching down on a section of the runway that’s slightly downhill (admittedly by a trivial angle). Why would that be preferable?
The scale of all this stuff is ridiculously small. If there was some effort done to correct for Earth’s curvature for the Shuttle runway, it had nothing to do with landing, but likely just a construction issue of some sort. The size of the changes due to curvature are utterly irrelevant to flying the shuttle or any other aircraft. We’re talking about a few inches over a distance of several miles.
??? Where R is the radius of the Earth, and X is the length of the building,
delta = sqrt( x^2 + R^2) - R
is approximately proportional to x, and the lowest nonzero order is linear. I make it x/R, but I’m just scribbling on a piece of paper, and it’s been 20 years since I did any arithmetic.