[Tom Haws]

When they do the job, flat earth (Euclidean) approximations are a lot easier to understand and a bit easier to use than spheroid approximations, ellipsoid approximations, or geoid approximations. In our daily work, nearly all of us are flat earthers when we can be. I think it would be fun to share examples from our professional lives of how we are flat earthers and the limits of those assumptions.

Here's a bit from my civil engineering career:

1. All the civil engineering plans I have ever drawn have been flat. In AutoCAD, they are drawn on a Cartesian plane. This generally works fine.
2. Nearly all the property lines and descriptions I have ever seen (all but the ones on county, state, or continental level) have been flat. This generally works fine. But I am not a GIS guy. :-D Ignorance is bliss.
3. When I survey with an optical level (a little telescope sort of like a transit or a theodolite that only views level and does not measure angles), I keep in mind only a vague and gentle notion that I should maybe try to keep my sightings equidistant from my level to minimize Round Earth errors. This generally works fine within 1/2 mile.
4. When I get more scientific about projecting a Cartesian plane onto a Round Earth for larger projects, I can choose from a published projection, probably either UTM or State Plane Coordinates, whereby a piece of paper has been wrapped without creasing onto a limited area of the earth to approximate that area as a cylindrical section or cone that can be unwrapped exactly onto a Cartesian plan. UTM wraps the entire earth with 60 six-degree longitudinal strips. The Arizona State plane system lays 3 strips longitudinally onto Arizona. Other State Plane coordinate systems lay strips latitudinally or wrap them conically depending on what fits the shape and location of the respective state.

Limitations:
1. All my projects are no more than a mile or two long. A surveyor in my office who worked right-of-way maps for the freeway loop system for the Phoenix Metro area had to go beyond flat earth approximations due to the metro area extent.
2. If you try to glue together too many properties, or if you try to describe too large a property according to surveyed measurements, it can't be plotted faithfully on a flat map.
3. You have to be more rigorous about level legs and gravity corrections if you are running regional level loops. My hat is off to early surveyors!
4. State plane and UTM projection approximations only work if you can limit your work to one zone. There is no hard boundary between zones, but any given zone works best at the location it was created for. The further you stray, the worse your fit gets, and the faster it gets worse, to the limit of absurdity and meaningless results. All my career work has been on the Arizona Central Zone.

[Dr David Thork]

Surveyors make mistakes. They aren't holier-than-thou. They rush stuff, they round, they bodge ... and you end up with stuff like this.
http://uk.businessinsider.com/is-millennium-tower-safe-still-leaning-sinking-2017-9?op=1&r=US&IR=T/#millennium-tower-rises-58-stories-above-san-franciscos-financial-district-1

If you can't even make sure you aren't building on a swamp, you certainly aren't concerned with earth's shape.

[Tom Haws]

BT, I don't want to derail the thread. But
1. That article isn't about surveying. It's about geotechnical engineering and construction management.
2. There are bozos and boneheaded mistakes in every profession. They tell us little about the greatest achievements and the standards of the profession. Any surveyor who is able to achieve high-level accuracy on continent-scale level loops is a master thinker, and my hat goes off to them.

[Tom Bishop]

Most civil engineers are flat earthers most of the time. For the small percentage of time the earth's curvature is accounted for, when have engineers verified that their structures actually sat on the theorized curvature?

Despite the "common knowledge" that the pylons on the Humber Bridge deviate in distance due to the curvature of the earth, the Humber Bridge authorities admit that they have never actually measured the top of their pylons.

Q. If the earth is flat, why do top of the pylons of the Humber Bridge deviate in distance horizonally by 36mm?

A. The pylons were built vertically in relation to the earth. The pylons were built to be exactly the same height. The difference in horizontal distance at the top of the pylons is only a theoretical figure for what the difference should be if the earth were a globe.

No physical measurement of distance deviation was ever detected on this or any other bridge. Forum user "Niceguybut" once tried to champion the cause that there was a physical, detected difference on the Humber Bridge. Here were his results:

Niceguybut wrote:

"I once tried to champion this cause, and in the interests of getting a definitive answer, I emailed the Humber Bridge Authority to ask whether the figure was measured or purely theoretical. Here's the reply:

Thank you for your recent email.

The two towers are build vertical to a tangent to the earth, i.e. radial to the centre of the earth, thus, theoretically, the shape between the two towers is an inverted trapesium rather than a rectangle with the length between the bottom of the towers being 36mm less than the length at the top of the towers.
The gap at the base is, of course, the one that was actually "measured" with the apparent increase being a result of building the towers "vertically".

Regards
Peter Hill General Manager & Bridgemaster

So there you have it, straight from the horse's bridgemaster's mouth. I'm man enough to admit I backed a wrong 'un, so can we let this one go now?"

[Tom Haws]

Most surveyors are flat earthers most of the time. For the small percentage of time the earth's curvature is accounted for, when have surveyors verified that their structures actually sat on the theorized curvature?

I haven't addressed structures. Generally, structures are not big enough that flat earth assumptions fail. My comments about surveying were specifically about continent-scale level loops where surveyors are forced to account for earth curvature (gravity vector variation) because they otherwise cannot get good closure on their loops.

In the sentence above I used the technical term "closure on their loops". Let me explain. When a pioneering or verifying surveyor (pre-GPS) is establishing a prime bench mark, say, in North Dakota, they have to run a level "loop" from the ocean. We say "loop" because they start at the ocean-side bench mark, run their leveling to North Dakota, then turn around and run it back to the ocean-side bench mark using error-revealing (not self-canceling) procedures on the way back. The closure on the loop is the error in the final arriving elevation at the ocean-side bench mark vs. the known starting elevation at that bench mark. Usually this error is normalized by dividing by the distance of the loop. This is all optical, and for such a high-level loop, it includes accounting for all known conditions such as atmospheric disturbances.