Laser levels are great for measuring level on most construction sites, where you need to know level over a distance of maybe a few hundred feet at most, and only accurately enough so your building doesn’t fall down or look like it was put together by drunken monkeys.
But how do you measure level over much larger distances (i.e. distances over which the curvature of the earth matters), and accurately enough for a physics experiment? I just read this Newsweek article discussing a couple of experiments in which flat-earthers produced results that conflict with their flat-earth theories.
One of the experiments involved three poles spaced across a total distance of about four miles, with the tops of the posts all at the same level. On a flat earth, a laser placed at the top of the first post and aimed at the top of the third post will just graze the top of the second post. On a round earth, the laser will hit the second post about 2.4 feet below its top. This particular experiment didn’t work because the laser beam was too dispersed for an accurate measurement by the time it reached the second and third posts. But even supposing a hypothetical laser with zero beam dispersion over infinite distances, the other prerequisite for a valid experiment is positioning the tops of all three posts the same distance from the center of curvature of the earth’s surface. How does one go about assuring that this is the case? In theory, a manometer could do the job, since water seeks its own level. But operating a manometer over a 2-mile distance isn’t practical. What other solutions are available?
A two-mile long ditch full of water is perfectly feasible.
And it’s not “the same distance from the center of the Earth’s curvature” that you want, though over small distances that’ll be close enough. What you want is “along an equipotential of the Earth’s gravitational field”. Due to the deviations of the Earth from spherical, these are not the same thing.
It mentions that one should use a theodolite with automatic correction for misalignment between the instrument’s vertical axis and the plumb line, so that accurate zenith angles can be measured.
That is for river crossings, though, not a hundred-km-long particle accelerator.
I haven’t looked at the link and I’m not an expert but I’ve been involved in such surveys. Back when I was involved we used an optical level that coud read height markings on a vertical pole over a distance, then move the instrument and/or the pole to get relative height difference between points.
They’d be able to get height differences as far as you want and calculate the differences from known points (benchmarks). Many redundant measurements are made to quantify the measurement error and spead it around so it doesn’t all land on the last point.
Oh, and you also want to make sure you know what you actually want. For most very large buildings, you want level (what a ditch of water gives you), but for most scientific experiments, you want straight (what a laser level gives you). In practice, assuming you accept standard scientific knowledge like the curvature of the Earth, it’s probably easiest to use the laser level and then apply a known calculated correction for the curvature of the Earth.
For the experiment I described in my OP, it would be be a way of finding “level” that satisfies both flat-earthers and round-earthers. The ditch-full-of-water method seems to fit the bill.
I haven’t actually watched the documentary yet. I’m not sure I want to sit through all 95 minutes, but I may skip to the parts where they explain how they set up this experiment.
This is exactly how land surveyors work, but this doesn’t give what the OP wants.
In the procedure you described, the sightline through the crosshairs in the survey instrument is actually a curved line, which is parallel to the curvature of the earth.
The reading on the pole shows the relative difference between the height of the ground where the instrument is standing, and the ground where the pole is standing. But both are standing on the curved surface of the earth.
The curvature is ignored, because it is irrelevant to most engineering projects.
I’m not sure what you mean. A line through “the same distance from the center of curvature of the earth’s surface” is “a curved line, which is parallel to the curvature of the earth”. What am I missing?
Regarding your quote from my post…you’re not missing anything. What you said is exactly what I described.
You also quoted Machine Elf, and yeah, I think I’m missing something there, because I don’t understand what he meant. The whole point of the experiment is to prove that the earth is curved by setting 3 poles , all exactly the same height, in a straight line. Shoot a laser beam just touching the top of the first post, and it will not touch the tops of the other two,
What you are asking about is the science of geodesy and specifically about a geodetic datum. The method mentioned by @74westy was in common use before civil access to high precision Global Positioning System (or similar Russian, European, and Chinese systems) but now most if not all land surveying uses GPS-enabled theodolites which capture position information that is recorded and can be fed into a system which will automagically correct a collection of measurements that are in a broad enough field that curvature of the Earth may be of concern, or more frequently to just simplify the process of rectifying complex survey measurements. The standard horizontal reference datum that is in almost universal use is the World Geodetic System 1984 (WGS84), which is an ellipsoidal base datum with local corrections for mass concentrations (MASCONs) that cause the gravitational field to vary, and then local geographical altitude data for vertical datum.
Originally, this degree of precision had essentially one application; calculating the impact position of a vehicle reentering from space; i.e. a spacecraft or ballistic missile reentry vehicle, with some very niche applications in the study of seismology and plate tectonics. Even the largest constructions did not require precision measurement across such a wide span, and would be subject to local subsidence anyway. However, with the advent of very large science machines like the Large Hadron Collider (which requires extremely precise and accurate measurements to be able to align the beam with experiments) and satellite observation of ground movement (i.e. changes to ice sheets, permafrost fields, and subsidence due to compaction of subterranean aquifers) it has become a much more broadly used area of measurement science that is crucial to modern geophysics of the crust and upper mantle dynamics.
I note that the “ditch of water” is how the pyramids were supposedly built so level. They cut a channel in the bedrock around the perimeter and measured up from that to set elevations.
Indeed. And I now remember that the experiment mentioned in the OP was along a canal. If the canal is not flowing, the water should be level to within much less than 2.4’.
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Either you’re missing a couple of words in your post, I’m confused, or you’re confused.
The sightline through the survey instrument is absolutely positively straight. It might not be even close to level, but it will be straight. (Less a teeny fraction of a nanometer for light propagation bending in the presence of Earth’s gravity, but we’ll skip that quibble).
Let’s say we magically have a few miles of dead level “flat” ground on our curved Earth (maybe the Bonneville salt flats?). Let’s also say our survey instrument was perfectly level = perpendicular to local gravity at the instrument’s location. Given that …
If we march away from the instrument into the far distance and keep taking readings of the height of the sightline (or laser beam ignoring dispersion) we will have the perception that the sightline / beam is slowly climbing higher and higher and at an increasing rate as the distance increases. It’s apparently curving upwards. But what is really happening is we’re going over “the edge” of the curvature of the Earth and therefore dropping farther and farther below the dead-straight sightline. Which is increasingly unlevel compared to local vertical, but that’s because local vertical is changing, not because the sightline is bending.
Sightlines aren’t curved unless you’re taking a very weird approach to what you’re treating as fixed and what you’re treating as relative.
okay let me try again…'cause I left out some stuff.
Yes, the sightline thru the crosshairs of the survey instrument is straight, through the air.
But when surveyors measure a “straight” line (or plane surface) at a given height, (say, 5 feet above the ground), they are actually measuring a curve. (but the amount of curvature is so minimal it is usually ignored.)
Suppose a construction project needs a flat slab of concrete for a parking lot. It is common for the surveyors to set marks in a few dozen places, all at exactly the same height. Those marks are all visible thru the crosshairs of the instrument on a "straight: seeningly flat surface, at exactly the same reading on the measuring rod.(say, 5 feet above the height of the spot where the instrument is standing.)
Those dozens of points all seem to be on a straight, flat plane. But they are not really. They are on a curved plane, 5 feet above the curvature of the earth.
That’s what I meant when I typed that the “sightline thru the crosshairs is actually a curved line.”
The sightline is straight, the readings on the measuring rod are all exactly the same 5 feet, but the line (or plane) follows the (negligible) curvature of the earth.