@geeoddmike Thanks for the detailed image and the documents linked. I will work my way through them, but I have to recognize I struggle now with all the terminology.
What I wanted was a rough estimation of the error, an order of magnitude for these optical theodolites, i.e. less than 20 cm per km. Or in plain words, "is this instrument precise enough for the use I intent?
For me, if the error is less than say 0.1m per km that is good enough since head losses in pipes are in the order of 10m/km.
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I see we continue to have communication problems.
1. You want a rough estimate of the error using "optical theodolites." An theodolite is a surveying instrument measuring horizonatal and vertical angles. One can use the vertical angle feature to determine height differences using trigonometry.?ÿ
Optical theodolites can use techniques to determine distances (e.g. stadia or subtense bar) or use survey tapes to measure distances.?ÿ
2. Modern optical instrumentation are combines the angle measuring with a built-in electronic distance measuring capability. These are referred to as "total stations." There are versions that require prism reflections and those that do not.
3. Levels are designed specifically to precisely determine differences in height. Some include the ability to measure rough horizontal angles.?ÿ They come in optical and digital versions.?ÿ
Optical theodolites (e.g. the venerable Wild T2), total stations (e.g. Leica TC-1205) and levels (see models and specs below). I provide these manufacturer/model numbers for you to review and gain a sense of their capabilities.
My answer to your question is two fold. You can use the manufacturer's specifications as a guide in the choice of instrument. You must also recognize that even the best equipment will not meet specifications if not operated correctly, not kept in adjustment, nor failing to follow specifications.
An optical level (like those in the screen capture) is the cheapest, easiest to use and most accurate.
Operating any survey equipment requires attention to detail and an understanding of possible error sources.
Hire a surveyor to "train the trainers" if possible.
You may find the materials linked from this site to be useful: https://geodesy.noaa.gov/pub/corbin/Training/Leveling/precise-leveling-workshop/?ÿ Obviously you do not intend to perform geodetic leveling. Nonetheless there is lots of useful information on leveling.
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@geeoddmike Thank you, very informative and useful