Oh boy, this is more complicated than I thought.
That is what everyone who earnestly evaluates this subject concludes! Measuring the entirety of the world is no small feat, and there are those who speculate that it is not an attainable goal at all (as the world is speculated by some to be boundless, and by others to be MUCH larger than we currently presume etc.)
Perhaps you could direct me to a few experiments used to determine the shape of the earth which I could repeat myself.
Experiments cannot be used to determine the shape of physical objects. I cannot be more clear about that. Experiments are solely for testing hypotheses by establishing, ideally, causal relationships between IV(s) and DV(s).
In terms of procedures/methodologies for measuring, there are a great many. You can try using lasers, lidar, radar, sonar, “maser” and other range-finding technologies - though they are not without their own issues and inaccuracies (especially over long distances). You can also, and I recommend, use more traditional approaches like strings/lines, spirit levels, surveyor's wheels and even wooden stakes.
The world is big, and measuring it is not trivial. Whatever methodology you employ, I recommend you validate it (do “sanity checks”) via other (ideally more direct) means as well. There are many others that have walked down the same road as yourself, and many here may be able to point you to specific procedures you might want to replicate. Searching the forum (as well as the “sister” forum) for such procedures is also a good idea. “Frozen lake” observations/tests/“experiments” are one such search to begin with.
I, for one, do not speculate as to the size and shape of the entire world because I lack the verified and verifiable data to make such a determination (like everyone else). Problems that are too large to address are best broken into smaller, more achievable, problems.
Determining the shape of water at rest is one of the most direct ways to determine if the globe model “holds water” or not (yuk, yuk, yuk). It will not help you determine the true shape of the entire world, but it will help you determine the local shape which can be used to extrapolate within reason (and/or ultimately build a composite).
As I mentioned, I have tried viewing distant objects over water but surely there must be more than one way to measure/observe the shape of the earth. yes?
There is more than one way to measure, but rigorous measurement is the only way to establish the shape of physical objects. Measurement is called for, not observation/viewing.
Many get bogged down in trying to “see” the curve of the earth. What those people have learned, is that there is no such curvature that is observable from the highest heights attainable (hydrogen balloon). Understanding why the horizon does not curve at any attainable height is valuable in this subject, but through that understanding you also learn why that does not establish the true shape of the world either.
Arguably the most valuable lesson that is learned from going down that road is that merely “seeing” is not measurement, nor can it ever be. Often what we see, is not what is - and empirical science requires rigorous measurement instead for good reason.