1) how can water curve? Why does a zoom lens somehow overcome a ship disappearing miles out behind a supposed curve of water?
2) s the actual calculation of earth's curve 8 inches per mile squared? There seems to be a lot of debate around the exacting formula and as to whether a bridge builder or tunnel digger would need to take that into equation in the planning phase. No one here seems to be an engineer or architect.
3) Coriolis effect. A sharpshooter has to make a correction at long ranges for the supposed spinning of the earth. Or is that related to earth's pull or something? I was reading pilots or flight path planners also have to arrange their flight path as a result? We are told that we can't feel it, ok, but when I jump in the air and come straight down technically I have actually moved a miniscule amount then? And taking that further, if I jumped up and down enough eventually I'd be at the end of my driveway due to earth spinning beneath my feet as the cumulative amount added up over time spent suspended between earth and sky?
Itemized lists are appreciated, thank you. Brief answers for now, if you want more details ask and I'll get to it when I can, some of these are off the cuff and might need refining. Plus they might be jargon-y.
1) Water curving: water is just a pile of molecules hanging out together. The shape of the surface is determined by the shape of the force pulling on them, it'll pull the molecules around until all the molecules have the lowest energy possible. For a flat surface with a uniform downwards force, that's a level surface. For a sphere with a spherically symmetric force pulling towards the center of the sphere, the water forms a spherical shell around the sphere. For a 5 gallon bucket that you spin round-n-round, creating the imaginary "centrifugal force" pointing towards the bucket bottom in the water's perspective, it sticks to the bottom of the bucket even as the bucket passes above your head.
Zoom lens: If the lens is able to make it visible again, that would mean the object was not hidden by the curve and it wasn't visible for some other reason. Possibly resolution limits on the camera, or if we're talking about the eye then the object being too small for the eye to resolve at that distance.
2) I'm not certain about the 8 in/ sq-mi thing yet, still looking into it. Looks like that is an approximation that assumes we're dealing with very small distances relative to the earth's radius though. One thing that catches people out with this is doing the math as if your eyeball was on the ground, instead of calculating based on your eyes being 5-6ft off the ground.
I'd think CivE projects would have to take this into account depending on scale. Digging a ditch in my small backyard is likely unaffected, but if you're doing a canal through a city you'd have to make sure that you're constantly getting closer to the surface of the earth for water to flow down. Not following the curve would result you getting farther from the surface of the earth as you went along, so the water wouldn't flow properly. I'm not an engineer or architect either so never had to train for CivE projects, but I'd imagine you can dig up textbooks, or planning documents for projects of sufficient size and see how things are compensated (I think with something called a "datum"). I also found some engineers claiming they do have to compensate, using that thingy I mentioned, but that should be fairly easy to run an internet search for.
3) I'd have to review it, but I think the answer is no. It's not that the earth moves under your feet when you jump, it has to do with the fact that angular speed (which should be constant for every part of the globe, basically how many degrees you rotate each second) is related to linear speed (how many feet you travel each second) by a factor of the radius. In SI units it'd be r ✕ ω, where r is the radius of the circular path you're moving along, and ω is the angular speed. The circle you travel gets bigger as you get closer to the equator since you're farther from the earth's axis, so things on the equator have a higher linear speed than things at the poles, and the in-between bits are in-between. If this speed difference isn't compensated for as you move from pole to equator or vice versa, then your path will be screwy. Wikipedia has a cool gif:
Caption:
https://en.wikipedia.org/wiki/Coriolis_force
So if you started levitating (so you're not touching the earth, meaning it can't nudge you faster as you travel) then traveled towards the equator you'd have a problem, but just hopping straight up and coming back down won't be an issue.