I will take out my navy manual and perform the calculation which was derived from tabulation, mathematics, and empiricism and says nothing about the shape of the earth.
Can't speak to Navy manuals, but the FAA makes it pretty clear that a globe earth needs to be factored in when it comes to navigation - See chapter 16 for starters:
https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak/media/pilot_handbook.pdf
I have no question that the FAA believes the earth is round and would justify their views through the equations they use. However the methods and equations and tools they use say nothing of the shape of the earth, but only of predictable rules gathered through observation, mathematics, tabulation, and empiricism.
Further, I spent the time in the middle of my work day humouring you and reading Chapter 16. You are correct it assumes a round earth; however, the practical knowledge that one can use from this chapter (time zones, longitude and latitude, etc) hold no particular bias to whether the earth is flat, round, or donut shaped. All of it can (and was) determined through tabulation, mathematics, and empiricism. In fact, TheEngineer, a moderator here in the past and a pilot, has provided first hand accounts of how nothing he does when flying shows a round earth.
I will take out my navy manual and perform the calculation which was derived from tabulation, mathematics, and empiricism and says nothing about the shape of the earth.
Can't speak to Navy manuals, but the FAA makes it pretty clear that a globe earth needs to be factored in when it comes to navigation - See chapter 16 for starters:
https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak/media/pilot_handbook.pdf
It is really not necessary to say anything about the shape of the earth in the manual because in the real world the shape of the earth is the globe and is a known fact . In the real world you deal with reality. I realize that this is the FES website and FE's minds are programmed to deny any thing of reality. In the navy and the FAA you work in the real world.
The FAA also makes it clear that a globe earth needs to be factored in when it comes to the spacing of microwave repeater stations.
The navy also makes it clear that they use Oceanic Charts made from a projection of a globe.
Its not necessary because all that is necessary are the rules that are needed to be performed; rules that were calculated using empricism, tabulation and mathematics - not some imaginary theoretical layer that attempts to say something. I have asked you again and again for an answer - how does science tell us the shape of the earth if its powers are limited to prediction through tabulation based rules?
The fact that they use a globe as a model again says nothing of the shape of the earth. A flat non-euclidean closed surface earth would have an identical map. As would a model where the North pole and south pole were both in the center.
The "round earth" formula for estimating the distance from an observer to the horizon takes into account the curvature of the earth.
It does no such thing. The round earth theory takes into account the distance to the horizon to calculate an assumed curvature of the earth - this is in contradistinction to your claim that it works the other way around and that the formula somehow magically knew there was a curvature to the earth in spite of it being based off pure tabulation, mathematics and empiricism. You are putting the cart before the horse.
It also seems you are again and again purposefully missing the point.
Do the calculations provided by science work? Yes, more often than not.
Do they say anything about the shape of the earth? No; perhaps you can show me why they must rather than citing one after another when I already disproved your hypothesis by example: there have been many cultures over the years who have been able to calculate eclipses, or the distance to the horizon without the use of a 'round earth theory'. How did they do it? The same way they did any other science - by tabulation, mathematics and empiricism.