Here are some empirical observations which qualify as evidence for me of events that I have personally experienced, rather than regurgitating dubious anecdotes and one line answers trawled from the Internet. Can also be used in response to the Standard reply 'It looks flat so it is flat'.
Whilst on a large ship in February of this year I awoke in my cabin and could only hear a subdued hum from the ship, consistent with being stationary. As I could also feel no movement of any sort, I assumed we had docked in Amsterdam, one of our stops. As we were in an inside cabin with no windows, I went up on deck, only to find that we were still at sea in a flat calm, but moving at probably about 10knots from the wake. My senses had told me we were not moving, they were wrong.
A few years ago, whilst learning to fly a glider on instruments, I entered cloud, flying in a straight line. After about two minutes, I felt a movement to the left and an increase in speed, which I interpreted as a entering a gentle descending turn to the left. As I had no visual frame of reference, I applied a normal amount of backward pressure on the stick to ease the descent and made a corrective rudder and aileron movement to the right. The sensation of flying straight and level returned, however the instruments suggested that I was actually still turning to the left and still descending. I increased the back pressure on the stick and added more right turn with the ailerons. Everything felt normal but the sound of air rushing past had increased considerably and the instruments continued to show a left turn and descent. At that moment I came out of the cloud and became aware that the ground was above my head to one side and that I was in a slow steep spin to the left. The control inputs I had made and made the situation worse, with no indication from my own senses that my orientation was wrong. THe lesson I learnt from that is to never just trust your senses if you don't have access to all the facts.
I was in Dover in the UK recently with the family and walking along the beach was thinking that the French coast was only 20.7 miles away. It was a cool clear day but even my binoculars and high zoom camera could only see a distant horizon. About an hour later, We went up to walk along on 350ft high cliffs and could see very clearly the foreshore and buildings of Cap Gris Nez in France, without binoculars or camera zoom. Using camera or binoculars, the details were sharp and clear considering the distance, although totally hidden by the horizon at sea level.
For many years I have made passages on various small boats including my own, which have required me to use charts and navigational equipment, taking bearings from coastal observations, allowing for tidal and wind errors and getting pretty good at it. I also quickly found that the curvature of the earth prevented me from seizing more than about 3 miles from my eyeline unless an object was tall enough to appear. Recently, I put a camera at the top of my mast which enable me to see about 6-7 miles to the horizon and I can remotely control it. That of course is quite clearly why the old sailing vessels had a crows nest up the mast for observation from the highest point. The advent of GPS a few years ago also meant that I could verify my position using GPS as a secondary backup and I have found it to be extremely accurate in all cases at sea, often a lot more accurate that my own plotting. All my flying and sailing plots are fully logged and verifiable.
As a final empirical observation, I used to glide from Challock in Kent which is on a ridge about 400ft high. From the ridge on a clear day, the view was magnificent across the surrounding countryside as far as the horizon, about 24-25 miles. As soon as I took an aerotow to 3000ft, the view steadily expanded until I could easily see the white cliffs on part of the French coat 60 miles away and the English south coast curving away into the distance. The higher I went, the further I could see.
These are just minimal examples of my personal observations of the world around me and I would be very pleased to see similar accounts from pilots, seagoing sailors, surveyors or anyone who regularly uses those type of observations and are also subscribers to the Flat Earth theory (or other shapes)
Thank you,
Roger