On the flat lands of Kansas, the curvature of the earth can easily be discerned, by proving that the horizon exists. You can do it with a sextant or transit, and a water tower or grain elevator, a couple of cellphones, a buddy with a transit measuring pole. You might need a telescope for accuracy. How do you do it?
Using the sextant/transit at 6 feet off the ground, view the buddy who has the measuring pole, and note when you can only see the guy's head as he walks away from you... and the level of the pole at that point. Then, go 100 feet up the water-tower/grain-elevator, and measure again. Use the cellphone to tell your buddy to move back until only his head is showing... and, of course, the stick. You might need a good telescope on the transit.
Measuring like this will prove that the horizon of a globe shaped earth exists. The neat thing about this form of measurement is, you can make many measurements, in many directions, from many grain elevators. You will find that the earth is a globe, of course.
