Here's a procedure for observing the curvature of the Earth right where you stand, assuming you select a good spot, without getting on a rocket that takes you outside beyond the atmosphere.
Or, if one is more ambitious, one may also calculate how much of a distant feature gets obscured by the curving surface of the globe and then compare this estimate with real-world observations.
There are variations of these procedures scattered piecemeal across the web. Although most of them are accurate, I've found them to be fragmented (fragmentary; pieces scattered) and either overly complex or lacking in detail. I also wanted to work out the geometry and algebra for myself and develop a spreadsheet that does the calculations for any location desired. I also describe a supplementary procedure for calculating the radius of the Earth based on a sighting of a distant tall feature.
Yes, you too can do low-tech geodesy like Persian scholars did a millennium ago or like the ancient Greeks of over 2 millennia ago. Low tech! Old school! Click down below on the PDF instructions and Excel spreadsheet.