Put the blindfolded person in a car and tune into an FM station. Then drive however long it takes for that local signal to distort, fade and vanish, say 100 km. The radio beam travels in a straight line So the signal is gone because it's above your head, and the only way that can happen is if you dropped below it, i.e. you are on a sphere.
To verify this, take a flight from your local airport, if you can still hear the signal, then that supports the idea that it is not the signal loss due to horizontal distance that is affecting it, but instead it's due to vertical distance.
From Light of Sight Radio Propagation
Line-of-sight propagation means radio waves which travel in a straight line from the transmitting antenna to the receiving antenna. It does not necessarily require a cleared sight path; at lower frequencies radio waves can pass through building walls and foliage. Line of sight transmission is used in short to medium range radio transmission such as garage door openers, cell phones, cordless phones, walkie-talkies, wireless networks, FM radio and television broadcasting and radar, and satellite communication, such as satellite television. Line-of-sight transmission on the surface of the Earth is limited to the distance to the visual horizon, about 40 miles.
A high powered directional radar beam would be better, but enough already....