Answering the earlier version of the question first (on Columbus mistakes).
There were two main sources of mistakes:
exaggerated size of Asia and underestimate of the size of the Earth.
Columbus was relying on the work of his contemporary geographer Toscanelli, with whom he corresponded (some of this correspondence survives).
Toscanelli estimated the ...
I think that observing ships disappear over the horizon would be an imprecise method of calculating the size of the Earth.
[added 01-13-21 I found a quote where Aristotle (384-322 BC) mentioned that the circumference of the Earth was estimated at about 400,000 stades, and thus not large compared to stars.