Christopher Columbus' crew had a lot to be worried about as they set sail. There was the possibility that they might wind up with scurvy or meander into a vengeful weather front, and of course there were all those warnings about where there be monsters.
But falling off the edge of the planet? Not so much. The idea that Columbus was endeavoring to attempt the unimaginable, defy all existing scientific precedent and become an international celebrity for not toppling off the world is false.
People have known since the learned and logic-laden age of the Greeks that they lived on a great, big globe. There were lots of obvious clues, like the way ships sailed over the horizon.
There were many objections to Columbus' plan to reach the East Indies via a somewhat novel route, but a tragic (and expensive) plunge into the abyss wasn't one of them. Most contentious were the logistics. Given the estimated (and not too shabby) size of the globe, there were steep odds his ships wouldn't successfully reach their intended destination. In the 1800s, the "knowledge" that our goofy, dark-ages ancestors had just up and forgotten the shape of the thing that they lived on started to circulate.