The issue in the 1490s was not the shape of the Earth, but its size, and the position of the east coast of Asia, as Irving in fact points out. Historical estimates from Ptolemy onwards placed the coast of Asia about 180° east of the Canary Islands. Columbus adopted an earlier (and rejected) distance of 225°, added 28° (based on Marco Polo's travels), and then placed Japan another 30° further east. Starting from Cape St. Vincent in Portugal, Columbus made Eurasia stretch 283° to the east, leaving the Atlantic as only 77° wide. Since he planned to leave from the Canaries (9° further west), his trip to Japan would only have to cover 68° of longitude.
Columbus mistakenly used a much shorter length for a degree (he substituted the shorter 1480 m Italian "mile" for the longer 2177 m Arabic "mile"), making his degree (and the circumference of the Earth) about 75% of what it really was. The combined effect of these mistakes was that Columbus estimated the distance to Japan to be only about 5,000 km (or only to the eastern edge of the Caribbean) while the true figure is about 20,000 km. The Spanish scholars may not have known the exact distance to the east coast of Asia, but they believed that it was significantly further than Columbus' projection; and this was the basis of the criticism in Spain and Portugal, whether academic or amongst mariners, of the proposed voyage.
The disputed point was not the shape of the Earth, nor the idea that going west would eventually lead to Japan and China, but the ability of European ships to sail that far across open seas. The small ships of the day (Columbus' three ships varied between 20.5 and 23.5 m – or 67 to 77 feet – in length and carried about 90 men) simply could not carry enough food and water to reach Japan. The ships barely reached the eastern Caribbean islands. Already the crews were mutinous, not because of some fear of "sailing off the edge", but because they were running out of food and water with no chance of any new supplies within sailing distance. They were on the edge of starvation. What saved Columbus was the unknown existence of the Americas precisely at the point he thought he would reach Japan. His ability to resupply with food and water from the Caribbean islands allowed him to return safely to Europe. Otherwise his crews would have died, and the ships foundered. The academics were right. It was not possible for a 1492 ship to sail west across open oceans directly to Japan, because the mariners would die long before their arrival.
Today I learned.
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