I'm watching the video Colonization of the Philipines and the video starts with an animation of a boat sailing South-West until it hit South America. Then it followed the coast until it passed the Americas, before sailing North-West through the Pacific Ocean.
It got me thinking as to whether there were any attempts to optimize sailing routes in order to save time/money
I am an Economist. I studied the Age of Exploration, specifically the Portuguese Empire as a hobby at University. It is something that I still study and learn about. I lived in Brazil and Portugal. I also took a course on The History of Economics.
The video you watched, it sounds like the voyage of Magellan. This route was later deemed far too dangerous and non-optimal because of how dangerous it was to traverse Cape Horn. Also, you had no ports for trade or re-stocking along the way. The Portuguese were the ones that discovered a majority of the optimized routes when it came to trade from Europe to Near, Southeast, and Far East Asia and the return routes. This is partly because of the papal bulls that prevented other nations to explore for years, as the Portuguese had convinced the Catholic leadership that they should be given exclusive rights to sea navigation and exploration. The Portuguese became quite good at optimizing their trade routes to reach specific locations with least resistance, such as: the wide swing to reach the Cape of Good Hope, where to cut across the Indian Ocean to reach the Straits of Singapore. There is also the fact that Chinese magistrates only pointed out to sea and said "Japan is that way." They provided no assistance beyond this. It is assumed that the Portuguese had assistance from someone, potentially the local pirates.
You have to remember though that during this time a lot went into knowing where you were at and understanding the ocean current. When the Portuguese first attempted to sail down the western coast of Africa to reach the southern cape, the current is strongly pushing up, towards the equator. The amount of time and resources consumed when they attempted this route was woefully inefficient. The Portuguese had several explorers (Bartolomeu Dias, Vasco Da Gama, Pedro Cabral) that would recognize the issues at hand and found a solution. Dias, by studying the currents south of the equator. Eventually the path that led fairly close to Brazil would prove the best for quickly getting around the southern cape of Africa.
During this time the Portuguese created the Caravel that was a great design for "speed running". They also used an astrolabe and released rope with wood tied to it to measure out speed and nautical miles, thereby helping plot the travelled course. This is important for repeatability.
Da Gama and Cabral would tinker with optimizing the routes around Africa. Cabral overshot a bit in a hope to improve the use of the current and they noticed birds that are land nesting birds that would not go too far out to sea. Confused and intrigued because no land previously was known to be in the area. They ventured further and eventually reached the Brazilian coast. They followed the coast line and then swung back towards the Cape of Good Hope. This was a major discovery and game changer as well, especially for Portugal. The islands of Canary, Madeira, and Azores were also used and re-stock and prep points that helped them tremendously.
The Portuguese also recognized that going to a major port that would allow for trading, re-stocking, and repairing was crucial. So if it would cost you a few days, it was still worth it. Because it provided logistic optimization. You didn't need ALL of your supplies from Portugal to China. You could resupply accordingly along the way. Another reason that Magellan's route was so inadequate.
This would all play into why the Portuguese probably invented/innovated "speed running", haha.
Map (decent and free to view):
https://www.studentsofhistory.com/routes-of-famous-european-explorers
Books:
Age of Discovery, 1400-1600. David Arnold.
Portuguese Voyages, 1498-1663. Charles Ley.
https://www.amazon.com/History-Portugal-Portuguese-Empire-Vol/dp/0521603978/