Debate on the route
The analysis of Francisco Albo’s Derrotero has allowed us to observe some interesting issues that merit commenting:
Did Magellan sense the immense extension of the Pacific?
I have reflected a lot about the route followed by Magellan to cross the Pacific. Magellan knew that the Moluccas were at the same height as the equator, and in theory, he sets sail towards them from the moment he enters the Pacific. I have read everywhere that, at the time, no one suspected that the ocean would be so immensely vast. The diameter of the Earth was still unknown, but it was thought to be smaller than it actually is.
Cristopher Columbus thought he could arrive to the Indies in approximately two months of journey through the Atlantic. After reaching America, thinking he had reached Asia, he denied having discovered a new continent, despite the evidence.
Another proof is that Magellan did not stop in Chile to get supplies before crossing the big ocean, and that, although probably seeing the coast of Valdivia, he decided to continue his journey. Until here, everything shows that very probably Magellan thought the ocean would not be that large and that they would soon reach the Moluccas.
However, the route they followed shows that, once they crossed the Strait of Magellan, and they set sail to the north to reach a warmer climate as soon as possible, it took them a very long time to reach the equator. They had to cross more than half the Pacific to reach it.
Therefore, if Magellan had thought that the journey through the Pacific was going to be short, he could have left the Moluccas to the north and navigated south the equator for 10,200 km. He would have passed by the Moluccas.
If we look at the map, they did not reach the equator until February 13, 1521, after sailing around 10,200 km since they first started to cross the Pacific. At that moment, they still had to do 7,400 km to reach the Moluccas on a straight line.

It is reasonable to think that Magellan considered the circumference of the Earth to be at least 7,400 km smaller than it is, so that it was around 33,000 km long instead of 40,000 km. If he had thought the Earth was even smaller, the route he followed would have been absurd.
This makes us think that it was a big mistake not to stop in Chile to get supplies, as it would have prevented much of the scarcity they had to face and many of the deaths by illnesses, especially if Magellan knew he still had to sail 10,000 km to reach the Moluccas. Following this reasoning, Magellan did not know the Pacific was going to be so vast, although he did think it would be, and he sailed more than two times the distance between the Canaries and Santo Domingo to reach the equator, where he expected to find the Moluccas.
After crossing the equator, he went 1,500 km north, which leads us to continue thinking about where Magellan really expected to get. Although usually in the equator he would have found weak winds and it would have been convenient to deviate, that was not the case, and they were able to advance. They were not forced to go north.
Magellan ended his journey through the Pacific navigating for about 5,000 km without deviating too much from the Cochin parallel (India), even north of Malaca (Indonesia), where he had already been and where the Portuguese had established commercial settlements. However, I am reluctant to think that it was there where he actually wanted to go, but that instead he had heard from locals of some undiscovered lands further east. We should not forget that Charles V had named him governor of all the lands he discovered, which might explain his interest is exploring the area.
If there still are doubts, Elcano says: “Magellan and Caravallo never wanted to take that route [to go to the Moluccas], but they were told to do so, because I, pilot of their ship, witnessed so”. Declarations of Juan Sebastián del Cano after the trip to the mayor Sancho Díaz de Leguizamo.
About the fact that Magellan knew the Moluccas were in the equator, we have as a reference the Memorial he left to the King Ferdinand of Magellan when he left for his expedition, declaring the location of the islands of the Spices, and of the main coasts and capes that were in the demarcation of the Castilian Kingdom, in which Magellan tells the King as follows:
“The islands of Maluco are five, and as it is convenient to know, the three that are closer to the second line of demarcation, are all North South at two degrees and a half, and the island in the middle, is below the equinoctial line. The other two islands are as the other first two, so North South, and 4 degrees east the second line, and it is convenient to know, two north of the equinoctial line, and two south the equinoctial line, taken by the Portuguese pilots that found them”.
Did they leave the San Matias Gulf (Argentina) unexplored?
That coast line was a territory that had never been explored before. It is hard to believe that they passed by that gulf leaving behind an inlet of land to the west that may had led them to the Pacific Ocean – still not know by them at that point of time. According to the Derrotero, between February 20 and 21, 1520, they went from 40º 17 'to 42º 4', passing by the mouth of the San Matias Gulf. If it were correct, this would have been the day with the greatest distance travelled in the entire navigation of the American coast -about 270 km. It could have been like that, but it is quite shocking that it was exactly at the mouth of that gulf.
In addition, the following five days were devoted to exploring the New Gulf, which is much smaller than the San Matias Gulf, and which does not seem to merit a 5-day exploration.
We do not find any special mention in other documents about these days. Therefore, it could be that they actually explored it and we are facing some measurement errors or mistakes in the Derrotero.

Did they sight the Chilean coast at the same latitude of Valdivia?
I had to review many times the positions in the journey between the days 1 and 15 of December 1520, when they were bordering the American coast towards the north after having crossed the Strait of Magellan. In theory, if they maintained the direction every day, they would have reached land after day 13, which is obviously not possible.
Therefore, it seems obvious that the “dizzy needle”, as they called the compass, was marking a false north, setting it more to the west than it actually was. In fact, Pigafetta mentions that Magellan finds the mistake in the compass and orders for it to be corrected.
It is impossible to know with certainty how far the Chilean coast was from them at the latitude of Valdivia, and if they saw it or not, but if we also take into account the height of the Andes, and that during those days they could not measure the Sun to obtain the latitude, it is hard to believe they didn’t, despite not being mentioned in any original text.
Furthermore, the daily annotations indicate they went towards the coast for several days, more or less in the same direction, until they veer once they see it, navigating parallel to it for three days.
Against this hypothesis is that the coast is not mentioned in the Padrón Real of Diego Ribero, elaborated from the information given by Elcano after he returned. Not in this or any other map of that time.
Therefore, were they able to stop for supplies in those coasts with good climate before veering west, or did they simply not see them? It is hard to respond to this question.

Which were the small islets they discovered in the Pacific?
In the latitude established by Francisco Albo during the days 45 and 25 of January there are no islands, but he most probably refers to the Puka-Puka Island. According to the Relation of Ginés de Mafra, this first islet they found in the Pacific was at 15º, which is more proximate to the real 14ª82’, and rules out the other islands more to the south.
Considering that those days their direction seems consistent, and describes an almost straight line, it seems likely that the measurement error is not of just one day, but that it has been repeating for several days, which is quite weird. It could be that they had measurement errors in the declination tables, but it is hard to believe, because they were made in land with great care and as precise as possible, and they had been embarked in Seville. There is no simple explanation.
However, the second islet- the Island of Sharks (Tiburones)- seems to be precisely calculated by Albo, as it coincides with the Island of Flint. There is no doubt on this.
On the other hand, it is interesting to see how, west the this islands, from the 25th to the 27th of February, it is almost certain that they passed by other atolls, that they did not see, either because it was night time, or due to the haze, or simply because they did not have enough height to see them until they were almost there.
The latitudes according to Albo are marked in the map.

Why do we find several wrong measurements during the trip along the South African coast?
The hardest part to understand of the Derrotero is the one that deals with the South African coast. I have reviewed it over and over, and have devoted much time to solve it, and yet I am not quite certain of the real route they followed. On the contrary, there are many unknowns.
When they reach South Africa they find themselves facing what they identify as the Rio Infante, 33º south. It is evident that they have some maps of the coast. What map was it? Definitely a Portuguese map from before 1519. Bartolomé Díaz and Vasco de Gama had reached that river, nowadays known as the Great Fish River, in 1488 and 1497 respectively.

Albo’s description of the coast leads us to doubt, as it says it is “very rocky, without any trees”. However, it is hard to believe that the estuary of the Great Fish River has changed so drastically in five centuries, because now it does have a beach with rocks, but after the beach there is a lot of vegetation. Therefore, I thought there could have been a mistake in identifying the river, and that they actually were in front of a different one. In fact, many important rivers end in this coast, and I searched for which one had similar characteristics to that described by Albo. However, I could not find it.
Another factor that raises doubts is the determination of latitude that they were able to make during those days, because it happened to be cloudy and they could not measure the Sun. On the 7th they say they were in 33º58 ', and a day later they see land. On the 11th, when they leave the area, the clouds disappear and they can finally re-measure their latitude, they say they are 10 leagues "or more" from the river, at a latitude of 32º51'. However, if true they would be inland. On the map I have given them a latitude of 33º 67', almost one degree more, which would be the corresponding latitude about 10 leagues offshore of the mouth of the Great Fish, but this again makes me doubt whether they were actually facing another river further north.
Two days later, on the 13th, they were able to measure the latitude again, and again there is an error! This leaves me completely bewildered, or actually convinced that they were not in front of the Great Fish, but of another river further north, which would make the measurements correct. However, the following day they fund out to be too south, and therefore far from the coast, which contradicts the direction followed. But it also contradicts what they say- that they are only 7 leagues (38 km) from the Cape Agulhas, which they could be seeing if they were so close, in case of good visibility. But if they actually were at the latitude they say, they would be 31 leagues away from the Cape, not 7.
However, between these two days the distance travelled does not cease to be amazing in one way or another. They sail about 425 km. If instead of being in the Great Fish they came from another river even further north, the distance would even be greater, which would start to be difficult to believe. It is an important point against the hypothesis that they were actually in another river further north.
In short, as you can see, it is not easy to establish what was the true course followed during those days. They could have reached a river further north, but they could also have carried a map that included mistakes, and induced them to make erroneous remarks. In any case, those were very difficult days for our men, due to the frustration of having run into a coast that they thought they had overcome when they started their turn northwest from the Indian Ocean, but also because of the strong winds and tides that broke their foremast and foresail yards, and which even made them consider throwing overboard the valuable load of clove they were transporting.