Without our modern technology of food storage, how would a ship go about feeding its crew for long trips, ex. sailing from Europe to the Americas? I'm inquiring information for larger crews (300+) and their diet, daily intake of calories and how the food was stored. Also, what actions would the captain take if a ship starts to run out of supply due to unforeseen events? And would individuals try to fish to supplement the food supplies?
The average time of the Transatlantic crossing in your timeframe is roughly 2 months (Give or take a month).Fishing was a major part of the sailors diet. There was never a true certainty that a ship would arrive at its destination on time. So if food supplies were running low, there were plenty of fish around the boat, all that was needed was for them to be caught. It would take quite a large storeroom for all the food needed for 300 men, so more often than not many ships relied on the waters they traveled to feed them.
For drink, ships used wine & rum to kill off bacteria & pathogens. The alcohol would be kept at a lower content, so the sailors could function. Water was used sparsely on transatlantic voyages, as it had higher probability of carrying diseases. And the rum was always carefully rationed, since hungover sailors & no rum doesn't make for easy sailing.
Meats were generally packed to keep for long amounts of time. Smoked & salted beef, pork, poultry, and other meats were kept, as well as fresh fish. Boats more often than not carried some sort of livestock to butcher once at sea, to keep some fresh meat as far into the journey as possible. The cook usually made a stew, since it kept longer than just grilling the meat.
The core of the sailors diet came from bread & beans. Sea biscuit and hardtack kept for a while, and if combined with some oil or wine made for an alright mash. Beans can be kept for months, and are tightly packed, which are 2 big pluses when packing a ship. If a vessel was going to a rice growing area, they would probably purchase some rice as well for variety.
Mind you, there are several stops between Europe and America, the two most prominent being Bermuda & the Azores (closest to Protugal). A captain can stock up at those places if it is along his route, and refresh the crew. The success of Bermuda in its early days was a port for the British ships going from England to the Southern US colonies.
Scurvy was a major issue, and most mariners did not know much about preventing it, until Captain Cook. As we know fruits and veggies prevent scurvy. But Sauerkraut could be used to prevent it as well, and stored for a very long time. So after these findings (In the late 1700s) scurvy dropped dramatically in the sailor demographic.
If a ship was lost in the ocean due to storm or whatever circumstance, the situation went downhill quickly. With a compass or sextant, a navigator could find the ships position and direction it was heading. Without such tools, there was little hope of finding land. There was been several reported cases of cannibalism as last resort, but in an ordered society such as a British Navy vessel, I think the captain would ration out food to stretch as long as possible.
SOURCES:
I've answered a few questions about victualling (including drinks), repair and logistics during this period in the past that may be of use to you:
https://www.reddit.com/r/AskHistorians/comments/3wyzlw/during_the_age_of_sail_would_warships_have/
To answer your question more directly, in the period I study Royal Navy ships would have been stored with foods that lasted a long time, and would supplement them with purchases made at ports or from fishermen while abroad. Sailors' daily meals would consist of mostly bread and salt meat, with hard cheese and dried vegetables (often peas) rounding things out. The ration was around a pound of bread or hardtack daily, a pound of meat or its equivalent (salt pork and salt beef most commonly, but two days a week were meatless and men would eat duff instead), half a pound of cheese and a half pound of vegetables. The daily alcohol ration, which more of in a minute, was a gallon of beer if in local waters, or a pint of rum or its equivalent overseas (wine in the Mediterranean, arrack in Indian waters, etc.)
Protestant sailors, at least, did not eat much fish; the cod fisheries of the Americas supplied the Catholic navies of Spain, Portugal and France much more so than the English and later British. Sailors would not generally fish to replace victuals, as the pelagic zone is largely devoid of attainable marine life near the surface, but they might well buy fish from local fishermen.
The nature of scurvy (that it was related to vitamin C deficiency) was not well understood in the 17th century, but captains understood that "greenstuff" or fresh fruits and vegetables would ameliorate symptoms. They would attempt to resupply with fresh food whenever possible, and particularly when the Navy would be stationed overseas for a long period of time, local victualling agents would be in charge of purchasing fresh food and supplying it to the fleet.
Now the issue of alcohol in the Navy is one that's badly misunderstood. A couple of my posts above get to this, but the idea that sailors drank beer or rum because water was unhealthy simply isn't borne out by evidence. The daily rum ration (which, granted, wasn't set until after this time period) was a half pint total, served twice a day, mixed 1:3 with water; it's simply impossible for a working man to sustain himself on two pints of liquid a day. And in any case we know sailors drank water from an openly available scuttlebutt, as the quality of water over the course of a voyage is a source of much complaint in primary sources.
I can chip in here with a previous response that explains how the situation was managed by the Dutch East India Company around 1600-1700 on the much longer voyage (initially up to 18 months+ with one revictualling stop) from the Netherlands to Java:
The tl:dr is that the vast majority of food had to be taken with the crew in the form of cask meat and legumes. Early in the voyage this would be supplemented with fresh livestock kept on deck in creates, and there was an onboard "greenhouse" in which some vegetables were grown. The biggest difficulty in terms of producing palatable food was the lack of fresh water for cooking. Cooking was therefore done in brine and typically the rations were excessively salty when served.
There're also some interesting sidelights in terms of the taste of the various insects that got into the hard tack.