The Infinite Sea, how narrow can that be?

Question

I have a Roleplay setting on the books. It's a constructed pocket universe that the Dragons built to hide from the Great Old Ones; because of its structure, there are vast bodies of water, potentially millions of kilometres, of deep, open ocean water without so much as a speck of land. Such expanses are generally considered by those who live on their shores to be effectively infinite since even with a healthy dose of magic the distances involved are just too great.

Over millions of kilometres, without any land-based support and resupply, any ship will eventually founder. But what I'm wondering is how narrow an ocean might be and still be effectively infinite to a sail-based maritime civilisation. Human civilisation is rather variable in this world so as the technological benchmark for creating a relevant answer use the height of the Age of Sail and ships like the Cutty Sark or possibly a sturdier version of the Wyoming; iron or steel framed but wooden hulled vessels in the 90-150 metre range with displacements up to 10,000 metric tonnes. My question is what would be the maximum range of such a vessel that was built specifically to go as far as possible, and conversely, how large would an ocean have to be to defy effective exploration by such a vessel?

Please note that while the world contains magic I have deliberately left that tag off with the intention of excluding it from consideration within this particular question, with one exception; a ship's crew can use magic to evacuate if they cannot find land so exploration trips can be made to the absolute limits of supply endurance.

Answer 1

You should read Antonio Pigafetta's journal. He was one of the first sailors to make a voyage around the world, a member of Magellan's crew. They almost died of starvation while crossing the Pacific. In fact, given what he wrote, the width of the Pacific might do for you.

Notice that it is not just the width that will make an ocean hard to cross... The Pacific got its name due to a part of it where the weather is so tranquil, sail ships had a hard time going anywhere in feasible time (i.e.: there were winds, but they were too weak). That's what caused many sailors to die from starvation in Magellan's voyage.

If your oceans have little to no wind (absence of wind could be explained by magic), or if the winds will never blow towards shores, your sailors may be trapped forever there. Just reduce this effect to cause them to take years to cross it.

But remember: humans are quite the explorers. In times of peace, there will always be someone who will gather immense amounts of food in very large fleets and set out to explore. They may even prepare to survive on fish and filtered/magic water only. At some point they will conquer your ocean.

Answer 2

Wow - so you have a pocket universe, which is great. You can use any topology in a pocket universe, which means you can have an effectively infinite sea within a topological space.

For instance, you could use some form of continuous fractal surface - the sea would not have any discontinuities, it would be infinite in it's size, but it would fit within the pocket universe. Yet, and with no difficulty, every point in the sea would be a unique point so that you could provide a pair of coordinates that pinpointed a specific place, and yet even if one was nominally 'next door', one would never ever be able to travel the distance by sea - because the sea journey is infinite.

Answer 3

Renan has a great answer, but doesn't consider magic. You've said that crews can magic back to safety if need be, so we can take advantage of this to massively increase our range. I'm going to use some assumptions here, but you can alter these assumptions based on your world.

Assumptions

1. Your exploration fleet is 25 ships. This is based on the size of the fleets the British Navy had during the age of sail. I'm not a historian, so please alter this to fit how many large ships your nation can build for this expedition.

2. You can crew these ships with a barebones crew of 50 men. This is based on Magellan's crew. He started with more than 200 and finished with 18. I'm guessing 50 could crew a ship effectively.

3. These ships can sail the Pacific in 3 months. This is also based on Magellan's trip.

4. Your ship can carry enough supplies to support 150 sailors for 3 months, or 50 for 9 months. This is also extrapolated from Magellan's expedition.

5. The width of the Pacific ocean is 17000km

The Strategy

You will sustain all of your crew members off the supplies of a single ship. When that ship's supplies are depleted, these sailors magic home, and the remaining sailors eat from the next ship, and so on until there is only one ship left.

The Math

Using the numbers from above, if you start with 25 ships, you have 1250 sailors. This math is very much like the Rocket Equation, but I'll do the math by hand for simplicity.

If 50 men can survive 9 months, then 1250 men can only survive .36 months. There's no more use for that ship or the men, so they magic back and there's only 1200 men. These 1200 men can survive for .375 months and so on...

1250: .36
1200: .375
1150: .391
1100: .409
1050: .429
1000: .450
950:  .474
900:  .5
850:  .529
800:  .563
750:  .6
700:  .643
650:  .692
600:  .75
550:  .818
500:  .9
450:  1
400:  1.125
350:  1.286
300:  1.5
250:  1.8
200:  2.25
150:  3
100:  4.5
50:   9

Now we sum the whole thing and get 34.34 months of sailing for the last ship. If Magellan's ship could go 17000km in 3 months, then this ship could conceivably have traveled 194593km in its 34.34 months. That's with a lot of guesswork, but you can use my method with whatever numbers you have to get numbers you think apply to you.

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Edit: In the comments a number of limitations have been raised - I'm pulling them in to the answer because they're valid concerns.

This doesn't take into account the fact that supplies -- even fresh water -- have shelf lives. Spoilage and/or loss to mice, etc., will take a toll. As will ship repairs after any storms, etc.

Sailing is not only about supplies. You have to repair the ship sometimes. You need to remove barnacles from the hull periodically, for example, or else the ship will become slower. Sailors of old did so by careening their ships, which can only be done on shallow water. Bottom line: your food may last for years, but if you don't stop here and there every once in a while your ship will deteriorate as fast as if it had been abandoned.

Consider that both of these need to be addressed to make this strategy viable. It's my opinion that they can be solved with magic, since your world allows it. Otherwise, you'll have to find a non-magic solution to these problems, which may or may not be possible.

Answer 4

I propose an alternate approach to a wide sea, and a pleasantly mythological one. The Sea of Worms! At a certain distance from shore, your ocean teems with hardy creatures, the eponymous worms. These little beasties feed on the cellulose of deep-ocean plants, but prefer the warm, upper waters to spend their time in (and who wouldn’t!). A wooden hulled ship sailing through their waters would be akin to you discovering that there’s a tray of donuts passing by while you’re relaxing in a hot tub: a delicious and welcome surprise.

They can be a more voracious and numerous version of the Teredo navalis, which has a stupendous effect on submerged wood: Assuming you have their habitat also be in a doldrum-prone area of the ocean, so they have time to do their wicked work, you have a virtually impassable barrier for wooden hulled ships.

Answer 5

It seems like most of the answers are assuming the residents of this place have an infallible way to navigate. I put in a comment...

What are they doing for navigation? It's pretty easy to turn a boat around once it leaves sight of land. Pocket universe doesn't have to contain stars, magnetic is easy to mess with, currents change. Nobody could tell, until they arrived home again. Even if it just has the closest star (like a sun) that's only useful part of the daytime. Heck two continents could be a couple hundred miles or km apart and be unreachable, in effect.

...asking about details.

Lacking details, for now, There is a reason that, for most of our history, most boats who returned from their voyages stayed within sight of land. Ignorance, mostly, not know what there was, not knowing how to make sure they got there, belief in magic that didn't actually work.

Much of the exploration of the pacific was facilitated by all the islands, as indicated in other answers, from a survival standpoint, and from a navigation standpoint. Take away all land, no stars and and uncertain (unmappable) currents, and you don't need vast distances. If it's overcast at sea, you don't even get the sun much (assuming there is one)

This means that if someone knows the secret of traveling the seas, and it's not all that far, some one power can be very powerful indeed.

Answer 6

Given an infinite amount of time they can just build a bridge to the other side of the ocean. (either a floating one or not) So, it has to be at least as wide as the bridge they can build using their land ressources.

Answer 7

At least 14028 square miles if using modern sails in ideal conditions or 7260 miles if you are sailing at the speeds of a Cutty Sark

Let's assume the Dragons are scared and Over-engineer to avoid detection and believe that the crew is perfectly optimized with perfect food storage

Crew Size

For a ship like the Wyoming, a crew of at least thirteen people needed to be working for its operation.

Space

From the wiki, we learn that

a cargo capacity of 303,621 cubic feet (8,597.6 m3)

this means every person gets provisions for (8,597.6/13) -> 661.4 m3 of supplies

Food and Water

According to this site a sailor will need about 3.7 liters of water or 125 ounces per day or (0.0037 m3).

Common knowledge on the back of any food product will tell us the recommended amount of food is 2000 Calories.

If we are eating a balanced diet and proper portions

1. 5 1/2 ounces of lean meat - roughly 1 cup
2. 2 1/2 cups of vegetables
3. 2 cups of fruit
4. 3 cups of low-fat or fat-free milk or the equivalent dairy products
5. 3+ ounces of whole-grain products - roughly 3 cups

10 cups of food or (0.000236588 cups in a meter3) 0.00236588m3

which ensures people consume (0.0037 + 0.00236588)-> 0.00606588m3 of food and water per day.

since we have 661.4m3 of room for supplies, we divide by 0.00606588m3 to get around 109036 days of travel before

Speed

How fast can our ship go will determine how big the ocean must be. If we look at the upper limit of current technology, it seems that the fastest we can go is around 64.45 knots or 75.2 miles (a world record but seems achievable with magic).

Assuming tireless workers, that is (75.2*24) = 1804.8 miles in a day that could be traveled

For a ship like the Cutty Sark -> this should be 20.14mph -> (20.14*24)-> 483.4 miles in a day that could be traveled

Total Travel Distance

1804.8 * 109036 => 196788172.8 miles -> before you run out of fuel and need to teleport back outside of pocket realm

483.4 miles * 109036 => 52703640.96 miles -> before you run out of fuel and need to teleport back outside of pocket realm

square root of 196788172.8 is 14028.1207865 which is the area you would need for modern ideal circumstances

square root of 52703640.96 is 7259.72733372 which is the area you would need for operating a sail at the speed of a Cutty Sark

Answer 8

I see some excellent answers using a lot of calculations to derive some potential distance limits. Allow me to propose an alternative possible method.

It has been proposed that sudden releases of methane gas from the sea floor can create plumes of water which are markedly less dense than normal water. Should a boat enter these less dense areas, they would immediately sink to the bottom. The disadvantage of this method is the requirement for massive amounts of methane gas, a non-renewable resource short of underwater or under-seafloor fields of cows or other cattle.

If magic is on the table, it becomes much easier to have regions of permanently less dense water which would provide a completely impossible to cross barrier for sailing ships, unless one knew the secrets of how these regions were laid out. However, as the question specifically didn't want to use magic as the solution, I mention this only in passing.

Note that magic is NOT required in order to have these less dense regions. As another alternative one could even postulate giant sea creatures which instinctively target boats and release enough gas into the water to drop them below sea level far enough to fill up, and then naturally sink thereafter. Giant kraken or other aggressive anti-ship sea creatures would also provide a means of preventing any ships from returning or any survivors at all.

Place the other coast of your ocean out of visual distance from these less-dense and/or dangerous creature-infested regions, and your ocean can be any distance greater than the minimum distance required to see land from these regions, which according to some internet research is approximately 12 nautical miles (22.2 km; 13.8 mi), give or take depending on your height from sea level.

Thus, if you wish these less dense regions (and thus any disappearances) to be out of sight of land, then you would need to place them around 13 nautical miles from the first coast, and the opposite coast another 13 nautical miles.

This gives a minimum possible distance of 26 nautical miles as the most narrow possible ocean. Note that this assumes a planet approximately the size of Earth. This value will change depending upon magical visual capabilities, size of vessels (notably height of the tallest mast), and actual size of the planet, among other factors.

Answer 9

Distance is a function of velocity and time.

Distance is determined by the average windspeed, and the headway your vessel can make in both directions using (or fighting) that wind. For example: Perhaps, given a wind I chose, let's say your vessel can make 7 knots outbound and 1 knot inbound. In other words, the vessel can travel 21 nautical miles and return to it's starting point in 24 hours.

Time is a function of the crew size and cargo capacity. Let's pretend that one surveying expedition has an extra-small crew of 30 because they don't intend to land (landing is next season's task), and the cargo capacity of the vessel can carry 250 days of food and water for those 30 sailors.

250 days x 21 nautical mile range per day = 5,250 nautical mile range for the entire journey.

Of course, this is an oversimplification: It assumes excellent navigation skills and precise tools. It assumes a constant wind, no storms, no currents, no doldrums. The crew arrives home with no food or water left...which stinks if they're only, say, two or three days late. Also, a crew of 30 may be too small to keep the ship afloat in a storm and to make repairs afterward.

People are clever - fishermen charted the storm seasons and currents long before explorers used that knowledge ranging out into the deep waters in search of adventure.

Then you get into staging (like rocket stages): Extra vessels that turn back early, carrying extra supplies for the expedition to boost it's range.

Answer 10

It would have to actually be infinite. To make crossing it truly impossible? It would have to be infinitely big.

Let's say you have a boat that can carry enough supplies to travel X distance.

If you instead send 2 boats, then at .5 X, both boats have half supplies. You magic back the crew of one boat, and transfer the supplies across to the other. That boat continues on, X distance - it has now travelled 1.5X. Do it again, adding two more boats to the fleet, and you will be able to get the final boat to 2 X.

Every time you double the number of ships in the fleet, you will increase the distance you can travel by .5 X. Which means that a sufficiently determined civilisation is capable of crossing an arbitrarily large ocean.

Even if you remove magic, and require the the emptied boats retain enough supplies to return, it's still possible, you just need a lot more boats.

Answer 11

Infinitely big, or rendered impassable by other means (rough water, etc).

While explorers could brave the waves in search of adventure, etc, the ones who will really test the limits are those who have no other alternative.

The Polynesian migration is one example of the distances this can bridge, given enough time.

So when there's a good enough reason to leave (war, resource exhaustion, running out of space, etc), those who can, like those already living off the bounty of the sea, will start to spread out.

With appropriately designed ships, and the correct skills, they could live at sea indefinitely. Islands would provide landmarks, and places to put down roots for a generation or so, but eventually they'd expand and at least some would move on.

Repeating that cycle long enough will fill any size ocean, unless there are hard limits to expansion:

• Impassible currents, though technology will eventually find a way around this
• A continent with a firmly established civilization, though this doesn't work with the premise
• Hostile and dangerous creatures, though humans will figure out how to eat these eventually, so breeding quickly is a plus
• Something which makes navigation unreliable, which is implausible, but effective. Making this work would allow you to make the ocean almost as narrow as you'd like.

The root of the problem is finding away to make whatever limitation you decide to use reasonable and consistent. What you don't want is the equivalent of the invisible walls video games were so fond of during the 90's.

Answer 12

You need to specify some other things. What is the typical weather they will be encountering? Is there going to be regular rain, which can resupply fresh water? Are there marine animals that can be fished and eaten? Do they have technology that can distill fresh water? How is their food preservation? Do they understand concepts like scurvy, so that they understand they not only have to take into account the amount of food, but also the right kind of food necessary? If they do, they could go a very, very long way.

To use real-life example, Reid Stowe sailed the Anne (a 70 foot schooner, 60 tons) out of sight of land except for departure and return and with no resupply for 1,152 days, and still had an estimated year's worth of food aboard (not counting plants he was actively growing). Assuming an average speed of 12 knots, generally constant favourable winds, and a similar crew to cargo ratio with the capability of gathering freshwater without needing to land, that puts the distance theoretically covered in 4 years as 420,480 nautical miles.

If your ship was designed specifically to operate with minimal crew, had generally favourable weather, was well-constructed to not need major overhaul, and things like acquiring fresh water and fresh food (through fishing and/or growing plants) to extend the endurance of the crew, five years would be entirely reasonable. Keeping the average speed to 12 knots (which it won't be, but magic), that gives a potential range of 525,600 nautical miles.

Beyond five years I think the issues are that things are going to start breaking that can't be repaired, and the crew is probably going to start going wiggy.

Answer 13

In a constructed universe, you can cheat in ways that let you have the ocean be much smaller. If you have some undersea trench that (by whatever mechanism) pumps water from under the known islands through the core of the world and out the other side, there will be a constant current against any attempts to explore. If there are no winds (or minimal winds) over large stretches of the open ocean (for whatever reason), then you can hit a point where it's simply not possible to make realistic headway against the currents. You might be able to do somewhat better with decks of rowers, but at that point you start running into serious food supply issues.

Answer 14

If it's a pocket universe, perhaps it doesn't have the usual topology one might expect. So the sea might not be infinite in size, but might somehow "roll around" or "roll up" or have strange interconnections, that prevent a person from travelling from some points in the universe to other points in the universe, while staying within that universe. Or perhaps its metric (the thing that defines distance) isn't constant but shrinks further from the centre so it takes more and more time and effort to travel the next bit of distance.

That's your infinite sea - and it will work, whatever time and resources are allowed, as long as travel (magic or not) is restricted to being within locally connected points in that universe.

Answer 15

They would not live long.

They need fresh water to survive, unless they know to harvest rain water or process ocean water in the ship. For all life forms, this does not bode well.

Also The vessel would disintegrate without any maintenance, for which land is required.

Human hybrids with fish like gills can solve your problem. No need for a ship.