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The idea is that a population of beings have a superior claim over others for the privilege of oxygenated air in a city/large settlement. I wanted to make this work that the other residents in the city have less oxygen saturated air in the outskirts of the area where the tree or trees are located.

How large would a tree need to be to sustain a group of 100 people with its oxygen production and how far would the reach be that others in the outskirts (let’s say 5000) would potentially need a breathing apparatus to survive?

I had considered the idea of plankton as a generator of oxygen but I encountered the same issue as I’m querying now. I’m not sure of the volume that would be needed to sustain a population of 100, with a reach that would almost sustain 5000 with the air of breathing apparatuses.

For added context this is a dark fantasy world, the population of 100 would be elves and the other 5000 would be of other fantasy races.

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    $\begingroup$ First you say 100 people, than you say they are elves. What are their metabolic needs? $\endgroup$
    – L.Dutch
    Jan 25, 2023 at 10:19
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    $\begingroup$ This won't work how you think it does. The kind of breathing apparatus(es) you think of do not create oxygen, merely freshens up the air you breathe in too breathable quality. If they do provide fresh oxygen, there is no need to live near your tree. It also means that your 5000 extra people do not use any less oxygen than the first 100, only that they can make do with a worse quality of air. Your tree will need to provide oxygen for 5100p. $\endgroup$
    – vinzzz001
    Jan 25, 2023 at 10:29
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    $\begingroup$ Gases mix freely. If you have an oxygen source somewhere the oxygen won't stay near the source; the gas will try to mix with the entire atmosphere of the Earth. $\endgroup$
    – AlexP
    Jan 25, 2023 at 10:36
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    $\begingroup$ I saw it said in another worldbuilding question that assuming 100% optimal conditions (IE a high-tech greenhouse) then you need about 50 square meters per person for oxygen production. In a basic open-air environment you could probably 5x that. Even the biggest tree isn't going to have enough surface area for more than a couple of people. $\endgroup$
    – Kaz
    Jan 25, 2023 at 20:21
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    $\begingroup$ You need growing plants. They take the carbon from CO2 and use it to grow. An old tree or forest with a stable mass is just a carbon storage, not a carbon sink + oxygen producer. $\endgroup$
    – Michael
    Jan 26, 2023 at 9:27

8 Answers 8

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A small frame challenge:

Scaling up a tree will not provide more oxygen, as, absent some new biochemistry, larger trees tend towards net neutral oxygen production, eventually becoming net oxygen absorbers before dying. This is almost certainly an absolute cap on volume of the tree, just as how far a tree can draw water up is an absolute cap on the height.

This could possibly be circumvented by something like the quaking aspen, where there is a sort of cluster of trees all joined by roots.

We generally think of old growth forest as a carbon store, not a carbon absorber, and part of this is due to tree age. There's some good research by the US forestry department on it, but I'm struggling to find it at the moment.

However, if your giant trees have some form of highly efficient photosynthesis, all bets are off on size of tree.

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    $\begingroup$ It's important for people to remember that plants do photosynthesize... but then they turn around and use their own sugars they just made for metabolism. And like most life on Earth, they use oxygen for that. Mostly only plankton does net oxygen output. $\endgroup$
    – John O
    Jan 25, 2023 at 21:39
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    $\begingroup$ @JohnO - trees definitely do produce net oxygen during their lifetime, but most of their net oxygen production will happen during middle age $\endgroup$
    – lupe
    Jan 25, 2023 at 21:55
  • $\begingroup$ @JohnO - The tree needs to be big enough to shade the ocean so it doesn't boil off and all the plankton die, because that's where 80% of it comes from, +1. If we kill the seas, which would only take a few degrees difference, then we all die right here, right now. $\endgroup$
    – Mazura
    Jan 26, 2023 at 1:20
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From https://space.stackexchange.com/questions/26668/how-many-plants-would-be-needed-to-produce-oxygen-enough-for-20-humans

"A 100-ft tree, 18" diameter at its base... very roughly, seven or eight trees' worth per person"

Approximating a tree as the volume of a cylinder, πr²h, the typical tree mentioned above is 56.25π cubic feet.

So for 100 people, the tree would need to be 700-800 times the size of a 100-ft tree, 0.75 feet radius at its base.

100 people would need a tree 42187.5π cubic feet. The tallest trees are about 320 feet tall, so if the radius is 11.5 feet, they will be big enough to provide oxygen for 100 people. Or taller and thinner, as long as r²h ≈ 42187.5

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    $\begingroup$ I don't think the oxygen-producing capacity is linear in the size of the tree, but in the number and size of its leaves. $\endgroup$
    – chepner
    Jan 25, 2023 at 18:59
  • $\begingroup$ Agreed with chepner, I would think it more useful to approximate a tree as a sphere of leaves and determine oxygen output per volume of leaves. $\endgroup$
    – Drake P
    Jan 25, 2023 at 19:49
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    $\begingroup$ Applaud trying to work out the maths here, but I think this is pretty close to the "assume spherical cows" of physics lore. This is definitely not going to be a linear relationship between tree mass and O2 production. It's probably not even a linear relationship between leaf mass and O2 production $\endgroup$
    – lupe
    Jan 25, 2023 at 19:52
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    $\begingroup$ @DrakeP As the size increases towards ridiculous proportions, it would be the surface area of the sphere of leaves that matter, not the volume, as the vast majority of leaves by volume would be in darkness. $\endgroup$
    – forest
    Jan 26, 2023 at 4:26
  • $\begingroup$ FYI, the tallest tree ever measured was a 480 ft tall Australian Mountain Ash (also the tallest flowering plant). Unfortunately, this species was extensively logged and the tallest specimen alive today is only 328 ft tall. $\endgroup$
    – Bohemian
    Jan 26, 2023 at 20:46
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Ultimately, the carbon cycle (between CO2 and food) is a closed cycle, so a tree or plant that can provide oxygen for 100 people could, if edible, provide enough food for 100 people. That should give an idea of the size required. It's a lot of broccoli !!!

There are other sources of oxygen that rich people could use. Spacecraft and personal breathing apparatus use substances like potassium superoxide, that react with CO2 and moisture:

2KO2 + H2O + CO2 --> K2CO3 + 2O2

With our current infrastructure, people do not like living near power stations. In future, a solar, wind or hydroelectric power station might be used to split water into hydrogen and oxygen. The hydrogen could be used as a fuel directly, or used to synthesize more easier to store/handle fuels such as ammonia (in combination with atmospheric oxygen) or hydrocarbons (in combination with a source of CO2.) The oxygen could be dumped into the atmosphere, and in an oxygen starved world, this could make the area round a power plant an attractive area to live, perhaps even causing a city to grow around it.

Of course, for an existing city, hydroelectric is the most conceivable type of power station, as it doesn't involve building a huge number of windmills or solar panels. The first city that comes to mind is Las Vegas, which is very close to the existing Hoover Dam.

EDIT: I just noted this is a fantasy setting. But elves are smart, and if they are the only ones who understand electricity, other races would see it as no different to magic. In post-apocalyptic novels, rustic people give their awed views of advanced tecnology (without the author spelling out what they are.) For example in the Chrysalids a "fish shaped flying machine" is described (presumably a helicopter) and in the Tripods, heros from a rustic England move to a slightly less rustic France and encounter a machine called a "shmand fer" which is a railway train (French chemin de fer).

I can't think of any other ancient industrial process that could produce vast quantities of oxygen. Perhaps some kind of precious metal refining.

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    $\begingroup$ How do you use the produced hydrogen as fuel if you have no atmospheric oxygen to spare? Hydrogen and derivatives is a useless energy source because it costs energy to create; it's primary use is as an energy storage material. In this world, you would use the electricity to crack valuable oxygen out of water and CO2 for breathing, then discard the hydrogen and carbon which is mostly useless (unless you want to make other products like ammonia (from atmospheric nitrogen) for fertilisers etc. or artificial carbon materials). $\endgroup$
    – BBeast
    Jan 26, 2023 at 0:05
  • $\begingroup$ P.S. Although, if you have access to fusion power, then my above argument doesn't apply. With some space-magic-tier fusion reactor, you could have some device where you feed in water and it spits out oxygen, helium (which probably gets vented) and electricity. $\endgroup$
    – BBeast
    Jan 26, 2023 at 0:13
  • $\begingroup$ @BBeast Oxygen starved doesn't mean no oxygen; if there were no oxygen, humanoids wouldn't be able to breathe at all. People would pay a premium for good air. Similarly people in Africa get by drinking dirty water, while those who can afford it spend more than a dollar on a small bottle of mineral water. $\endgroup$ Jan 26, 2023 at 19:01
  • $\begingroup$ Perhaps. If the hydrogen is produced in one place, shipped elsewhere, then burned, that would result in a concentration of oxygen around the production plant. This requires there to be other sources of oxygen production (or else some of the hydrogen is not burned), though, otherwise the whole system is net neutral in oxygen production. But if you can deal with that you'd get the location inequality which the querent wants. $\endgroup$
    – BBeast
    Jan 28, 2023 at 9:18
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163,200,000lbs or 74,026,275kg plus 5% per year for everyone.

Or 1 general sherman just for the elves.

Assuming you have a way to contain the gasses. It takes six molecules of CO2 to produce one molecule of glucose by photosynthesis, and six molecules of oxygen are released as a by-product. A glucose molecule contains six carbon atoms, so that’s a net gain of one molecule of oxygen for every atom of carbon added to the tree.

A mature sycamore tree weigh 4000lbs, including the roots and leaves. If it grows by five per cent each year. The actual calculation is a huge mess, big trees grow faster than small ones, see source below) so we are ballparking it. It then produces about 100kg of wood, of which 38kg will be carbon. Allowing for the relative molecular weights of oxygen and carbon, this equates to 100kg of oxygen per 4000lb tree per year.

A human breathes about 9.5 tonnes of air in a year, (lets say elves are the same) but oxygen only makes up about 23 per cent of that air, by mass, and we only extract a little over a third of the oxygen from each breath. That works out to a total of about 740kg of oxygen per year. That is about eight 4000lb trees worth or 32,000lbs per person.

So for a rough ball park estimate your tree should be at least 3200000lbs or 1,451,496kg or roughly 1 General Sherman just for the elves. But it also means the tree needs to grow by about around 5% or 160,000kgs per year. So start with 3200000lbs and then add about 5% per year it has been supporting those elves.

keep in mind if those humans are using fire for anything, cooking, heat, ect. they need a LOT more trees.

Now lets add in the extra people this is easy, 32000lbs times 5100, or 163200000lbs and again add 5% for every year it has been keeping them alive.

http://conditdatacenter.org/pdfs/StephensonConditEtAl_Nature2014.pdf

Note:I did get many of the starting number from a BBC publication I use in class about this. xerox of an article. But I don't know the original author is, if anyone does, please post in comments and I will add it.

Just for the elves you need this.

enter image description here

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It seems small, faster-growing plants are a better bet than most trees. You might want to follow what this bloke does.

Reply to comments: Yes, it would be nice to have families live in a. single giant tree (I am thinking of Robert Silverberg;s 'Lord Valentine's Castle'). If we cannot find a single tree that fits the bill (and why would there be one - a tall tree has put a lot of effort into being tall and getting the sunlight, though genetic engineering could do anything) but you could have a second species like the strangler fig using the larger tree as a support.

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I think that the tree would have to be really large with long branches and leaves, covering like 100 or 200 meters wide, each leaf double the size of a normal tree thus generating much more oxygen and maybe the same in height, i'm not a biologist but i'm pretty sure such a large and tall tree could produce lots of oxygen, I don't know how long the tree would have to be living in order to achieve such measures, maybe the soil where it lives is so nutricious that the tree grew 100x what a normal tree would.

EDIT:

After some initial research, i found out that generally speaking, a mature tree can produce oxygen at a rate of around 48 pounds per year. Therefore, a group of 100 people would need around 4,800 pounds of oxygen per year, which would require approximately 100 mature trees.

Therefore maybe a tree that is the size of 100 mature trees would seal the deal.

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How large would the tree be?

Trees release O2 when they absorb CO2 into themselves. So, it's not a question of how big the tree is, but of how fast it is growing. One person consumes ~400L of oxygen per day which is ~17 moles. 17 moles of pure carbon is ~200g. So for 100 people, a tree would have to gain at least 20kg (not including water) per day.

Done a second way to check our work, 1kg of coal is 7000 Calories. A person consumes about 2000 Calories per day, so a tree would need to gain about 1kg/7000Cal*2000Cal*100 = ~30kg per day.

If a tree is 50% water, that means it must gain 40kg-60kg per day. This would also hold for bamboo, aglae, etc.

How far would the reach be?

Let's assume there is no wind. Oxygen in air has a diffusion coefficient of 0.176cm^2/s. In 3D, this gives a variance of 6Dt = 9 m^2 per day for a standard deviation of 3m. This means that after a day, 68% of the oxygen will have traveled 3m or less, 95% of the oxygen will have traveled 6m or less, and 99.7% of the oxygen will have traveled 9m or less.

Your city would still have to block wind from blowing all of it away.

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Most of the mature tree is not the living tissue. The substance we understand as "wood" is the dead tissue that still serves its function of water transportation and mechanical support. Hence your question simplifies to how many leaves per person do we need while the trunk and the branches must be such that these leaves still could be distributed acceptably, receiving enough of the sunlight.

A single large tree is capable of providing the oxygen for about four humans. Hence your tree must have about 25 times more leaves as an ordinary large tree, placed such that they all receive enough light (the stem will deliver water). Up to you how do you arrange them.

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