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Biological Design - Plants & Oxygen Production

In a question posed on another site (which no longer exists, but this acts as an address placeholder) a person asked "How many plants are needed to make enough oxygen for one person for one hour? We are experimenting with Anachris plants."

(Note, the answer to this is very important if we wished to design a world where enclosed environments are capable of providing and scrubbing their own air supplies by using natural plant growth. In sci-fi stories, we often see dome environments or spaceships with plants that provide the air, but these are usually very inaccurate as to how many plants are needed per person. We humans tend to think of "outside" as "uncontained," but we need to remember that a planet is essentially a gigantic dome environment, with the atmosphere acting as the dome. How many plants are on the surface of our planet? And how many organisms do those plants successfully support? The answers are undoubtably enormous. Remember this when designing your enclosed environments!)

To answer this question, the author ("wizkid") of the site's answer broke down the question into smaller questions:

1. How much oxygen does a person need in one hour?

The author essentially tells us that a resting, healthy adult on an average, cool day breathes in about 53 liters (L) of oxygen per hour. An average, resting, healthy adult breathes in about 500 milliliters (mL) of air per breath. This is called the normal tide volume. Of that 500 mL, about 150 mL go to non-functioning areas of the lungs called "dead space." The average breath rate of this person is 12 breaths per minute. The amount of air breathed in by this person that is available for use is:

12 breaths (500 mL - 150 mL) = 4200 mL/minute.

This answer must be multiplied by 60 to get an answer for an hour:

4200 mL × 60 minutes = 252,000 mL/hour. There are 1000 mL in 1 L. Converted to liters, this answers is 252 L/hour.

On the average, cool, clear day, only 21% of that air is actually oxygen. Therefore, we must take 79% of that answer away to get exact oxygen consumption:

252 L/hour × 0.21 = 52.92 L/hour. Round this up to 53 L, and we have an answer. The person uses 53 L of oxygen per hour.

There are a lot of assumptions in the above reasoning - average, healthy, resting adult on an average, cool, clear day. Any change to health, activity, size, sex, etc. of a person or the temperature, humidity, barometric pressure, etc. of the day will change teh figure we calculated.

2. How much oxygen does a plant produce in one hour?

To answer this, the author of the other site used data on how much oxygen leaves produce in an hour:

5 mL.

If the average plant has 30 leaves, that would be:

5 mL × 30 leaves = 150 mL/plant/hour.

3. Based on the above, how many plants will provide the oxygen needs of the person for one hour?

If the average person needs 53 L (53,000 mL) of oxygen per hour, and the average plant produces 150 mL per hour, then:

53,000 mL ÷ 150 mL = 353 plants.

Since these are round figures, let us just say that between 300 and 400 plants are needed to produce enough oxygen to keep a person alive in one hour.

Again there are many assumptions - average leaf, average plant. Not calculated, but mentioned, is the fact that as carbon dioxide (CO2) concentration increases, oxygen production in a plant decreases. Assuming the person is in a confined space with these plants, the CO2 concentration will rise due to the person's expiration. This will inhibit the plants' photosynthetic rate. Also in need of consideration is how much light and water are needed for the plants to continue to produce oxygen. Here ends the original article.

Unanswered Aspects - Anachris Plants

Now, even though the author of the other site's answer to the original question provides us with excellent information, it is really not an appropriate answer to the question. The query was indirectly about Anachris plants, not "the average leaf." Let us try to answer that question more appropriately by re-asking "How many Anachris plants are needed to make enough oxygen for one person for one hour?" The author already answered most of this question, but they did not convert the "average leaf" to the "average Anachris leaf." We will follow his lead:

4. What is the size of the average leaf?

We are going to have to make some assumptions of our own to get a better answer to this. Growing up as children, we are shown that the average leaf is unassuming, somewhat teardrop or pear in shape, and probably about 7.5 centimeters long (about 3 inches) long by 4 centimeters (about 1.5 inches) wide. A close, real world example of leaves close to this size is the the red-tipped photinia shrub. This is a common ornamental shrub that has leaves with flame-red tips. So let's assume the author of the site mentioned above was using this size leaf for the "average leaf." Therefore, one average leaf of this size is capable of producing 5 mL of oxygen per hour.

5. What is the size of the average Anachris plant leaf?

What is an Anachris plant? Anachris plant is the average aquarium plant seen in most home or office aquariums. They are tiny, and an entire plant can fit in the palm of a full-grown man. So, we can see how the author's answer did not really help the person asking the question. The average leaf is about as long as a third of the entire length of one stalk on an Anachris plant, if not more. To answer question number 5, we are going to average out how many Anachris leaves are equivalent to one average leaf.

The average leaf on the average Anachris is about 2.5 cm (about 1 inch) by 0.5 cm (about 0.25 inches). In order find out how many Anachris leaves are equivalent to the "average leaf," we need to find the area of both:

7.5 cm × 4 cm = 30 cm2/avg. leaf,

2.5 cm × 0.5 cm = 1.25 cm2/Anachris leaf.

We can clearly see there is a huge size discrepancy between the surface area of the average leaf and the surface area of an Anachris leaf. So, how many leaves of Anachris are equivalent to a single average leaf?

30 cm2/avg. leaf ÷ 1.25cm2/Anachris leaf = 24 Anachris leaves/avg. leaf.

6. How many leaves are on the average Anachris plant?

Now, this is hard to count since all the leaves on the Anachris plant are not the same size. A mature leaf meets our specifications above, but young, tender leaves are much smaller. We will simply ignore the new growth and focus on the established leaves. Anachris comes with 5-7 stalks of leaves on average. So how many mature leaves are on one stalk? The answer is roughly 270 leaves per stalk, therefore:

5 stalks × 270 leaves = 1350 leaves/Anachris plant,

7 stalks × 270 leaves = 1890 leaves/Anachris plant.

So we can see that each Anachris plant has between 1350 and 1890 leaves. But we need to find out how many average leaves this equals so we can find out how much oxygen these plants produce in an hour. So, we will divide the answers by 24 to find out how many average leaves these equal:

1350 leaves ÷ 24 leaves = 56.25 average leaves,

1890 leaves ÷ 24 leaves = 78.75 average leaves.

Now we can see that the average Anarchis plant is equivalent to between 56 and 79 average leaves. Now we can figure out how much oxygen is produced per hour from our Anachris leaves:

56 leaves × 5 mL/hour = 280 mL/hour,

79 leaves × 5 mL/hour = 395 mL/hour.

7. How many Anachris plants produce the required amount of oxygen in one hour?

Now that we know how many leaves are on an Anachris plant and how much oxygen they produce, we can figure out how many Anachris plants are needed to keep the average, healthy, resting adult alive for one hour on an average, cool, clear day.

Above we figured out that the average, resting person needs 53 L (53,000 mL) of oxygen per hour. So:

53,000 mL ÷ 280 mL/hour = 189 Anachris plants,

53,000 mL ÷ 395 mL/hour = 134 Anachris plants.

So our answer is that it takes between 134 and 189 Anachris plants to produce enough oxygen for one healthy, resting person in one hour. Again we have a lot of assumptions and have not exactly calculated the surface area in the most appropriate manner (leaves have 2 sides, rectangles have 4). But this is still a much better answer to the question posed than we had before. However, we still do not know the size of the enclosed space, the amount of light and water available, and how quickly under these conditions that CO2 concentration rises to lethal levels, for both the plants and the human. We can use this answer to roughly calculate other answers.

Taking it to the Next Level - Plants in an Enclosed Space

So you want to design an enclosed, natural space...

Well we can use the data above and a few other variables to crudely estimate what it would take to calculate how many plants are needed per person in an enclosed environment. Now, anachris plants are small and portable and would make a wonderful oxygen-producing plant for a contained space, but they are also boring. They have no trunks, no intricate root systems, no flowers, and no fruits.

Humans, or human-like intelligent beings, need variety in their visual environment, otherwise they will become understimulated and/or depressed. Humans have amassed an amazing list of plants they consider "pretty" or "attractive." We would not waste the time and energy to do so if we did not need the variety of flora in our lives from an emotional, intellectual, and spiritual standpoint. So let us consider the amount of plants and types of plants we come into contact with every day.

In the average suburban yard you will probably find :

In the non-average suburban yard you might also find:

So why mention permaculture? Well, any intelligent, sufficiently advanced creature is going to eventually adopt a system of permaculture, especially in any enclosed space with plants. Permaculture is the most self-sustaining system of gardening. Plants are planted together in order to sustain nutrients for each other in the soil, water is usually harvested from rain using barrels as rain catchers (because it is naturally higher in nitrogen), etc. If this culture has not achieve "Star Trek" technological status, and they do not have the seemingly magical replicator systems, then they will probably be practicing a form of permaculture in order to sustain their dietary needs. Another reason to sustain plant growth is medicine. Many old fashion herbal cures work because the plants are just the weaker version of what is put into our pharmeceutical pills.

Even today, Columbian drug cartels pay their employees with coca leaves. Why? Because, in their natural state, coca leaves are completely safe and are used to soothe headaches. High-altitude peoples of the South American mountain ranges use coca leaves to aclimate to the thinner air when coming from lower altitudes. Handing someone coca leaves is like handing them medicine that they can sell to people who need it. It is only when the coca leaf is refined that it produces the deadly narcotic cocaine. We would assume a sufficiently advanced culture learned millenia ago the dangers of refining and tampering with natural forms of chemicals.

Another necessity of plants that is virtually never considered in our science fiction stories with enclosed environments containing plants - bugs. Only Japanese science fiction animes seem to pay attention to this detail. No plant on earth can exist without bugs. If there are no bugs present, humans must do the work of the bugs. This is a huge waste of time for humans when bugs are available. We have more important problems to consider and solve for the benefit of all species.

It is natural to think that bees, buterflies, wasps, spiders, worms, ladybugs, preying mantises, etc. would also be found in an advanced, balanced, artificially constructed eco-system. Bees are doubly useful - they provide pollination for plants, which gives us the fruits we eat and seeds to plant, and they also provide honey, which is a natural sweetener that never goes bad and also serves as an old fashioned, throat-soothing cure.

Now if the culture is sufficiently advanced, but only eats natural food, they will probably have robotic microbugs and nanobugs to do the work of real bugs, but more efficiently and at a 100% predictable rate. This is a great, highly-underutilized idea. Who wouldn't want robot bees that can act as honey factories and will never be so afraid of you that they have to sting?

So how many plants are needed for one person?

Let us assume that a culture in an enclosed environment has a set number of trees, shrubs, flowers, leafy plants, and grasses for every individual in that habitat. We would assume they calculate for maximum activity, on the worst days, in the worst conditions just to be safe. They would always want too much oxygen versus too little. Atmosphere can always be vented when levels become too toxic. It is highly unlikely, through natural processes, that the oxygen content would be so high as to be flammable. (Commonly, we only see this condition in the real world in hospitals, where, in my grandmother's experience, a man on an oxygen tank can light a cigarette and blow his entire hospital room out of the side of the building while causing structural damage to the entire wing.)

So let's assume that per person, we have a maximum activity oxygen consumption rate. According to this site, a 78 kilogram (171 pound) person participating in a marathon will consume 124.8 L of oxygen per hour (during a sustained run of 8 kilometers per hour at a consumption rate of 15.6 L per km). So let's reassign 125 L of oxygen as our baseline for consumption for one person per hour. A healthy human woman, having less musculature to feed, would naturally use less. Since healthy males use more, we will use them as our per-person standard. This is just the smarter thing to do to ensure one does not run out of oxygen.

So, we know from above that the average leaf (7.5 cm x 4 cm) produces 5 mL of oxygen per hour. Now we need to figure out how many average leaves are needed per person per hour:

125,000 mL of oxygen/person/hour ÷ 5 mL of oxygen/leaf/hour = 25,000 leaves/person/hour.

That's a lot of leaves. So we would naturally assume one would want to use trees since they offer thousands of leaves in a single unit. Let's say they use a tree with our average sized leaf. Pear trees have leaves about this size, as well as producing edible fruit, so we need to figure out how many leaves are on the average pear tree.

How many leaves are on a pear tree?

To estimate this we will consider three parts - twigs, small branches, and regular branches, with twigs being the smallest branches attached to the small branches, themselves being attached to the regular branches, which attach to the top of the trunk. To figure this out we have to ask certain questions:

To figure out these answers, we will use this image of a damaged pear tree to see inside its crown (the leafy top of a tree). Don't get overwhelmed, and don't insist on being 100% accurate. No two trees have exactly the same number of leaves, twigs, and branches. It is futile to calculate an exact number. Using the questions above, we will figure out how many leaves are on one tree.

How many leaves are on a twig?

Using the image in the link above, we will estimate that a mid-section twig has about 180 leaves.

So how many twigs on a small branch?

180 leaves × 12 small branches = 2160 leaves/small branch.

So how many small branches on a regular branch?

There seems to be a repitition of an average of 12 in this tree, so we will guess there are about 12 small branchs on the regular branch, so:

2160leaves/small branch × 12 regular branches = 25,920 leaves/regular branch.

How many regular branches on a single pear tree?

It seems like this tree currently has 18 regular branches, but it is also missing about 6 branches that filled in the front of the tree. We will estimate that this tree had 24 regular branches:

25,920 leaves/regular branch × 24 regular branches = 622,080 leaves/pear tree.

Now we know about how many leaves are on a single pear tree. How much oxygen is that for our average healthy male working at maximum capacity?

How much oxygen is produced by our pear tree?

Our pear tree has 622,080 average leaves, of which we know will produce 5 mL of oxygen per hour:

622,080 leaves × 5 mL/hour = 386,983,526,400 mL of oxygen/hour.

So we know our person needs25,000 leaves/person/hour:

622,080 leaves ÷ 25,000 leaves/person/hour = 24.8834 hours of oxygen per person. So we only really need one mature pear tree to supply oxygen for one person for one day. However this doesn't take into account the buffer needed for the carbon dioxide concentration buildup. We would assume each person would have several smaller plants to act as the CO2 buffer in this enclosed environment. The more people, the larger the buffer needs to be per person to keep the concentration down.

So a team of 10 in a small, enclosed environment probably only needs about:

But a team of 1000 in a larger, enclosed environment probably needs about: