# Possible height and size of a giant tree on an Earth-like planet?

I'm working on a story about another dimension of this same Earth but without the same human development and history. The land and natural conditions would be the same except for the ones directly affected/created by humans.

In this dimension, I want a human society living IN tree cities (cities created inside giant trees). I've already though of the "technology" possible for that and how a few selected trees became giantic (short version: humans are really good at bioengineering in this dimension). The trees would be from different species autoctone to each the zone (Iberian peninsula, in this case).

However, I'm not sure how big those trees could be but I'm sure there are physic limitations for that.

I don't want a massive city yet I would like if it the tree could be big enough to contain a minimun of a thousand people but, hey, the more the merrier!

So, basically, How big (height and witdth)could a tree be keeping the Earth physical laws?

edit: the tree extra-needs (such as more nutrients to keep growing or those nutrients reaching the parts of the trees needed) are handled by the humans living in it.

edit: To be more specific as it seems that the question is not clear enough. I don't know much about physics but I though maybe the athmosphere or the weitght of the branches/leafs could affect its size.

• There is a book that was written just for you. It is Geoffrey West's Scale. Commented May 13, 2018 at 12:22

## Purely mechanical consideration of maximum height

The tallest tree cannot be taller than the height at which the downward pressure of its own weight exceeds its compressive strength.

The strongest wood has a compression strength of about 40 MPa (when green, that is, alive) to about 60 MPa (when dry, that is, dead for a long time). Let's say we have a super-wood with a compression strength of 60 MPa while the tree is alive. The density of strong woods is around 0.75 to 0.8, but let's cheat a little and make it 0.6. In these conditions, the maximum height of such a superwood tree cannot exceed 1000 m, because higher trees would crush the wood at the base under their own weight.

$$\small \begin{array}{l|c|c|c|} & \text{Compression strength} & \text {Density} & \text{Maximum height} \\\hline \text{Real-life live oak, green} & \phantom{0}\phantom{0}37.5~\text{MPa} & 0.80 & \phantom{0}470~\text{m} \\ \text{Fantastic superwood, green} & \phantom{0}\phantom{0}60.0~\text{MPa} & 0.60 & 1000~\text{m} \\ \text{Best bricks (for comparison)} & \phantom{0}100.0~\text{MPa} & 2.00 & \phantom{0}500~\text{m} \\ \text{Inconel 718 steel (for comparison)} & 1000.0~\text{MPa} & 8.20 & 1200~\text{m} \\ \end{array}$$

(In this table, "maximum height" means the maximum theoretical height of a column made of the respective material.)

## As for maximum diameter...

Trees grow thicker by 5 to 10 mm/year; let's say the Fantastic Superwood increases its diameter by a whopping 50 mm/year. In 10,000 years it would reach a diameter of 500 m, which would make it a mind-blowing gigantic tree, but still rather cramped for a city...

• Of course, he's seriously hollowing them out, so that has to be taken into consideration, too. Commented May 12, 2018 at 21:54
• I think that would actually increase the height -- maybe significantly -- but I don't have the engineering skills to back that up. Commented May 13, 2018 at 6:43
• You neglected the tensile forces on the wood due to Poisson's ratio. This is particularly important considering tensile strength perpendicular to grain is tiny Commented May 13, 2018 at 6:50
• @Prasser: You are right, of course. The problem is that I have no idea how to explain the effect sufficiently clearly. Reader's who may be interested can start with the Wiki article on [Poisson's ratio])en.wikipedia.org/wiki/Poisson%27s_ratio). What happens is that as the wood is compressed axially by its own weight, it will tend to expand radially, inducing a strain on the direction perpendicular to the axis; this is bad, because the strength of wood is much lower for efforts perpendicular to the grain. Commented May 13, 2018 at 8:28
• Does this answer not make the assumption that the tree is an exact column? If it is significantly wider at the bottom (imagine a cone shape) then the downward forces on the wood at the bottom would be greatly reduced and allow for a lot more height to be possible. If I get time later I'll have a go at doing the numbers on that Commented May 13, 2018 at 9:11

Terry Pratchet in his novel the Long Cosmos had trees miles high. This was on an alternate earth where oxygen levels were higher but otherwise was earth. His trees were infused with hydrogen to support their weight and got around the leaf limitations in RonJohns post by using sacks to carry water up hollow cannals using hydrogen gas. I dont remember the details on how the hydrogen was seperated but thinknit had to do with a symbotic fungus.

Point being if you are going to use genetic manipulation, why allow the limitations of our trees be your limits? So long as there is a justification for whatever attributes you have. (One example, your trees can grow so high because they modified the proteans that make up the cell walls to be similar to spider silk, increasing their strength).

And finally, be sure to consider the consequences of very large trees in your world. Higher oxygen for example. Or different views on wood harvesting (are there laws saying ones building in the tree cant harm the tree, or is selective pruning allowed?)

• This is some great creativity! In the same vein, humans could do actual physical engineering in addition to the bioengineering (ie physically reinforcing branches, etc.) Commented May 13, 2018 at 0:05

https://www.livescience.com/14667-tall-trees-grow.html

Two main opposing forces affect a tree's height; one pushes it upward while the other holds it down. By analyzing the interplay between these forces, a team of biologists led by George Koch of Northern Arizona University calculated the theoretical maximum tree height, or the point at which opposing forces balance out and a tree stops growing. This point lies somewhere between 400 and 426 feet (122 and 130 m).

"As trees grow taller, increasing leaf water stress due to gravity and path length resistance may ultimately limit leaf expansion and photosynthesis for further height growth," the biologists wrote in a 2004 article in the journal Nature. This limit lies at or just above 400 feet.

Thus... no cities in trees when following your desire to "(keep) the Earth physical laws".

EDIT after you changed the question: No one has studied how big trees could grow if capillary/transpiration were enhanced by humans. To grow tall, a tree must have deep roots, and grow wide for stability. But you can handwave that away just as you handwave away gravity pulling against capillary/transpiration forces.

• But the tree needs are provided by humans and they have the technology to handle those problems (nutrients provided by photosynthesis and such). Commented May 12, 2018 at 20:20
• @Sombrapluma did you read the article? Sequoias grow so tall because they are in excellent conditions for growth. But eventually gravity overcomes the upward pumping force. If you're going to handwave away "(keep) the Earth physical laws", then remove the science-based tag and make the trees grow as tall as you want them to be. Commented May 12, 2018 at 20:25
• @Sombrapluma to simplify RohJohn's answer: stuff needs to get from one end of the tree (roots) to the other (leaves). Gravity sets a hard limit on that, at 122-130m. Maybe, for your idea of tree-cities, you can look at how broad trees can get, not just how tall. Commented May 12, 2018 at 20:32
• @RonJohn I did read the article but it was a problem I've already though of . The mantainance of the tree is made by humans, so the cost-effect for the tree to keep developing wouldn't be the same, the tree wouldn't need to overcome the upward pumping force if it's the humans the ones that go there and do the job. Commented May 12, 2018 at 20:33
• @Galastel I'm actually asking for both height and size (as in broad) I'll edit it, so it's more clear. Commented May 12, 2018 at 20:36

RonJohn's answer deals with the limits on the height of trees, but there does not seem to be a limit on the horizontal size of a tree, if you remove the limit on the 'tree' being a single stem.

For an example, consider the aspen groves of the western US. These are single organisms, having many trunks connected by a shared root system. This one https://en.wikipedia.org/wiki/Pando_(tree)/ covers an area of 106 acres / 43 hectares and is estimated to be about 80,000 years old. There are others of similar area.

The size seems to be limited only by environmental conditions. They typically grow along mountain meadows and streams, in areas where there is enough water to support them (they don't survive in the drier surrounding soils). Using a little creative bioengineering, it wouldn't be difficult to create one with larger trunks and a wider spread.

IMO, reality is a good starting point:

https://en.wikipedia.org/wiki/General_Sherman_(tree)

The article includes some data on now-dead trees which were known to be significantly larger.

However -- more importantly -- the article points out that 'General Sherman' is the largest living single-stem tree in the world. If your alter-Earth people take the step of engineering multiple-stem trees, like baobobs:

https://www.sciencenews.org/blog/wild-things/huge-hollow-baobab-trees-are-actually-multiple-fused-stems

...then hypothetically there may be no limit to the diameter of a "single" such tree. Height-wise you're still up against the strength of the wood, but that may not be relevant if your fused-stem trees can be, say, a couple hundred yards in diameter.