Land area required in order for every UK family to have a Christmas tree

I’ll use the Christmas tree example as an illustration of how you can get rough, but useful, aporximations of carrying capacities through thinking through first principles.

Our smallish Chistmas tree is about 2m in diameter at the base.

If the trees need a little extra space around them in order to grow let’e assume a diameter of 3m

The total area occupied by a tree is therefore given by \(\pi r^2\) with r=1 and pi=3.14

r=1.5
area=pi*r^2
area
## [1] 7.068583

How many trees per hectare? One hectare is 10000 square meters

So we get

trees_per_ha=10000/area
trees_per_ha
## [1] 1414.711

To check this estimate for sanity the Cranbourne estate plants 50 acres with a total of around 60,000 trees.

https://www.cranborne.co.uk/christmas-trees/

cranborne_trees_per_hectare=round(60000/(50* 0.404686),0)
cranborne_trees_per_hectare
## [1] 2965

Which is around twice that of my more conservative estimate based on a large tree. So might need to lower the area slightly, but we will stick with the high end.

However the trees do need time to grow. Our tree is about 8 years old.

hectares_per_tree = 8*1/trees_per_ha
hectares_per_tree 
## [1] 0.005654867

There are approximately 20 million households in the UK. However many people gather together at Chistmas, and some trees are used outside households. So we need an estimate. Let’s say between 5 and 15 million trees needed in order for everyone to have one. The real number will be much less as some people have artificial trees and some people don’t have one at all.

upper = 15000000 * hectares_per_tree 
lower = 5000000 * hectares_per_tree

There are 100 hectares in a square km

So we need between 283 and 848 square kilometers planted with Christmas trees based on my high end estimate or between 141 and 424 square kilometers if the stocking levels are similar to Cranborne. In fact it might be a lower still if most of the trees are harvested before 8 years old.

However, we now have some ball park areas that we can think about, rather than wrting “vast swathes” of land are needed in order to fulfill the annual demand for Chritmas trees.

For reference, the area of the New Forest is 566 square kilometers. The area of the Isle of Wight is 380 km 2 and the area of the highlands of Scotland is 26,484 square kilometres