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, approximations of carrying capacities through thinking through first principles.

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

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

The total area occupied by a tree is therefore given by \(\pi r^2\) with r=1.5 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 Christmas, 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 kilometres planted with Christmas trees based on my high end estimate, or between 141 and 424 square kilometres 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.

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

This is only a very approximate estimate and other factors can be taken into consideration that add to uncertainty.

However, we do now have ball park areas that we can use, rather than simply writing “vast swathes” of land are needed in order to fulfil the annual demand for Christmas trees. The area needed is comparable to the New Forest. It could be a bit less, it could be rather more, but we have an area to think about. Let’s just mentally imagine that its between half the area of the New Forest and twice the area of the New Forest in order to have something tangible to think about.

Notice that there was no need to look up any published paper in order to come up with a useful approximation. It would be possible to find published data on this, but the message here is that its not needed in order to engage in informed debate regarding the impact of planting Christmas trees. The next step might be to think about what the land might have been used for if it were not planted in this way.Clearly the trees are really planted in small areas such as the 50 acres (~25 hectares) corner of the Cranbourne estate, not in one block the size of the New Forest. So they may enhance an otherwise uniformly agricultural landscape. On the other hand, they may occupy land that would have greater value for biodiversity, such as heathland and/or good quality grassland. More research would be needed. Likewise the amount of carbon in the trees could be estmated, under the assumtion that the carbon store is only temporary and carbon will be released back into the atmosphere at the end of the trees useful life.