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As I understand it, a massive battle with lots of bloodshed can cause pieces of land to become infertile, due to the amount of salt in the blood the land has to soak up.
If this happened, how long would it be until the land could support trees again?
I realize that the answer to this question is probably going to change with the scale of the battle, so I'm looking for some sort of equation that will allow me to calculate the time.
Let me know if you need additional details.
Blood does not contain enough salt to stop plant growth, and in fact it is used as a fertilizer. Dried animal blood is sold as "Blood Meal" and deliberately added to gardens to help plant growth.
During warfare "salting the earth" was used to deny the enemy use of an area for agriculture but that involved spreading actual salt in the area. There is not enough blood in even a large pile of corpses to have the same effect.
So in other words - all plants would keep growing immediately.
To look at the problem in more detail:
The human body contains in total around 220g of sodium chloride. Of that however only 28g is dissolved into their bodily fluids and only 16g in their blood. The rest is bound up in flesh and organs.
So in a worst case scenario a battle with ten thousand deaths would release a total of 2,200kg of salt. That sounds like a lot but most of this is going to be carried away by animals or consumed and the remainder is spread over a large area.
If you take a worst case real scenario and say that a quarter of the salt in blood makes it into the environment then that is a release of 4g per person. The ten-thousand death battle has actually only released 40kg of salt into the ground.
Again 40 bags of salt sounds like a lot but distribute it out over a huge battlefield big enough for ten thousand casualties and suddenly it is spread pretty thinly. For that many casualties the armies must have been far bigger than 20 thousand people on a side.
And this is where it falls down, it is very hard to increase the concentration at any point because to get more blood you need more people. That in turn means a larger battlefield, which spreads the salt more evenly.
In theory if you had some sort of massacre at a choke point you could have a localized concentration, but you are talking a very unlikely scenario.
The real question isn't about the bodies, since human remains would make good fertilizer. Rather the issue wold be the mechanism of death.
If the battle took place in ancient times, with the proximate cause of death being through edged weapons or blunt force trauma, then plant growth would be able to take place right away. The main issue would be the bodies would cover the ground and prevent plant growth where they lay until the remains were fully decayed, or scavengers ate them. In most instances, the bodies were stripped of armour and valuables and then buried, which would facilitate plant growth even better since there would not be a large quantity of metals or other inorganic materials to interfere with plant growth.
If the battle took place during the age of black powder warfare, the situation would be relatively similar, but there would be additional complications due to the quantities of inorganic materials embedded in the ground in the form of spent bullets and shells or pieces of shrapnel. Gnerally speaking, this would be localized in small areas, and if the water table was high, then lead and other compounds could leach into the groundwater and stunt some of the plant growth.
The battlefields of the Western Front during the Great War of 1914-1918 would have a much different issue, as the ground was churned up by massive quantities of artillery focused on very small areas of ground. Not only will there be a lot of contamination of the soil, but the very structure of the soil will be changed. Explosive shells would turn the soil and bring clay and other materials from deep below the surface; materials which is missing much of the organic matter needed for plant growth. The natural drainage would also be disrupted or destroyed, making plant growth more difficult as well. Use of chemical munitions will add complications to the regrowth of vegetation as well, either directly or indirectly as animals and insects which are beneficial to plant growth avoid the contaminated areas.
More modern warfare can have much more firepower, but the general trend has been to spread things out over a larger area through mechanization, as well as using more precise munitions to target things, so unless chemical munitions, nuclear weapons or biological warfare is unleashed, the effects of modern warfare on vegetation is very localized and diffused.
