### Calculating risk of fatality from falling tree

Gum trees (like the trees in question hanging over our house) are often referred to as

This post in particular, however, discusses a

The paper discusses the following formula:

**the widowmakers,**due to their trait of dropping branches unpredictably and without notice (read more on this here).This post in particular, however, discusses a

**scientific peer-reviewed paper**with a proposed method of**calculating the risk of injury,**and**risk of death from falling trees**. Namely, "Review of QTRA and Risk-based Cost-benefit Assessment of Tree Management" (Arboriculture & Urban Forestry 2013. 39(4): 165–172).The paper discusses the following formula:

**Risk of harm = Probability of failure × Target value × Impact potential**

- harm is defined as serious injury or death
- probability of failure is the annual probability that a tree or selected tree part will fail
- the target value is the probability that a person, a vehicle, or the property will be impacted;
- the impact potential is the probability of harm a falling tree, or part of a tree, can cause to a pedestrian or vehicle.

So, plugging in some numbers for the trees directly above our house:

- Probability of failure = 0.01 (i.e. 1% chance that some part of the tree may fall in one year)
- This is frankly a very conservative estimate, since the tree has dropped heavy branches that broke our roof and flooded our place just a few years ago.
- target value = 0.5 (i.e. 50% chance the falling part will fall on me or my house)
- Roughly 50% of the tree canopy is above the house.
- impact potential = 0.5 (i.e. 50% chance the impact will harm the property or someone when it falls on it)
- This should really be 100%, but putting here 50% to be conservative.

**Risk of harm = 0.01 * 0.5 * 0.5 = 0.0025 (i.e. 1 in 400)**

The paper further claims:

**The risk is deemed “unacceptable” if the ROH exceeds 1 in 10,000.**

Now in our situation,

**1 in 400 greatly exceeds that**!
The paper also gives a formula for calculating the risk of fatality:

**E = N * RoH * T (Number of trees * Risk of Harm * Time in years)**

So in a 1 year period, we have a 0.25% chance of dying, and in 10 years, a 2.5% chance.

Yet the council says we can only prune up to 10% maximum of the canopy, reducing risk of dying to 2.25%... great, thanks.

The council though thinks it's acceptable, because "the tree is healthy", which ignores all the identified precedent of the two Gum species identified dropping branches without any warning.

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