Forest tradeoffs

Classical Mechanics Level 2

Given the result we just obtained, what can we say about the relationship between the rate of fire setting events f f and the size the average forest fire ⟨ s ⟩ , \langle s\rangle, all else being equal?

The more frequently fires are set, the smaller they are, on average The more frequently fires are set, the bigger they are, on average The size of the typical fire is independent of the frequency with which they're set

Josh Silverman by Josh Silverman

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1 solution

Josh Silverman Staff
Oct 18, 2017

Our result shows that ⟨ s ⟩ = r f 1 − ρ tree ρ tree \langle s\rangle = \frac{r}{f}\frac{1-\rho_\textrm{tree}}{\rho_\textrm{tree}} so that ⟨ s ⟩ \langle s\rangle is proportional to 1 / f . 1/f.

This means that as lightning strikes occur more frequently, the amount of forest that is burned down in any given fire shrinks in proportion to 1 / f . 1/f.

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