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Fire: Positive Feedback

Fire is a turbulent feedback-driven fractal system.

Fire is a powerful example of positive feedback. Most people assume that when a piece of wood catches fire, it's actually the wood that burns, but this is not in fact the case. Here's how it works: when wood gets hot, it releases gases (mostly methane and ethane) and it is these gases that actually catch fire. When the gases burn, they release heat, which cause the wood to release more gas, which ignites, causing more heat, releasing more gas, etc.

Fire has many fractal characteristics. Turbulence - the motion of fluids - occurs over a wide range of scales, and we can see this in the motion of the burning gases in flames. Fire spans a broad range of scales, from a tiny match burning to a forest fire that spans millions of acres.

Although the positive feedback involved in spreading fire can be very dangerous, it can also be quite fragile, as anyone can attest who has tried to start a fire with soggy wood. The fractal nature of the fuel is important as well. You cannot start a log on fire directly with a match. Rather, you need a growing sequence of different sized twigs, sticks, and branches in order to ignite a large log. Conveniently, trees provide just the right fractal fuel for this.

Fire is also intricately connected with the atmosphere. Wind provides extra oxygen which can help a fire ignite, as well as help spread it to new areas. But wind can also blow out a match, making it impossible to start in the first place.

There is also an interesting negative feedback loop at work in the atmosphere, involving the relative levels of oxygen (O₂) and carbon dioxide (CO₂. Historically, the level of CO₂ has fluctuated up and down many times. When the ratio of O₂:CO₂ is high, it is very easy for wood to burn, and there have been vast forest fires that put huge amounts of CO₂ into the atmosphere, bringing the O₂:CO₂ back into balance. Likewise, when the ratio is too low, it is more difficult to start fires. The elevated CO₂ levels also stimulate the growth of forests, causing more oxygen to be returned to the atmosphere. Thus, negative feedback helps to keep the atmospheric levels of these gasses stable.

Forest Fires

When one tree in a forest is on fire, what are the variables that will determine whether or not the fire will spread to other trees?

• The relative moisture (i.e. how dry the trees are)
• How closely spaced the trees are (the density of the forest)
• The speed and direction of the wind
• Other factors?

We're going use a simulation to explore the sensitivity of fire to the conditions on the ground and in the atmosphere. Click in the green area of the applet below to place a 'spark'. Then click "Burn!"

There are several parameters or variables to play with, and you can adjust them while the fire is burning. Use the slider to adjust the probability of fire spreading. In the real world, this represents how dry the wood is, as well as how dense the vegetation is. The other slider controls the wind speed. Finally, you can adjust the wind direction by dragging the compass arrow. You can also click in multiple places in the green forest area to start multiple fires.

If the wind speed and/or the probability of fire spreading is too low, the fire will quickly go out. If the values are high, the fire will quickly spread and burn all the available forest. When the values are in between the extremes, you can observe some interesting burning patterns.

Play with the parameters of the forest fire for a while to get a feel for the way it behaves. Given that the real-world conditions are variable, you can see why sometimes the "Fire Danger" is high and sometimes it is not.

Start by setting a fire in the top left (northwest) corner, and pointing the wind to blow to the southeast. Try to find a combination of parameters that makes the fire last as long as possible.

Questions:
The parameters for the longest lasting fire are: Probability: [ ] Wind Speed: [ ]

As you explore the range of parameters between burning everything quickly and having the fire fizzle out, you'll find cases where there are pockets of green forest that survive the fire, surrounded by burned areas. Try to find the combination of parameters that leads to fire spreading all over the forest, but leaving the largest proportion of pockets of green forest surviving.

The parameters for the fire that covers the whole forest but leaves the biggest unburned holes behind: Probability: [ ] Wind Speed: [ ]

Sometimes in real fires, there are cases where 'miraculously' one house will survive when many around it will have burned up. You can see how this selective sparing might occur through a simulation like this.