Forest Fire Physics

Points of View on Climate Change

The U.S. was formerly a leader in the effort to combat climate change. In the new political climate, its role is much reduced (to the abashment of many citizens, who have since taken individual action to abate the issue). Now, China and Europe are partnering to fight the issue. Japan is also taking steps to prepare for climate change, especially the effects of the rising sea level. Although the U.S. is taking less political stake in the issue, it is as real as ever (ie, the forest fires currently ravaging California).

Forest Fires

Firefighters are obviously overwhelmed as the job comes- underfunded, overworked. They are constantly on alert and expected to save the day each and every time. Now, with the issues in the west, it is harder and harder to do so. Chronic drought has taken its toll on California especially.
Fires are started easily, and stopped with much more effort. In the aforementioned dry climate, fires become unstoppable. First off, the dry landscape provides underbrush fuel for the fires. And if the upper lying leaves and branches catch on fire, it spreads even faster.
In California and the west in general, mountains magnify the issue because fire spreads faster uphill. This is called the "slope effect" (Siegel), and occurs in part because the incline brings the fire up to fuel faster when it is pushed along by the wind.

Obviously, there are some parts of the state that are unreachable by traditional firetrucks- especially those that are most vulnerable to a fast spreading flame. This is where aerial firefighting comes in.

Aerial Firefighting

Aerial firefighting is when firefighters try to hinder fires from the skies, flying above them in airplanes. They drop slurry, a mix of water, fertilizers, and iron oxide, on the flames. In the early years of aerial firefighting, plain water was dropped on the flames. However, the other components have been added mainly as a means of weighing down the water and marking where it lands. Before, the water easily evaporated and was blown off course. Now, it is denser liquid and can be seen on the ground. Aerial firefighting is both a direct method for putting fires out and a way to lay down large amounts of fire retardant.

Slurry:

Water- water

Fertilizers- to help forests regrow

Iron oxide- red coloring

Fire retardant- to stop the spread of the fire

The Physics of Aerial Firefighting

Velocity

The planes in use for this job are constantly changing; originally being the slow and steady older models from the 1950's and 60's. Now they are updating to models made within the past 2-3 decades.

C-130H: 366 mph/318 ktas (Mach 0.52) at 20,000 feet (6,060 meters)

= 0.163617 km/s

Height = 6.060 km

Distance = California is 1,240 km long by 400 km wide point a to b will be the distance travelled from plane takeoff to the site of the fire

The above info can be used in the dx = velocity x time equation

Mass of Slurry

water: 18 g/mol

fertilizer: (NH4)2SO4 molar mass is about 128 g/mol

iron oxide: 159.69 g/mol

retardant: C10Cl12 molar mass is about 545.5 g/mol

Acceleration = -9.8 km/s^2

Now there should be enough info for one of the big 5 kinematic equations

Another Factor: Air Resistance

F = force due to air resistance, or drag (N)

k = a constant that collects the effects of density, drag, and area (kg/m)

v = the velocity of the moving object (m/s)

ρ = the density of the air the object moves through (kg/m3)

CD = the drag coefficient, includes hard-to-measure effects (unitless)

A = the area of the object the air presses on (m2)

Sources:

Allain, Rhett. "When Does the Air Resistance Force Make a Difference?" Wired, 9
     Jan. 2015, www.wired.com/2015/01/air-resistance-force-make-difference/.
     Accessed 13 Oct. 2017.

James, Randy. "What Are They Dumping on Wildfires?" If You Must Know, Time
     Magazine, 2 Sept. 2009, content.time.com/time/nation/article/
     0,8599,1919962,00.html. Accessed 13 Oct. 2017.

Siegel, Ethan. "The Terrifying Physics of How Wildfires Spread so Fast."
     Science, Forbes, 6 Sept. 2017, www.forbes.com/sites/startswithabang/
     2017/09/06/the-terrifying-physics-of-how-wildfires-spread-so-fast/#153cb0b27791.
     Accessed 13 Oct. 2017.