Fire is perhaps the most crucial process to sustain civilized life, yet it isn’t as simple as lighting a match. There is a way to perfectly engineer fire to maximize heat distribution, burn rate, and efficiency. Let’s engineer fire.
What fire needs
The campfire needs three things to occur: oxygen, heat, and fuel. This is the basic fire triangle, but creating a perfect fire isn’t just that simple. Believe it or not, several studies have been published regarding what is needed to create a perfect fire, the most well-known being one from a team at Duke University, published in Nature Scientific Reports. The team examined the many different ways people set up campfires and found that the best fires are about as wide as they are tall. This perpetuates the basic pyramidal shape that has been used for ages. However, a conclusion isn’t anything if it isn’t supported by data.
The team developed an equation that plotted fire shape as a function of temperature which can be seen below. When the height (H) to base length scale (D) ratio equaled about one, the team found that the temperature of the fire was the highest. The base-length scale is a unit the team used to disregard fire shape in the study, for example, a square fire of a width W would have the same D value as a conical fire with a diameter equal to width W.
Understanding the math
The reason for this maximized thermal conductivity range around an H/D ratio of one was found to be ability for air to flow through the varying densities inside the fire and outside. Any given fire is fed oxygen through a pressure differential with the air around it. As the fire burns, hot low-density air is built up inside, and (relatively) cold high-density air sits surrounding the fire. The rate at which air flows through the pressure differential is dependent upon the density of the surrounding air (ρ), gravitational acceleration (g), the coefficient of thermal expansion in the fire (β), the temperature differential (ΔT), and the height (H) of the fire. The team related these terms in the following equation.
Ultimately, it was found that airflow was maximized when the height to base ratio was one, as discussed before. As any good engineer would, when they recognized this point of maximum efficiency, they then moved on to understanding the behavior of fires at extreme shapes, a short wide fire, and a tall skinny fire.
When studying the taller skinnier extreme, the team found that as a fire surface became taller, while the volume stayed the same, the distance from any given point internal to the structure decreased. They related the densities of the surrounding air to the cross-sectional area of the fire structure. In turn, the team found that as a fire got proportionally taller, the body temperature decreases exponentially.
The team had now found what they dubbed the tall limit for fires. Moving on, they searched for the shallow limit for a fire. Using similar yet slightly varied equations, the researchers also found that as a body of fire becomes shallower, the body temperature decreases exponentially. All in, they found the sweet spot of height equals width, or diameter, allowed for maximized breathability, therefore efficiency, given standard temperature and pressure differentials in the surrounding air.
Picking the right variables
Beyond the mathematics of campfire airflow, there are also reasonable differences in the burnability of various woods. To get a fire started, you are going to need a fuel source that burns and ignites fast. For this, you can use a softwood like pine or spruce. This will create a hot fast-burning flame. After your fire is going, opt for adding a hardwood, like birch or maple. The wood also needs to be dry, or your fire can be quenched or expel excess energy in smoke.
Engineering the perfect campfire has more to do with thermodynamics and densities of materials, although Duke’s, and other’s, research only confirmed how humans have been making fire for ages. The ancient Egyptians had the pyramidal height to base ratio fire down centuries ago, and for the most part this fire-making technique has become basic knowledge. However, now you can annoy your non-engineering friends with the math behind a campfire, you will surely be a hit at your next party.