Question: Do people’s farts accumulate in the air?
Short answer: Yes.
Long answer: The fact that the average person farts about 705 ml worth of gas per day (Tomlin, Lowis, and Read, Gut, 1991) raises an obvious question: Where do all these farts go? This question is related to other concerns about the effects of human emissions on the atmosphere.
Fortunately, the half-life of most sulfur compounds is only about 2 days (Wang, Physiol Review, 2011), so most of the fart smell dissipates fairly quickly. But there are 7.9 billion people on earth and they do a lot of farting, so one wonders how much of the resulting smell accumulates in the air. The calculation is fairly straightforward.
We can start with the above mentioned 705 ml per person per day. This is a lot of gas, but most of it is just recycled air – what’s relevant here are the sulfur compounds, which comprise only 0.004% of fart gas, so about 0.028 ml per person per day. Multiplying by 7.9 billion, we arrive at the total daily H2S output, which is 221,200 L for all of humanity.
This figure, combined with the half-life of 2 days for H2S, means that the sum total of human fart gas released each day decays as:
Because the total gas on each day is accumulated from all previous days, we have to integrate over t:
The total amount of human fart gas in the air at any point in time is thus 221,200/0.28 = 632,000L, which fills 632 m3.
Critically, H2S is heavier than air, so it tends to sink to the ground. As a result, there might be a miasma of human fart smell lingering around the surface of the planet. How smelly is it?
The radius of the earth is 6371 km, so we can imagine a volume of breathable air surrounding the planet, at the very bottom of the troposphere. For air up to a height of x kilometers the volume is given by the volume of the corresponding sphere, minus that of the earth itself:
The fraction of farts in the atmosphere at a distance x from the surface is therefore 0.000000632/v.
At a distance of x = 1 m (0.001 km), the atmosphere is therefore composed of 0.000000001% human farts. This is well below the human olfactory threshold of 0.1 ppm. However, performing these calculations at different altitudes relative to ground suggests that the accumulated fart smell should be detectable very near the earth’s surface.
As can be seen in the plot, the ambient air should smell faintly of farts when one is within 10 microns of the surface of the earth. As a result, small terrestrial insects like fleas are probably immersed in fart smell, and it is possible that they use such odors to track their human prey.
Of course, the fart smell is not confined to the thin flatosphere surrounding the surface of the planet, for various reasons. The air is constantly being displaced by wind and other forces, and more importantly, our calculation neglects animal farts and other sources of H2S in the air. In fact, some places smell quite a lot like farts.
These considerations might explain why we occasionally encounter high levels of baseline miasma in our readings of air quality. Indeed, when we measure the baseline levels of stink very close to the ground, in the absence of any overt farting activity, our sensors typically record VOC levels of around 0.1 – 0.2 ppm, which falls squarely within the range that is indicated by the above theoretical exercise. Against this background of accumulated fart smell, it is often possible for people to generate air-purifying farts.
Overall, it appears that we live in a world that is pervaded by farts, just as other, less interesting work has shown that the universe is suffused in a constant background radiation. These fart particles are probably moving around all the time, particularly outdoors, where the average wind speed is around 7 mph. As a result, with each breath, we could be smelling the farts of people who are hundreds of miles away.