Question: How big is the flatosphere if animal farts are included?
Short answer: 2.8 mm.
Long answer: First, we must apologize for the lack of a new post last week. Our offices were closed to enable our members to attend a conference. In the meantime, we have received a question related to a previous post, which calculated the amount of human fart smell that is constantly lingering around the Earth. The conclusion is that the Earth is surrounded by a very thing (10 micron) layer of fart smell. The question is what happens when we add all the farts produced by other animals.
According to Bar-On et al. (PNAS, 2018), humans produce about 4.3% of all carbon gas contributed by animals. If we assume a constant ratio for sulfur gasses, and build on our previous calculations, we can obtain the total sulfur budget for animal farts: 5,144,186 L per day. As animals only comprise about 0.3% of the total biomass of the Earth, the total amount of sulfur gas produced by living creatures could very well be much larger. In fact, plants have by far the largest biomass, with bacteria being second, but we simply don’t know if either type of organism farts. So for now we will stick with animals.
The rest is just a straightforward adjustment to our earlier calculation. Consider the accumulation of farts across days and the decay rate of sulfur in the atmosphere yields a total of 14,697,674 L of fart-related sulfur gas in the air at any given time. This fills 14,698 L.
Given that the radius of the Earth is 6371 km, the total volume of air from the ground to x km above the surface is:
The fraction of fart gasses at distance x km is therefore 0.00014697/v. At a distance of 1 m (x = 0.001), the atmosphere is therefore composed of 0.000000029% farts, which is again well below the human olfactory threshold of 0.1 ppm. Some simple algebra reveals that the olfactory threshold is reached for x <= 0.0000028 km, or 2.8 mm. This is a bit larger than the thickness of a Euro coin: