Question: How many times do people typically fart in the hour following a meal?
Short answer: 3
Long answer: In our last post, we showed that the commencement of a meal is quickly followed by farting. The delay between eating and farting is on the order of 11 minutes, largely because of the famous gastrocolic reflex. Consequently, shortly after a meal begins, the ambient air quality will reflect a sort of competition between fart outputs and air circulation.
We have previously shown that these dynamics can be characterized by a leaky integrator model of the form:
where f is the quantity of fart particles, I is the rate of farting, and a is the rate at which fart smell is removed from the space. This equation provides a close fit to data measured on airline flights.
Our estimates of fart smell during eating came from measurements obtained in a large banquet hall, in which a dinner was served to approximately 300 people. We observed evidence for rampant farting that began within minutes of the food service.
To estimate just how much farting was actually happening, we assume that the rate of gas release is constant over some time interval h, which as detailed previously, can be recovered directly by fitting the abovementioned model to the data.
The banquet data, shown below, are well fit by this model, when the parameters are set to a = 0.03 and h = 107, the latter being effectively the entire duration of dinner. The value of a is roughly consistent with the fact that the air change rate (ACH) in a typical dining hall is 10 – 30 minutes.
These results suggest that the air circulation system in the banquet hall was unable to keep up with the continual release of farts by the diners, so that fart smell increased throughout the first hour of the meal and eventually stabilized at a level 1.1 ppm higher than baseline.
The asymptotic level of fart smell represents the equilibrium of our equation, when df/dt = 0. At this point I = af, and since a is 0.03, our analysis suggests a constant fart output of I = 0.03*1.1 = 0.033 ppm of VOCs.
The most recent estimates of fart smell indicate that a typical fart delivers a total of 167.8 ppm in our collection tube, which has a volume of 0.34 ft3. Given that the ballroom of this event was 5000 ft2 and the fact that farts tend to sink to the ground, we can confine the smell to altitudes of 5 ft and below, giving a volume of 25,000 ft3. Each fart therefore contributed 167.8*0.34/25000 = 0.00228208 ppm to the air quality of the banquet hall. To reach a steady state of 0.033 ppm would therefore require 14.5 farts/minute or 867.6 farts/hour. For the 300 attendees, this means that the event was marked by roughly 2.9 farts per person, per hour.
With all this farting, one might wonder why the banquet hall didn’t smell like farts. Indeed, the asymptotic level of fart smell was far above the olfactory threshold of 0.1 ppm. We suspect that the lack of objectionable smell was due primarily to masking by other odors present in the room. Indeed the masking of the subjective experience of hydrogen sulfide smell by other odors is well-known in the sewage industry (c.f. Sostrand et al., 2000). But the implications for fart smell will have to be the topic of future investigation.