Question: What is the maximum speed of a fart?
Short answer: 0.22 MPH.
Long answer: We have previously examined the speed of farts in some detail, with the main conclusion being that the speed of fart smell is extraordinarily slow, being governed by the laws of diffusion. However, we have also considered the possibility that non-smelly components of farts could travel more quickly, and that these particles might be responsible for fart plumes that are sometimes visible during pyroflatulence, for example.
Last week we announced that we have acquired a sophisticated anemometer, thanks to funding from NIH. This device measures air speed precisely, using a mechanical propeller coupled to electronic sensors. With this technology, we were able to tackle the question of fart speed directly.
Nevertheless, our initial attempts at quantifying the speed of farts proved disturbingly unsuccessful: Most farts registered zero change on the anemometer, which suggests that the propulsion of fart air is, like the propulsion of stink, quite weak.
Across many such measurements, the highest reading of fart speed we obtained was 0.22 MPH. This was recorded very near the source of the fart, and as such it represents something close to an upper bound on fart velocity. As can be noted from the following audio recording, the fart was sufficiently robust to have left a clear auditory trace:
Given a fart of any initial velocity, the subsequent progression of movement will follow the physical equations of motion, which take the form:
where k = b/m captures the linear drag caused by air resistance on a fart of mass m. The air resistance is given by b = 0.000008 N.s/m2, if we assume a spherical fart of diameter 0.05 meters. Integrating this equation, we obtain:
Where v0 is the initial velocity, which as mentioned above, has an upper bound of 0.22 MPH or 0.098 m/s. Given the well-established finding that a typical fart has a mass of 0.03 grams, we then have the general relationship between speed and time:
This indicates that a fart of velocity 0.098 m/s will slow down gradually over the course of several hours. (Note that this analysis only considers the component of velocity parallel to the axis of propulsion. In reality, gravity will also act on the heavier particles, pulling them to the ground and contributing to the composition of the flatosophere).
By integrating the previous equation, we obtain the spatial distance traveled by the fart, relative to the source:
Where τ = m/b. Plotting this equation again indicates that the progression of flatus will be quite slow:
Indeed, the initial propulsion of a fart will carry it no more than 5 meters during the first minute. During that time, further motion will be determined by the random diffusion of particles and the prevailing air circulation. As the latter force is orders of magnitude larger than the former, we conclude once again that to a first approximation, farts do not go very far under their own power. Put another way, the only reason anyone can smell anyone else’s farts is that the surrounding air is constantly in motion.