Depending on where you live, November just might bring the kind of frigid, biting rain that’ll chill you to your core within seconds of stepping outside.
If you find yourself without an umbrella and must traverse from one location to another, do you walk or run to stay the driest? Math can help you figure it out.
In the 1970s, several papers were published in math magazines debating this seemingly simple question, mainly because it’s both an academic mind game and a real-life challenge. This “hobby math” problem continues to be contemplated because as more and better model parameters are included, the result becomes more accurate—and sometimes changes.
It comes down to this: If you run, you get out of the rain faster, but you’ll encounter more raindrops. If you walk, you spend more time in the rain but will be hit by fewer raindrops from the side.
According to physicist Alessandro De Angelis, the simplest math model assumes rain falls vertically; running as fast as possible is the best choice and will get you 10% less wet than if you walk quickly.
De Angelis and meteorology professor Alex DeCaria separately concluded that if you add wind speed as a parameter in the model, it’s best to move at the same speed as wind if the wind is at your back. Otherwise, it’s best to run as fast as you can. A 2012 episode of the show Mythbusters tried out the experiment for viewers to watch.
According to engineering professor Franco Bocci, “What complicates the question is the human shape; for simplicity, previous attempts to crack the thorny problem assumed people to be thin sheets or upright, rectangular boxes.”
Bocci and math professor Herb Bailey both began examining the influence of the shape of the human body. Bailey concluded—taking into consideration rain from the side—that a heavier person should always run as fast as possible, while a slimmer person should walk with the horizontal speed of the rain if it comes from behind.
Still, none of these models account for wind gusts, raindrop size, body angle while running, arm and leg movements, puddles splashing from footfalls or a host of other parameters you can imagine.
Perhaps someone could invent an app where you upload photos for AI to analyze your body size and shape, input fitness data from your health app, enable location and distance to traverse from your mapping app and pinpoint weather data from the weather app. All this information could converge into a model to provide you with an instantaneous recommendation on the optimal pace to move through the rain. It might look something like this.
Or, for a more practical solution, it might be wise just to carry an umbrella.
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Several scientists have tried to explain math solutions for running in the rain through poetry:
When caught in the rain without mac,
walk as fast as the wind at your back.
But when the wind’s in your face,
the optimal pace
is as fast as your legs will make track.
Dank Hailman and Bruce Torrents—math professors and rain math hobbyists—point out the last line is not accurate for current models and offer some more accurate limerick options:
When you find yourself caught in the rain,
while walking exposed on a plane,
for greatest protection
move in the direction
revealed by a fair weathervane.
Moving swift as the wind we’ll concede,
for a box shape is just the right speed.
But a soul who’s more rounded
will end up less drowned
if the wind’s pace he aims to exceed.
We wrote about prime numbers in a previous edition of Math Monday. Last month, the Great Internet Mersenne Prime Search (GIMPS), a global community project dedicated to finding incomprehensibly big numbers, found the new largest prime number.
Durant’s achievement also marks a major moment in the hunt for Mersenne prime numbers—it’s the first of its kind to be found through the use of graphics processing units (GPUs) instead of traditional central processing units (CPUs).
