by Paul Räcke
It rains a lot in Glasgow. How often have you left the Kelvin building thinking to yourself that you should have brought that rain jacket of yours today or should have bought that umbrella the other day? In these moments it is probably better to stop thinking about things that can no longer be changed and start thinking about what to do next! During such a time many people wonder if it is better to run as fast as possible in the rain to escape getting wet or to walk instead, as you are going to get wet anyways? Wouldn’t you get wetter if you are hit by the rain on the face? On the other hand, if you walk slowly, you end up spending more time in the rain and thus get much wetter. So what is the right course of action one can take in this dire situation?
In principle, there must be a logical approach to work this out. This is what theoretical physicist and YouTuber Henry Reich thought and to finally settle this issue, he made a video helping us through this dilemma on his channel MinutePhysics.
It is sensible to start with a few approximations to make calculations as easy as possible: “Assuming you are not fully soaked yet and you are not jumping into puddles, the answer is simple”, Reich states in his introduction to the problem. He assumes that the rain falls completely vertically with respect to the planar ground, without any wind or other effects. Furthermore, he imagines that the concerned person (let’s say that is you) is a rectangular cuboid.
There are two contributions to your overall wetness: rain from above and rain from the side. First consider the rain from above (i.e. the rain falling right on your head), which will be constant no matter how fast you are going. This might or might not be intuitive, but it becomes perfectly clear with Reich’s clever way of visualising the mathematics behind it. Consider the raindrops stationary in space and yourself (in fact the cuboid that represents you at the moment) and the ground moving upwards. The slant of the parallelepiped that encloses all raindrops that hit your top surface depends on your speed, but the volume of the rain, i.e. the amount of rain, does not change. This can be seen in the picture, where the problem is already reduced to two dimensions, due to the symmetry in the third dimension. So, you get a constant amount of rain from above plus an amount of rain from the side that increases with your velocity component parallel to the ground. Solving this equation leads to the odd result that you should stay at the same point and not move at all to minimise wetness. That cannot be right. And it isn’t. It is provable with parallelepipeds again, that the amount of rain hitting you from the side while going from point A to B does not depend on the speed, but only on the distance.
So, in conclusion, the correct equation gives the total wetness after going from A to B as:
Total wetness = wetness per s (from top) x time in s + wetness per m (from side) x distance in m.
The second part in the sum is of course constant if you want to get from A to B, while the first part depends on the time you need. So run! Be careful and don’t hurt yourself or others. But run as fast as you can!
Henry Reich explains in an interview with Brady Haran (another very engaged YouTuber with many channels on sciences and mathematics, etc.), that the idea of drawing stick figures and simplified objects to explore and solve physics problems was born during his master’s when he was trying to explain his research on general relativity to undergraduate students. This concept ended up being so popular and effective that he now produces YouTube videos full-time and has started a second channel called MinuteEarth where he discusses ecology, ecosystems and the interactions between humans and their home planet.
Other enlightening videos from MinutePhysics include the answers to questions like “How to see without glasses?”, “Is there poop on the moon?” or “What is sea level?” as well as considerations about the Higgs Boson, our expanding universe and the mysteries of quantum mechanics.
Be sure to check out Reich’s videos as well as the many more YouTube channels that bring together science education and entertainment in brilliant ways for a wide audience and specialists alike, such as: Physics Girl, SciShow, thebrainscoop, Veritasium, Vsauce, SmarterEveryDay.