## Tuesday, October 12, 2010

### The Rain Formula?

When I was walking home yesterday, it began to rain. As it progressively began to rain harder and harder, people began running towards their destinations in order to get there less wet.

However, does running in the rain keep you less wet? Perhaps you are in the rain for not as much time, but then you are hitting more raindrops along the way - horizontally. I suppose that if it was really pouring, you might get wet either way - but in a moderate rain, is it better to walk and hit less raindrops, or run and hit more?

There must be some sort of equation that includes distance, speed, amount of rain and the surface area of the person. I don't know if such a formula could be applied to real life (like measuring the amount of raindrops per second - or knowing your surface area...) but I still think it is something worth pondering.

Noah said...

This is an interesting mathematical problem (and I feel you have mentioned it to me before). Lets attempt to quantify it.

Given: Vrain is the velocity of the rain falling, assuming it is completely in the negative z direction (not always a good assumption in nyc with wind).
Vperson is the velocity of someone walking, assuming in the entirely positive x direction.
Ahead is the vertical projection of a person onto a x-y plane.
Afront is the projection of someone onto the y-z plane.
Qrain is the density of rain drops per second in a cubic meter (because I like english units better).

Given those few parameters, a relationship should be able to be formed whereby the paralelogram of water in front of a person that they intersect with as they walk in a second and the parallelogram of water above them that they intersect with as they walk can yield the number of drops that hits them.

Number of drops that hits a person that moves 1 meter = (Afront+Atop)*Qrain*(1m)*(1m/Vperson)

Anonymous said...

MythBusters tested this.

They originally concluded that walking was better but revisited it in a later episode where they confirmed that running was really better.

Eitan

Michelle said...

Years ago I read a book by Tom Robbins, "Another Roadside Attraction". I remember a quote about rain that has stuck with me all of these years. Here it is:

"As was my custom in such elements, I hunkered against the rain... and proceeded in misery. But my hosts... reacted in quite another way. They strolled calmly & smoothly, their bodies perfectly relaxed. They did not hunch away from the rain, but rather glided through it... they directed their faces to it... and almost revelled in it... The Zillers accepted the rain. They were not at odds with it, they did not combat it or deny it; they accepted it and went with it in harmony and ease... I tried it myself... I let it do to me what it would. Of course, it was not trying to DO anything to me... it was simply falling as rain should, and I, a man, another phenomenon of nature, was sharing the space in which it fell...