A precipitation physics question

Walking Akela the Wonder Dog in the rain today, I got to wondering...

The route is a fixed distance, about a mile. Would I collect more raindrops or fewer raindrops by walking faster?

Walking faster means I gather more raindrops/minute due to the horizontal component of motion, but I spend less time in the rain.

What effect would the ratio of frontal area vs. plan area (i.e., area viewed from directly above) have on the problem? How would the amount of raindrops received vary if I were on hands and knees instead of standing upright but moving at the same speed?

How does the severity of the rainfall enter in when viewed as a function of forward velocity? Perhaps the optimum velocity differs depending on how fast the rain is falling?

Are there too many inter-related variables for there even to be a definitive solution?

tanstaafl.

The simplified version of the question ("which gets you wetter: walking or running") was one of the winning questions in an Omni Magazine "Games" section contest about 30 years ago. Recently, it was tackled by Mythbusters. I forget the answer.

Walking was better in Mythbusters

Some folks seem to disagree with that assertion. In particular the discussion of frontal vs. plan area was interesting.

tanstaafl.

There is a definitive answer....... use a bigger umbrella

Seems like it ought to be a fairly simple 4D vector calculus problem.

I would guess that there are too many variables for there to be a foolproof solution. At one extreme, if the wind was blowing hard enough so the rain was effectively horizontal and you were able to walk at the same speed as the wind, you wouldn't get any wetter than the initial 'clear out your spot in space' time frame. At the other extreme, if it was a deluge, it could be like walking through a swimming pool.

Didn't Mythbusters re-do that segment in one of their revisited shows?

Yes. They came to two different conclusions.

My first room-mate at university described for me how he was set this problem by a favorite instructor he had in his home country, Russia.
I can't remember the outcome, but I seem to remember that the key was to look at the limits of each option.

Having sat down and worked it out, the answer does all depend on the angle of the rain. In vertical rain, or a headwind, or a sidewind, then you hit less water the faster you go. In a tailwind, it's sometimes possible to do better if you can match the horizontal component of the velocity of the rain. The terminal velocity of raindrops is about 20mph, says Wikipedia, so, if the rain is coming down at an angle of arctan(3/20) or 8.5 degrees to the vertical, and you walk at 3mph, you get less wet than running -- though this does assume that your plan area is much less than your frontal area.

Of course in practice there are other factors -- the relative porosity of various parts of clothing, wind-drying effects caused by running, and, for those who remember Glastonbury 2004, the fact that once you're soaking wet you aren't getting any wetter however fast or slow you go.

Peter

You get hit by fewer raindrops by walking faster because you reach your destination sooner.

/thread

Edit: Now if you had said "fixed time period" instead of a fixed distance of 1 mile, then that's a different story.

It's the total time you spend in the rain, which determines how wet you get. So faster is better.

You don't get wetter from horizontal impacts due to your speed. The equation has time as a factor, equally on both sides.
Since time drops out, speed isn't a factor.

The horizontal impacts are proportional to the difference between your speed and the horizontal speed of the rain. Time doesn't drop out as a factor if there's a tailwind.

Peter

We should also take into account terminal wetness, which is the maximum amount of water your skin, hair, and clothes can absorb. Once terminal wetness is achieved, it doesn't matter if you walk or run.