Should you walk or run in the rain?

One of the problems in X and the City, a book I mentioned the other day, is deciding whether you’ll get wetter by walking or running in the rain.

The author takes several factors into account and models the total amount of water a person absorbs as

T = frac{Iwd}{v}left(ct costheta + l(c sintheta + v)right).

This assumes a person is essentially a rectangular box of height l, width w, and thickness t. The rain is falling at an angle θ to the vertical (e.g. θ = 0 for rain coming straight down). The distance you need to walk or run is d and your speed is v. The rain is falling with speed c. The parameter I is the rain intensity, ranging from 0 for no rain to 1 for continuous flow. The book goes into greater detail, deriving the formula and estimating numerical values for the parameters.

Conclusion?

If the rain is driving into you from the front, run as fast as you safely can. On the other hand, if the rain is coming from behind you, and you can keep pace with its horizontal speed by waling, do so!

14 thoughts on “Should you walk or run in the rain?

  1. Alternatively, if you prefer avoiding toy models, the Mythbusters have actually run the experiment (though they didn’t vary wind conditions). They concluded it was better to walk than to run in the rain.

  2. The advantage of a model, even a toy model, is that it can simultaneously address many possibilities. John Adam identified eight variables and gave a formula for the amount of rain absorbed for all possible values of these variables. A single experiment has to choose a particular value for each variable.

    I’m not saying we only need to make toy models. If experiment and model disagree, then we accept the results of the experiment for that set of parameters, assuming the experiment was conducted well.

    Models and experiments complement each other. Though Adam’s model is simplistic, it suggests that we would need to run several experiments varying θ, v, etc. and that there isn’t a single answer to the question for all conditions.

  3. John, you’re right the model gives insight into a much wider range of conditions. The Mythbusters did their experiment in 2003 and concluded that walking was better, but then revisited in 2005 and reversed their opinion.

    http://en.wikipedia.org/wiki/List_of_MythBusters_episodes

    As you mention you’d have to vary several parameters, but although the number of parameters in the model is 8 (I w d l c t v theta) there are many fewer nondimensional groups. Every physical model should be nondimensionalized, it eliminates redundant symmetries.

    In this example the left hand side is T, a volume.

    I is already nondimensional (fraction of the volume filled with water), and so is theta, so with the remaining 6 parameters and 2 characteristic dimensions (one for time and one for length) you can create 4 nondimensional groups.

    For example one of them is the ratio of rain speed to your speed (c/v) and another is the ratio of the volume you will carve out with the frontal area to the volume that will fall on you if you stand still for the same time and the rain falls straight down (wld)/(wtc * (d/v)) which turns out to be l/t.

    I’ll leave it as an exercise to the reader to fill in the rest since I’ve got to get back to work.

  4. I really like Mythbusters, but it seems to me that some of the myths could be dismissed easily with paper and pencil. Sometimes they do calculations, but it is a pretty minor part of the show. It would be more realistic, in the sense of being truer to what goes on in science and engineering, if they did a little more calculating up front. Maybe that would make it boring for most of the audience, but not for me.

  5. @SteveBrooklineMA

    Often, what I find refreshing about Mytbusters is, while you’re exactly right about science, that they actually try these things. At times, their findings are utterly unscientific. however, they don’t just accept ‘expert’ research as fact, they really test things; moreover, by actually trying some of these things they prove to the average viewer what a bunch of math never would.

    I’m sure they do lots of math, off-screen, to see what is a viable test. I like math, but doing realistic science is a persons career, for a reason. Not because they know HOW, but because they are willing to ‘just do the math’/

  6. Beyond the simplification of a human shape and motion (not just swinging arms and legs but some degree of non-linear motion of the center), it seems there would be other (probably minor?) factors for wetness. The absorption or adhesion of the water would seem to depend on certain traits of the contacted surface, the impact speed of the raindrops, and the size of the raindrops. (The real world also adds water on the ground–and complicating factors of avoiding being splashed upon by not using a direct route or varying pace–and predictions about future rainfall.)

    In the real world, minimizing wetness might not be a well defined (mean wetness over time, total wetness over time weighted by some importance factor for various degrees of wetness) or even a desirable goal. (Wetness might be a coarse surrogate for comfort (which can vary based on activity level and kind, temperature, clothing, time until dried off after leaving rain, etc.), inconvenience to self or others, or some complex combination of such factors.) Defining requirements in the real world, especially when dealing with psychological factors, can be very difficult.

    (The above is probably just “blah, blah, blah [I know all that]” for the readers here, but I find this simple problem–and how it so easily becomes more complex–interesting, especially as I sometimes am a pedestrian without an umbrella during rain storms.)

  7. It’s too subjective to be measured. Having some volume of water spread over your head and shoulders is probably more “wet” than having the same volume spread over your entire front.

  8. I’m in agreement with F. Grosshans that the formula may have a typo. Let x = thickness cos(theta) + height sin(theta). If x>0, then v should be made as large as possible to minimize T. I can believe that. If x<0, then as v approaches zero, T eventually becomes negative?

  9. many years ago – perhaps in the 1970s, Ann Landers (or a close equivalent) in a dead tree newspaper, had a column or two about this.
    The only thing I remember – and god knows, memory is a poor crutch – is that quite a few Professors Of Math (or Physics) wrote to Ann, and 50% concluded run, and 50% concluded don’t run.

  10. The paper.. The best strategy in rain..u can input the title in google and u can see the paper.

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