Do You Walk or Do You Run? (Which One Will Get You Wetter Through the Rain)

I was finally able to work and finish(?) on a self imposed problem! However, the results I got were pretty disappointing as they did not jive with my earlier assumptions/predictions.

As I have mentioned in an earlier post, I was challenged by a Mythbusters episode to do my own experiments to determine whether a person would get wetter if he/she runs through the rain as compared to if he/she walks (actually, they worked on this twice and ended up with different results. So, I was left unconvinced). Yeah, you can say it, I’m nuts… somebody has already told me that. But then again, my “experiments” were paper-based and did not involve anybody walking and running through the rain as you may have been thinking previously.

So with all the knowledge I have in math (limited as it may be), this is what I got…

(By the way, before I proceed, I'd like to make a few things clear... I'm not an expert, I'm just playing around with the idea using whatever resources that are available to me and I am not saying/declaring in anyway that this is definitive. If you think this is all wrong, please feel free to discuss it with me, hopefully, in a pleasant manner so that you will not be afraid to identify yourself... look at the comments and see what I mean).

Given (all conversions have been rounded off):

• Raindrop terminal velocity = 10 mph (14.67 ft/s)
• Average walking speed of human beings = 3 mph (4.4 ft/s)
• Average running speed of human beings = 10 mph (14.67 ft/s)
• Light rain = 0.25 inches per hour (or 0.0000694 inches/second)

Estimates:

• Surface area of the front of a person’s body (fa) = 1728 sq.in.
• Surface area of the top of a person’s head and shoulders (ta) = 216 sq.in.

Derived Values:

Amount of water hitting the front of a person’s body:

• Running = (fa x 0.0000694 in./s) = 0.1199232 cu.in./s
• Walking = [(fa x 0.0000694 in./s) x 0.3] = 0.03597696 cu.in./s*
  

*The 0.3 multiplier is derived from dividing the average walking speed by the average running speed. The reason behind this derivation is that the terminal velocity of raindrops is equal to the average person’s running speed and, as such, I am assuming that a runner will get hit by water on the front of his body as much as he will on his head and shoulders. And, understandably, a walker will get hit by water on his front much less than the runner would. And the most logical thing to do I can think of is this… the 0.3 thingie.

Amount of water hitting a person’s head and shoulders (and any other body parts that may be seen/exposed from the top):

• (ta x 0.0000694) = 0.015 cu.in./s

Computation:

Formula:

• Walking = (0.03597696 cu.in./s + 0.015 cu.in./s)t
• Running = (0.1199232 cu.in./s + 0.015 cu.in./s)t
  

Where: t = the amount of time it will take for the person to travel a given distance

Cases and Results:

@ 10 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)2.27 seconds = 0.115718 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)0.68 seconds = 0.091748 cu.in.

@ 20 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)4.54 seconds = 0.231435398 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)1.36 seconds = 0.183495552 cu.in.

@ 40 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)9.09 seconds = 0.463380566 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)2.73 seconds = 0.368340336 cu.in.

@ 80 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)18.18 seconds = 0.926761133 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)5.45 seconds = 0.73533144 cu.in.

@ 160 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)36.36 seconds = 1.853522266 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)10.91 seconds = 1.472012112 cu.in.

@ 320 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)72.72 seconds = 3.707044531 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)21.81 seconds = 2.942674992 cu.in.

@ 640 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)145.45 seconds = 7.414598832 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)43.63 seconds = 5.751776016 cu.in.

@ 1280 feet

Walking:
(0.03597696 cu.in./s + 0.015 cu.in./s)290.9 seconds = 14.82919766 cu.in.

Running:
(0.1199232 cu.in./s + 0.015 cu.in./s)87.25 seconds = 11.7720492 cu.in.

There…

So, why was I disappointed? Well, prior to doing this, my assumption was that in traveling short distances a person will reach his/her destination less wet if he/she ran through the rain as compared to if he/she walked, but as the distance increases he/she will end up less wet if he/she walked. And this is not what my results are telling me…

I even tried to compute for another value using Maurice Greene’s record sprinting speed of 26.7 mph (or 39.17 ft/s). But the results came out just the same considering that I used a multiplier of 2.67 for the amount of water hitting the front of his body at that speed. This proved even further that the faster you go through the rain the less wet you’ll get! Here’s what I got using Maurice Greene’s speed:

@ 10 ft = 0.087150685 cu.in.
@ 20 ft = 0.170949421 cu.in.
@ 40 ft = 0.341898843 cu.in.
@ 80 ft = 0.683797686 cu.in.
@ 160 ft = 1.367595372 cu.in.
@ 320 ft = 2.738542692 cu.in.
@ 640 ft = 5.477085385 cu.in.
@ 1280 ft = 10.95417077 cu.in.

From my results, I am now convinced that RUNNING THROUGH THE RAIN WILL ALWAYS MAKE YOU END UP LESS WET AS OPPOSED TO WALKING!