felix said:
You can't do anything about the frontal soaking but you can minimize the overhead contribution by running as fast as you can - or you can use an umbrella!
Not true if you
are using an umbrella though!
If you take the walker/runner as your rest frame, then the raindrops follow an air-resistance-limited ballistic trajectory towards the walker. Due to the air resistance, this would effectively be a straight line. However, the angle between this straight line and the ground would vary depending on walking speed, where at a walking speed of zero this angle is 90 degrees, and at a walking speed of infinity this angle is zero degrees.
We will assume:
1) a distance of 1.8m between the tip of the umbrella and the ground
2) umbrella is square, with two sides perpendicular to the direction of travel and two sides parallel, and each side is 1.2m long.
3) rain is falling vertically with a velocity of 5 ms^-1 (apparently 2-9ms^-1 is typical, so let's pick an arbitrary value)
4) the umbrella remains straight and level
5) the walker is infinitely thin, perfectly upright and resides entirely under the centre point of the umbrella
Now, falling at 5ms^-1, it will take 1.8/5 seconds for the raindrop to travel from the umbrella edge to the ground, 0.36s.
Now, in order to traverse the 0.6m horizontal displacement from umbrella edge to the feet, in 0.36s, the walker speed would have to be 0.6/0.36 = 1.7ms^-1.
So, our hypothetical rod can travel at up to 3.7mph before getting it's feet wet. Any faster and the rain will get him.