> Ok, so the answer is: run as fast as you can. Just don't fall down.

The other case, of course, is if the rain is slanted so as to hit your back when you stand still. CLEARLY (punching fist into open palm) if we are moving fast enough (V bigger than R Sin(A)) we can treat it just as before, except we replace R Sin(A) + V in both places by V - R Sin(A). In the walking person's reference frame, the rain is moving backward, even though it is moving forward in the reference frame of the ground.

On the other hand if V is less than R Sin(A), we get the same picture but in reverse. The visible surface area is now the top and back side of the cube, instead of the top and front side. (The person is overtaken by rain). The forward velocity of the rain in the person's frame is R Sin(A) - V. This is really nice, because we can now use the cube's symmetry and the fact that the horizontal velocity of the rain relative to the person is |V - R Sin(A)| to get a single function for all values of V.

We have to change the definition of A':
A' = Arctan[|R Sin(A) - V|/(R Cos(A)]. Also, the new relative rain velocity is
[R^2 + V^2 - 2RV Sin(A)]^0.5

So after a little modification, the total number of drops that hit the person is

DL[R^2 + V^2 - 2RV Sin(A)]^0.5 * [Cos(Arctan[|R Sin(A) - V|/(R Cos(A))]) + Sin(Arctan[|R Sin(A) - V|/(R Cos(A))])]/V

Here's the cool part: Mathematica gets hung up trying to optimize functions with absolute values anywhere, so instead I looked at each of the two functions you get by replacing |R Sin(A) - V| by either +(R Sin(A) - V) or -(R Sin(A) - V). The real function we're interested in will have the + sign for V smaller than R Sin(A) and the - sign for V bigger than R Sin (A). Well, the function with the + sign is decreasing, and the function with the - sign is decreasing. So the function with the absolute value signs actually has a minimum, right at the cross-over point.

What does that mean? It means the best speed to walk at V = R Sin (A).

So here's the final analysis, if you want to stay as dry as possible: If the rain's coming at you, go as fast as you can. If the rain's at your back, go at exactly the same horizontal speed (i.e. move so that the rain appears to be falling straight down).