I think what determines the amount of soaking you experience when you cover the distance from A to B (dx) in the rain are the following factors:
A) apparent speed (Va) f the rain, consisting of two factors
- The vertical velocity (Vv) of the rain falling down
- your horizontal movement speed (Vh)
where Va² = Vv² + Vh² => Va = SQR(Vv² + Vh²)
(Assuming that the intensity of the rain is constant over for the duration of the walk, the soaking per second is proportional to Va.)
B) The time exposed to the rain, which is dx / Vh.
As only relative soaking at different speeds is to be compared, the absolute intensity of the rain can be ignored in the calculation.
So the overall relative Soaking (S) at speed Vh is:
S(Vh) = SQR(Vv² + Vh²) * dx / Vh
With walking speed Vh approximating Zero, the soaking converges to the Y-axis, meaning infinite wetting.
With walking speed Vh approximating infinity, we get:
S(Vh)-> Vh * dx / Vh
so approaching infinite speed the soaking is the minimal amount based only on the distance.
Conclusion: Run if you don’t want to get too wet.
Hope this helps