Flaneur in the rain - iii

Suppose you're sauntering about Saint-Germain, Paris, from one cafe to the next, staying only as long as it takes you to knock down a few Brilliant problems. You're wrapping up at Brasserie Lipp and want to go to Cafè de Flore, which is across the street.

The only problem is: it's pouring rain!

If you want to absorb as little water as possible, how quickly should you run across the road?

Assumptions

• Approximate yourself as a shape with a vertical cross section of $A_\text{head}$, and horizontal cross section $A_\text{body}$.
• The rain falls straight down at terminal velocity $v_\text{rain}$
• All the rain that hits your body is absorbed.
• The width of the road is $d$.