covering disks with smaller disks

Just to help think about the problem, here is the natural cover by seven $\frac{1}{2}$ disks:
          

You'll need seven disks with $r=0.5$ to cover a disk with $r=1$. See http://mathworld.wolfram.com/DiskCoveringProblem.html.

A more general version of this question is discussed (and answered) in this paper by Dumitrescu and Jiang