You have a number (N) of identical planks of length L (0 < L <= 2). The planks have small width and negligible thickness, but very high strength and rigidity. No plank extends outside the circle. Both endpoints of each plank, with the exception of the N-th plank, must rest on either the circle or another plank. Neither weaving of planks nor cantilever designs are allowed. Covering the center means that the N-th plank crosses over the center of the circle.

For a given N, L is the minimum length plank necessary.
Obviously if N=1, then L=2.

What is the smallest L when N=2? N=3? N=4?

For larger N, is there an optimum algorithm to minimize L?

Can you determine a general relationship between N and L?