To my knowledge, there is no formula that will compute N(d;D) precisely. However, Eckard Specht has compiled a table of observed packings for N up to 900 (and beyond). From his data, it's clear that D/d varies smoothly as a power function of N.

There's a javascript calculator at the bottom of Fiber Stuffing Revisited | Saphum that uses Specht's data to estimate N(d;D).

For D = 72mm and d = 9mm, N = 51.

-peter