Analysis of Minimum F-stop for 18-200mm and 18-70mm Lenses
Prepared 2006-01-06 (146/46491) by Bill Claff

With today's modern lens designs there is no obvious relationship between focal length and aperture for variable aperture zooms.
(In the "old" days it was a simple linear relationship.)

Here is the relationship for the 18-200mm f/3.5-5.6 G ED-IF AF-S VR DX Zoom-Nikkor as well as the 18-70mm f/3.5-4.5G ED-IF AF-S DX Zoom-Nikkor.

Note that the new 18-200mm is slightly slower than the 18-70mm at all focal lengths (except 18mm where they're identical at f/3.5 ).

These line segments also give us some hints about how the groups move.

With the 18-70mm the rear group moves from 18mm to 46mm.

The 18-200mm is obviously much more complicated with at least two if not three rear groups involved in focusing.

Another, slightly off topic observation; is that the 18-200mm doesn't report any focal lengths between 170mm and 200mm.