Rotating Ballnut

Long ballscrews tend to whip at higher RPMs. The longer the screw
the larger the reqired diameter. I can't afford a large enough
diameter rotating ballscew for a router to eliminate whip at planned
RPM's with a 96 inch span. An alternative is to use a smaller
ballscrew and a rotating ballnut supported between bearings.

Would I be correct if I assumed that the diameter of a ballscrew
with a rotating ballnut is only dependent on the required dynamic
load? If I needed less than 800 pounds of thrust could I get by with
a 5/8 ballscrew (rated at about 800 pounds) 96 inches long? Mcmaster
has 5/8 ballscrews for $1.27 an inch. One inch (rated at 3,700
pounds) is $2.70 an inch.

Am I missing something?

I'm trying to build a router to go with my mill and lathe. I bought
4X48 inch supported linear rails 3 inches in diameter with matching
open bearings that I would like to use for the long axis of a 4X7
router. For the short axis VBXbearings has some inexpensive 20mm
round bearings and rails. I haven't done the math but I think they
will be OK on a 48 inch span. The rails came with matching ground
ballscrews that I will use on the short axis. I'm trying to figure
out how to do all this without breaking the budget (worse than I
already have).

Roger