What diameter of prop can you turn at 4000 rpm?

A Volkswagen is NOT a good direct drive aircraft engine because it
produces good power at 3200 to 3800 rpm. But it's a hell of a lot
easier to put a redrive on a VW than an O-200.

Actually, 46 to 48"

The VW 1600 was used that way with considerable success in the early KR-2
aircraft. However, that only meant 60 to 65 HP with the small displacement,
and the modestly oversized cylinders which would be fitted without fairly
radical case machining provided only a very modest addition of take-off
power. Cruising speed was only about 115 kts within the thermal capacity of
the stock heads--which has been discussed previously in this NG--so pilots
who were heavier or wanted to fly faster sought more oomph.

There were also successfull amateur conversions of the VW Type-IV engine, of
1700 cc, which was used in the Porsche 914 and some years of Transporters
and which was also rated to turn 4000 rpm.

Most of the more recent VW "Based" engines have more displacement and turn
slower to provide a larger propeller disk area.

However, there is no single "best" rpm for all engines in all aircraft. It
is best to think of an airplane as a large number of compromises flying in
close formation; and if the design is not intended for the mass market, the
designed is free to make his own compromises.

Peter