Roger wrote:

Open the door in level flight. Now close the door in level flight. It
won't close. Why? If you look, the door shape no longer matches that
of the opening. As I recall on the Cherokee 180 the mismatch was on
the order of half an inch.

The (4) PA-28 airframes I've flown (mostly 160HP Warriors) will close
quite easily if you follow the POH in-flight door closing procedure.
With the storm window open, cabin vents closed, and the right airspeed,
the door is almost sucked closed.

Was there something wrong with the Cherokee you were flying? G