RE: Balancing low-wing plane
That test must be done after the airplane is trimmed for high speed level flight, and the nose must be pointed straight down. Putting the airplane vertical takes the horizontal CG out of the mix and any elevator trim that was needed to compensate for horizontal balance problems will cause the airplane to deviate from a straight down course. Elevator down trim needed to compensate for a heavy tail will cause the airplane to pull to the belly ( nose "down" ) and vise-versa.
It also only works with an airplane that is set up without up or down-thrust. Throttling back for the vertical downline takes the thrust line out of the mix as well and in this test you wouldn't know whether the elevator trim was needed to compensate for balance or thrust line.
It's a pretty crude test that only really tells you whether you have a problem or not.
Jim