The Vertical Stabilizer is NOT a wing, it is a FIN. It has ALL LIFT designed out of it. It is symmetrical in chord
Bearfoil,
Yes if there is no Angle of Attack, it has no Lift.
BUT:
As soon as it gets minimal AoA it will start producing lift and pitching moment. Into the direction where it started building AoA.
The Flow around the round LE will start creating Lift due to Bernoulli Effect.
Take a good book on aerodynamics and you will see what I mean.
Look at aerobatics aircraft. They have fully symmetrical wings as well. And yet they fly. And they fly in the same way any other aircraft flies.
just with a little more AoA.
Or more technically:
If you look at a wing Polar of a symmetrical Profile (NACA Report 460, e.g. 0006 or 0009) you will see that the moment coefficient around the the Quarter Chord Line is constant (Null) for quite a large range of Alpha. That means the aerodynamic center is the Quarter Chord Line.
If your Cg is behind that point you get a positive moment coefficient i.e. the Wing will increasingly pitch into the direction where it started to pitch to, i.e. it is highly unstable.
Remember: Also a symmetrical Profile is a Wing !!!
It does just not produce lift at Alpha = 0.
and falls ballistically
No in all likelyhood it won't !
(See explanation above)
Edit:
It won't fall bottom first either, as the drag in that direction is much higher than LE first (High Cd of the lower side of the fin).
Only if the lower part would be very much heavier than the upper part, it could fall with the lower side first.
But I'm not aware of any reason why with an Airbus fin this should be the case.
So in a first move it would probably pitch in a dircetion where the drag is less, which would be LE in front and then the instability will take over.
Which likely will cause rotation around roughly the half chord axis
/Edit
Edit2:
The Fin is basically a Wing.
It becomes a fin by being placed so far aft behind CG and aerodnamic center of the plane itself.
/Edit2