Overweight takeoff / flight

This is way interesting

I agree, and I appreciate and admire your open mind.

I'd substitute "without risk of structural failure" for talk of
control surface integrity. Since control surface failure is indeed
structural failure, my definition would seem more restrictive than
yours.

I can live with your defintion. I only used "control surface
integrity" in order to stress that it wasn't necessarily the main wing
we were talking about.

Vo does differs a little from pt 23 certification requirements, in
that Va isn't exactly Vo, because Va calculations assume that airfoil
lift does scale linearly with AOA and as the square of airspeed
when in fact these are only approximately true.

The only distinction I see between Va and Vo is that Va says "not less
than" and Vo is "not greater than". Where do you see the distinction
you are drawing?

All the lift slope curves I've seen for straight wings are pretty
linear, at least up until the stall. But that does lead us into the
concept of a dynamic stall. Airfoils rapidly rotated to a high angle
of attack can generate a much higher lift coefficient than when in
steady state. (References available upon request.) The whole concept
of Va, or even Vo, protecting the wing are a bit fraudulent.

I'd bet that Vo and Va are pretty close. Allowing for the 1.5 safety
factor, I bet they're indistinguishable.

I'd say you're right. A friend of mine, who spoke with the FAA's
Seattle Certification office, said that Va might be a maximum of 5
knots over what sqrt(n)*Vs would be.

Isn't this just a warning that Va "may not be less than Vs.sqrt(n)",
and so could be higher?

Yes, exactly. Some people need it spelled out. g

I don't see that in pt 23. I see it being defined as 'may not
be less than' some expression involving gross weight parameters,
but there is nothing to say that this applies only to gross
weight (to be pedantic).

If I understand what you're saying, I agree. I guess it depends on
what "defined" means. g

The suggestion was that Va, should be scaled upward in an overloaded
airplane. We both claim that it should not.

Agreed.

I'd also scale my maneuvering speed downwards if underweight just to
stay within load factor limits, and I bet you would too.

Yes. However, those knowledgeable about aircraft structures maintain
that load factors incurred in turbulence are less stressful on the
aircraft than what are incurred via flight control movements.
Turbulence penetration speeds are calculated allowing higher load
factors.

I'd claim that Va shouldn't be increased because it is really
the minimum of a number of different speeds where things
start to fall apart, and without further data we don't know
which one does the limiting.

Very well expressed.