"Gary Drescher" wrote in message
news:CjWLb.15152$8H.35818@attbi_s03...
"Tony Cox" wrote in message
k.net...

1) Va by definition is just a number and _does not_ scale
with weight.

While I understand your earlier point about the certification regulations,
nonetheless Va is explicitly defined in some places as "the maximum speed
at
which you may use abrupt control travel" (C172P POH, for example), and
that
speed _does_ scale with weight (and the C172P POH, for example, specifies
different values of Va for different weights).

Hi Gary. As Julian pointed out, there may be terminology problems
here. It may well be that the 172 POH defines Va as you say, but in
that case Cessna are telling you something more -- they are telling you
specifically that their Va is defined to meet the equality condition in
23.335. So it is really just their own private definition, applicable to
that plane and model year only. And of course if the equality condition
applies, then scaling proportional to sqrt(w) should be adequate or
better as I pointed out earlier (and discuss further below).

Now my POH just gives me Va. Nothing about abrupt control
inputs or anything. So absent other information, it's not really
much use to me. I could yank the yoke at Va and watch the wings
fall off - all this in a properly certified plane. Odd, eh? Of course,
its not likely to happen because of the additional safety factors
built into the design, but I could still be exceeding the load factor.


4) Some of these component Va' don't scale with weight, some
scale as sqrt(w), and some no doubt scale in other bizarre
ways.

Here I don't follow you. If the components have constant mass and each
component has a maximum force that it can withstand, then each component
thereby has a maximum acceleration that it can withstand, does it not? And
for any given acceleration, the maximum airspeed at which abrupt control
deflection would not exceed that acceleration (namely, the maximum speed
at
which the maximum coefficient of lift would not provide enough force to
exceed that acceleration) does indeed scale in proportion to the square
root
of the plane's weight.


Well, the control surfaces don't care how much weight is in the
plane (at least to first order). If you yank them lightly loaded, you'll
stress the cables and hinges just the same as if you were over gross.
So that Va'(w) is flat if you plot it against w.

Things like baggage compartment objects stress should scale like
sqrt(w). Wing bolts (on a Cessna) are more complicated. At less
weight - lets assume this is mostly less weight in the cabin - you'll
be able to withstand greater acceleration; load factor isn't really
the issue here. Va'(w) in this case probably drops off less rapidly
with decreasing w than sqrt(w).

Now I think it is true that there is no component for which
Va'(w) falls _faster_ than sqrt(w) with decreasing w. In this case,
scaling an overall Va' at gross by sqrt(w) should mean that
it doesn't matter which Va' is the limiting component, you'll
always be _at or below_ it's corresponding Va'(w).

But caution two things. If you're certified over gross
(91.323), you shouldn't use the relationship to computer a higher
Va. Control surfaces might be the limiting factor, for example,
and they don't scale at all.

Second, if the equality in 21.335 isn't met, control surfaces
are the limiting factor. You can scale them by sqrt(w) if you
like, but it'll be meaningless -- the answer you get will _still_
be above the Va' for things that are load-factor limited.


5) Since you don't know without access to the engineering
design reports what these component Va's are, you can
never be certain how they scale with weight or which of
them is the limiting factor in any configuration.

6) Even at gross, Va' doesn't guarantee you protection
against full control movement. For that you need Vo, which
isn't available for older aircraft anyway.

Is there any better guideline for a pilot than to use the published
max-gross Va, scaled in proportion to the square root of current gross
weight, as the limiting speed for abrupt control deflections?


That's the key question isn't it?

As Julian pointed out, if you have Vo, then you should use
that. But my plane doesn't, and I don't think most of the fleet
does either. Vo is, I believe, a recent certification requirement.

Here's how I approach it. And of course, YMMV, so I hope
no one does the same without thinking about it first.

I think that for most GA planes, the equality in 21.335 applies.
Why overbuild control surfaces? The FAA says that you
*can* set Va above Vs*sqrt(lf), but to do so costs $$$'s and
lowers the useful load. So I think it is a reasonable assumption,
at least for my 182. This means, of course, that the sqrt(w)
relationship ought to be adequate to protect me, which is indeed
how I fly. But I realize I may be flying outside the load-factor
safety zone. After all, there should be a 50% margin to play with!

When I used to fly 172's, I noticed that some were certified in
the utility category at certain light weights. This suggests (but doesn't
guarantee) that the limiting factor in Va' is the wings, rather than
cabin load. Since this scales better than sqrt(w), I think you can
probably fly faster than the scaled Va without issue.

My 182 has no such certification -- it's all normal category.
It might mean that no one could be bothered to certify it in
the utility category, but it might also mean that the wings are
not the limiting factor. This I find comforting & I'm more careful
to maintain Va'(w) in rough air. (why in rough air is, I suppose,
where we came in).

BTW, that 'sqrt(w)' business is quite an approximation in itself,
and relies on quite a few assumptions which are probably not
that supportable over a wide range of w's...

Hope you've found this rant more informative than pedantic!

--
Dr. Tony Cox
Citrus Controls Inc.
e-mail:
http://CitrusControls.com/