"During a descending turn, or spiral, in addition to pitch and
yaw, the airplane will be rolling about the roll axis in the direction
of the turn. As the airplane rolls, it induces an upflow of air into
the descending wing. This results in the descending wing having the
greatest angle of attack. If a stall is encountered, the airplane
will likely roll into the turn." pp.40-41.


I'm having some trouble visualizing this.

Is it possible that Sammy has posited a reference frame that looks
only at AOA, ignoring bank and relative speed across the span? If I
wanted to keep my model and my math simple, rather than describing the
turn as a hollowed cylinder with inner- and outer-walls transcribed by
the wings during descent, I could look solely at AOA, in which case
the model of a turn would look similar to, if not exactly like, a slow
rolling motion. Our reference frame has no horizon. In fact, it is
purely scalar. AOA simply has a range of values across the wing. If
this is the case, I can see how it would be useful for a snapshot --
such as just prior to the stall, but confusing when describing the
dynamics of a turn in its fuller context. This is a kind of partial
differential: an alternative way of describing a turn, but only
predicts outcomes based on AOA. Good for analysis in a narrow band...
Certainly counterproductive if integrated haphazardly into a more
intuitive three axis model.

So it goes like this maybe. The observed effect of constant sink rate
and differential airspeed across the span of a turning airfoil when
described in terms of differential AOA can be likened to the rolling
motion produced by the ailerons in level flight. The downward moving
wing, during the rolling motion, exhibits an increasingly higher AOA
as you go out the span (ignoring that part of the wing with deflected
aileron) than the rising wing, which shows a descending value of AOA
with span. Thus, during a descending spiral, if the airfoil were to
stall, this "psuedo-rolling moment" could be said to contribute to the
wing drop typically experiended during a turning stall.

I'm not sure I see how this changes with level flight or a climb.
After all, if we establish the longitudinal axis as the basis for
measurement, up or down with respect to the ground shouldn't matter.

This seems to me a more useful short cut for the engineer than the
aviator. Just remember, similitude is not exact. But it is an
interesting concept nonetheless.

Maybe someone could do the math for change in AOA for a 15M glider
traveling at 100kph and rolling at a rate of 30 degrees per second,
ignoring the ailerons, of course.

Wow, that was fun. Thanks.

Chris O'C