From: braner@theory.TC.Cornell.EDU (Moshe Braner)
Subject: Re: Canard Pros -n- Cons,   Tail lift.
Summary: pitching moment is the key
Organization: Cornell Theory Center
Date: Mon, 14 Sep 1992 17:05:55 GMT

Perhaps I should add a bit more explanation to my previous posting,
although I am not an expert on this, and the best thing to do is to
consult a textbook on the subject.  My comments are based on reading
chapter 2 in Etkin's book.

For an aircraft to fly in an unaccelerated steady-state, both the
forces and the pitching moments must balance out.  The forces are
the weight of the aircraft, acting at the CG, the wing's lift, acting
close to the quarter-chord point, and the tail lift.  The pitching
moments are forces that want to turn the aircraft on its pitch axis.
Choose any point you want, e.g., the CG, and each force has a moment
equal to the product of the force and its arm (distance from the
place the force acts and the chosen datum point).  If we choose the
CG as the datum, the weight has no moment.  The tail lift (small)
times the tail arm (large) gives one moment.   The wing lift (large)
times the arm (small) is another.  The CG may be either in front
of or behind the wing's center of lift, so the wing lift's moment may
be positive or negative.  Finally, there is another, usually overlooked,
moment, caused by the aerodynamic forces on the wing.  The wing
itself want to twist!  That moment depends on the wing's camber.
In a "flying wing" aircraft the wing has negative camber.  With
the CG in front of the center of lift, the lift makes a nose-down
moment, and the negative cambered wing (trailing edge up) creates
a nose-up moment, and they balance.  But most conventional aircraft
have positive camber in the wing (for better lift) and that causes
a substantial nose-down moment, to be countered by the tail lift.

As the airspeed changes, lift still equals the weight, and the location
at which the lift forces act do not change much.  But the wing's
inherent pitching moment changes significantly!  That is one reason
why the tail lift must be changed to fit.  I.e., one must change the
elevator trim to keep a different airspeed.

Can the tail lift be positive at low speeds even though the elevator
is way up?  Think of the trim tab.  To keep the elevator UP the trim
tab goes DOWN.  The trim tab's lift is then UP, which pushes the
elevator UP, which pushes the tail DOWN!  The relationship of the
elevator to the horizontal stab is similar to that of the trim tab
to the elevator, although the elevator is a larger percentage of the
stab's area that the trim tab is of the elevator's area.  So it is
indeed possible that the stab as a whole, at high AOA, creates
positive lift even as the elevator itself is creating negative lift.

Is negative tail lift "bad" (inefficient)?  Only in the sense that
the tail creates induced drag (whether its lift is positive or negative,
that's why zero tail lift is best), AND in the sense that the main wing
must create a bit more positive lift to compensate, and then IT also
creates some more induced drag.  But at cruise speeds induced drag
is small relative to parasite drag, and the tail lift is small relative
to the wing lift, so the whole effect is not very important.

- Moshe
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