So far, my consideration of Weight and Balance has led to the conclusion that placement of the airplane center of gravity (CG) has critical implications for static stability. Before charging ahead, here is a quick review.
Static stability refers to what a system (airplane) does initially in response to a disturbance. If, after you raise the nose and release, the plane pitches forward to reverse the disturbance, the system is statically stable.
All airplanes are designed to be statically stable, and last month I demonstrated that this crucial characteristic is a weathervaning effect, dependent on the relationship of the CG to an airplane’s aerodynamic center (AC).
THE TDF THEORY
With a definition of static stability in place, it is time to pinpoint a widespread misunderstanding concerning pitch stability: it involves pitch changes, trim, and “tail down force” (TDF).
The TDF theory states that the CG must always be placed ahead of the center of lift of the wings. This relationship assures that airplanes will always be “nose-heavy” and thus require aerodynamic down force at the tail to balance, a factor held by the theory to be crucial for pitch stability.
The theory explains that when a plane is pitched forward, added airspeed increases the authority of the tail surfaces, produces more TDF and raises the nose, thus reversing the initial disturbance. Similarly, any pitch up motion will reduce speed and TDF, resulting inevitably in a corrective pitch down rotation.
Put simply, the TDF theory explains static stability as a function of elevator trim.
THE REBUTTAL
Neat, but untrue. The primary flaw of the theory rests on the inaccurate visualization that airplanes in flight pivot around the wing, and that “nose-heaviness” therefore results from placement of weight in front of that fulcrum. In truth, airplanes pivot around the CG: the CG is therefore the fulcrum, not the wing. When the CG is ahead of the center of lift, it is the upward lift of the wing trying to rotate the plane around the CG that makes the airplane want to pitch forward.
OK, as at least one pilot has pointed out, there appears to be no substantive difference: regardless which explanation you accept, airplanes want to pitch forward when the CG is forward of the center of lift. But now one must take another step: imagine that you raise the tail, start a dive, and begin to increase speed. Static stability determines that the nose will want to rise, and the TDF theory explains this reaction by saying that added speed increases TDF, which pushes down on the tail and raises the nose.
But, consider: added speed also increases wing lift, and lift is the force creating the pitch down moment in the first place (go back two paragraphs if this is unclear). More speed therefore adds more pitch down moment, and no matter how much TDF is added, its rotational effect is offset by the counter-rotation created by the wings. Thus, the tail and the wings cancel each other, there is no contribution to stability, and we need another theory (see last month’s column).
TAIL UP FORCE
The TDF theory also tells us that the CG must never be located behind the center of lift. This, says the theory, would make the plane “tail-heavy,” requiring tail up force for balance and making the system statically unstable.
Again, the flaw is in the visualization. When the CG is behind the center of lift, a “tail heavy” condition exists not because weight is aft, but because wing lift is ahead of the CG creating a pitch up moment.
This is no more unstable than having the CG forward: when you raise the nose and start to lose speed, loss of tail authority and loss of wing lift cancel each other, with the result that there is no contribution to instability. Again, we need another explanation.
In conclusion, an analysis of basic airplane design (except flying wings) reveals that as the CG is moved aft within its standard envelope, the force required to balance the plane inevitably shifts from tail down to tail up. This shift occurs well before the plane becomes unstable.
Why is all this important? First, because it’s accurate. Second, and most important, the inaccurate TDF theory never credits the CG for being the true center of rotation—a concept of great importance in understanding turns, stalls and unusual attitude recoveries.
