Aircraft C of G and wing pitching moment

[Oktas8]

I could find nothing on longitudinal dihedral (or decalage).

My text is AC Kermode's Mechanics of Flight if you have access to it. Briefly (vaguely, non-technically), longitudinal dihedral is the tailplane AoA subtracted from the wing AoA. As you point out, the vast majority of aircraft have a tailplane at some minor negative AoA, so are said to have positive longitudinal dihedral.

Regarding tailplanes generating upwards force - yes, I know it's almost unheard of in cruising flight. But since someone brought up the possibility of very precise locating of CP close to the CG, I thought I'd bring it up.

Consider a wing at +6° AoA and a tailplane at +2° AoA (both generating upforce on this mythical aircraft).
A gust giving an effective increase of AoA of 2° will:

• add approximately 33% to wing lift (new AoA 8°), and
• add 100% to tailplane lift (new AoA 4°).

Regardless of the absolute size of each lift force, the pitch-down tailplane moment will overcome the pitch-up wing moment in this case, and the aircraft will pitch down, giving us a form of positive longitudinal stability.

This is an example of longitudinal dihedral. Canard equipped aircraft are good examples of this kind of arrangement - front "wing" is at greater angle of attack than main wing, giving longitudinal stability (and unfortunately, quite a lot of trim drag ).

The original post referred to the possibility of a tailplane generating zero lift, and whether this was possible. Yes, it is possible from the point of view of longitudinal stability, although you may need electronic stability controls to ensure stability is maintained as CG moves in flight, or at extreme angles of attack.

O8

[spleener]

Hawk 37,
sorry my quote ref Airbus 330/340 should not have been so simplistic but I didn't wish to stray too far from the main thread.
Suffice to say that in the most basic FBW Direct Law [stick position= control surface position] the aircraft is stable [download on tailplane]and flyable. This Direct Law is overlaid by artificial means both in Alternate Law and [the usual case] Normal Law. In these cases [in pitch] stick position is usually a G command with Normal Law providing enhanced response and flight envelope protection. This provides enhanced stability to certification requirements. Therefore, CG can be controlled further aft [fuel trim tank transfer] with ensuing lower drag.
This is a short explanation only! please accept that there is more to this...
spleener

[hawk37]

Octas, thanks for your explanation on "longitudinal dihedral". I never had heard of it, but your explanation makes sense. I can only surmise there must be further stability problems with this method, since it has clear advantages over the conventional tail down force type of stability.
I'd summarize by saying the posters seem to be of the opinion that conventional airliners (all airbus and boeing) have a tail down force throughout their operating envelope, ie the CG must be forward of the CP, at all times. I'd add that when we hear of aft CG up to about 35% mac, this can only mean the CP can never get as far forward as 35%.
Of further note, this can only mean that these airfoils are NOT symmetrical, since if they were, the CP would be at the 25% mac, reqardless of Cl, and thus limit the CG range to 25% aft of the leading edge.
Make sense?
Hawk

[PleinGazSec]

Positive longitudinal static stability required for certification in direct law. The authorities won't yet allow fully unstable pax aircraft understandably in case of failure and flight control law reversion. However relaxing the stability requirements is OK within limits.