The horizontal stabilizer usually generates downforce in conventional aircraft, to balance the moment caused by the CG being ahead of the wing's center of lift. Moving the CG aft reduces that nose-down moment, thus the horizontal stab doesn't have to work as hard, and it will generate less induced drag.
But since the horizontal generates downforce or negative lift, the wing has to lift the weight of the aircraft and cancel that negative lift. Thus the aft CG will mean less induced drag from the wing and the horizontal stab.
Application can be seen in the 747, MD11, and A330/340. They all have a tank in the vertical stab to which fuel can be transferred, providing not only extra capacity but helpfully moving the CG aft during cruise.
The previous response was good, but I'd like to add a little. As the CG moves aft the aircraft generally goes faster, but it becomes less stable (the phugoid damping decreases). The fly-by-wire systems on the newer aircraft automatically stabilize the aircraft and allow it to maintain good flying qualities with the more efficient aft CG.
The fly-by-wire fighters (e.g. F-16, F-117) fly with the CG so far aft that the aircraft would simply not be controlable without the computers.
"Phugoid" damping refers to the pitch oscillations which slowly decrease in amplitude over time. When an aircraft is designed, two main types of stability are considered. First, static stability. This is the tendency for the aircraft to initially return to it's original attitide after being disturbed. For example, if turbulence pitches the nose up after being trimmed for staight and level, it is desirable for the nose to initially pitch down in an attempt to return to straight and level. This is called positive static stability. Is the nose stays where it is, it exhibits neutral static stability. If it keeps rising after the upset, then negative static stability exists (not very desirable in conventional aircraft).
Once positive static stability is attained, half the battle is won. Now we have to make sure that the aircraft returns to straight and level. As you know, we need postitive static stability to even consider the next type, which is dynamic stability. In our example situation, after the nose initially pitches down, it will overshoot the level flight attitude and pitch below until the airspeed increases enough to increase the tail-down force to bring the nose back up again. The nose will then overshoot straight and level again but the nose will not rise to the original position after the disturbance. This cycle repeats over and over with smaller and smaller overshoots until they are barely noticable and the aircraft is back in the original position. This is called positive dynamic stability. Neutral dynamic stability is when the nose rises and falls the same amount with each oscillation. Negative dynamic stability is when the nose rises and falls a greater amount with each oscillation (once again, not very desirable).
If our aircraft which is dynamically stable were to turn some smoke on, the path it traces would resemble a sine wave with decreasing amplitude but roughly constant frequency. The frequency would depend on the design of the aircraft (I.e. size of the horizontal stabilizer) and the loading of the aircraft (CG location), which brings us back to the original discussion. I'm sure everybody knows most of this stuff, so sorry to ramble. Hope this helps.
To answer the 'what is phugoid damping' question...
The phugoid 'mode' was described in the previous post. Phugoid damping is a measure of how much the amplitude decays from peak to peak. As the CG move aft the damping decreases so the aircraft will need more occillations to return to straight and level flight. The phugoid mode has a period (time from peak to peak) of about a minute, so it is actually possible to fly and airplane with an unstable phugoid (negative damping). The aircraft will require a fair amount of pilot effort to fly with an unstable phugoid, but the benifit is a very responsive airplane that just goes where you point it. Most competition aerobatic aircraft are flown this way as well as some of the pre-fly-by-wire jets like the F-4.
F16...true fly by wire. Aircraft would be unstable without computer interface. Same for Stealth F117.
F15...fly by wire system augments hydraulic system (CAS). Part of TR-1 flight for new Eagle guys is diabling CAS so they can see jet is quite comforable to fly. CAS acts as "power steering" and masks effects of stores...but otherwise not required for flight. It does, of course, improve roll and pitch authority.
F4...never drove it, but I think the Phantom guys will tell you it has NARY A BIT of Fly by wire. It is all hydromechanical.
Great post guys, Im really learning a lot. Aerodynamics is always been hard for me to understand because its kind of hard to me to picture what is going on. Your doing a great job putting this stuff into laymens terns.
How about explaing the reason some a/c pitch up when flaps are applied and explain the different kinds of drag.