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I don't quite understand what happens to the controllability of an airplane as the C.G. moves fore/aft.
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Is the airplane more or less controllable with an aft CG?
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Less. One of the problems with understanding is that the terms, stability, maneuverability, and controllability =sound= like English, but mean something different in aviation-speak.
haven't pulled out this personal FAQ in a long time, but FWIW, here goes.
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Stability, Maneuverability, Controlability
I just know I'm going to get in trouble with this one. I once got completely taken apart, chewed up and spit out for even suggesting some of the examples:
Start with definitions. Like any field that has it's own language ("terms of art"), there are common words that have very specific aviation meanings. In aviation terms,
stability: the tendency to return to a desired condition when disturbed
controllability: how easily the body responds to control inputs. (Not how easily it is to maintain control)
maneuverability: the ability of the body to withstand the stresses of being pushed around. (Not how easy it is to maneuver something around)
I mention these because these are not necessarily the way these words are used outside aviation. For example, something can be highly "controllable" in the aviation sense because it responds too easily to control movements. If it is also unstable, though, it will be very, very difficult to "control" in the lay sense.
I sometimes use a skiing analogy. Let's stick to the flat blue runs. There is an ideal part of the ski for your weight to be centered. Essentially, it's the CG that gives you the best balance between the ability to turn (controllability) and yet prevents you from losing control completely as the skis fly off on their own (stability).
Sit too far back on your skis and the skis become very "controllable" in the aviation sense. The smallest movement of your foot will make the ski fly of in another direction. Unfortunately, the ski's aft CG also makes it very, very unstable. Not only does the slightest foot movement send the ski in a new direction, but the instability magnifies the movement.
Move your weight forward, and the ski becomes very stable. Put it on track and it will tend to stay there. But have your weight too far forward, and it suddenly becomes more difficult to turn.
Not a very aerodynamic explanation and unlike an airplane, skiers can constantly shift their CG to handle changing conditions. But a useful analogy for some.
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Can you apply this to your questions?