Robert Deters wrote: > Andy Ross wrote: > > Robert Deters wrote: > > > Actually the F-4 is unstable, but only marginally. > > > Not in pitch, certainly? > > Yes in pitch. Besides, I think you are confusing static stability > and dynamic stability.
Er, normally one interprets an unqualified use of "stable" as referring to static stability. The rest of the conversation has been about stability augmentation systems (which have to do only with static stability -- phugoid damping can be done with an autopilot). I even went out of my way (two paragraphs worth!) to point out that I wasn't talking about the phugoid when we got into this. Apologies if I didn't get that across; and apologies for trying to explain to you stuff that you already knew. :) For those who are wondering what the difference is: static stability refers to weathervane behavior. If you point the aircraft "forward" (for whatever definition of forward you are using) in an airstream and then perturb it a little bit, does the aircraft feel a torque that tries to return it to the forward direction? Dynamic stability is a different beast. I described the phugoid earlier --- this is the "pitch up, slow down, pitch down, speed up, rinse, repeat" process. It turns out that, because of an interaction (a "coupling" in the strict sense) between the period of this oscillation and the regular "weathervane" static oscillation, some aircraft are unstable in the phugoid. Each time they pitch up, the pitch up a bit farther, and then lose more energy and pitch down farther, and the process diverges over a period of minutes. One way to imagine it is that the aircraft always "lags" the gravity effect. It has to wait a bit at the top of the curve to "point" downward again, so it loses a bit more energy than it should and slows down farther than it "should". When it gets back to the bottom of the curve, it's going faster, *and* it takes a bit longer to pitch back up to the right value. As you decrease the rate at which it changes its pitch to match its velocity (i.e. as you decrease the static stability) you eventually reach a point where the phugoid oscillation is no longer damped, or is actually augmented. So, the aircraft always tries to point toward its velocity vector, so it meets the criteria for being statically stable. But if you leave it alone, it's velocity doesn't approach any single asymptotic value. So it's not stable, either. This kind of effect is called "dynamic" instability. In principle, there are other kinds of dynamic instabilities. In practice, this is the only one people mean when they say an aircraft is dynamically unstable. As Rob points out, it's usually treated in textbooks as a set of differential equations in variables like: height, Vx, Vy and pitch angle. That is: "the time derivative of Vy is gravity plus thrust times the sin of pitch angle", etc... It turns out that after a series of variable substitutions that make my eyes cross*, you can characterize the solution as a polynomial. The difference between a convergent and divergent solution turns out to be equivalent to the existence of real or complex roots to the polynomial. But the effect is qualitatively understandable without the math. Andy -- Andrew J. Ross NextBus Information Systems Senior Software Engineer Emeryville, CA [EMAIL PROTECTED] http://www.nextbus.com "Men go crazy in conflagrations. They only get better one by one." - Sting (misquoted) _______________________________________________ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
