Notes on stability derivatives

WORK IN PROGRESS***

Regarding the various numbers that can be seen on the derivatives pane, generally, the absolute magnitudes matter less than how they compare to each other, because they can scale strangely as the plane grows and different parts get used.

Mw is the primary static stability parameter: it tells you whether the center of lift is in the correct position. If this is wrong, the plane is going to want to do back-flips or front-flips.

Yβ and Nβ tell you if the plane is yaw-stable (it's side force due to sideslip and yawing tendency due to sideslip, respectively). These will almost always be the correct sign at the same time (unless you add a massive dorsal fin), and if correct basically make sure that the plane wants to fly straight rather than skate sideways.

Lβ tells you if the plane is stable in roll due to sideslip. Roll angle itself doesn't directly cause a roll instability, but roll angle does cause some sideslip (plane's lift and gravity end up in slightly different directions, and this induces a sideslip velocity), and that sideslip can cause the plane to roll like mad. A lot of people who build planes with these afterthought-like vertical tails end up running into issues with this not being large enough compared to the other values.

Zw and Xu are basically just the effects of lift and drag, respectively (Z is positive down) as you increase downwards vertical velocity (increasing angle of attack) the plane makes more lift. As you increase your forwards velocity, the plane makes more drag. If Zw is incorrect, you're plane is very badly designed. If Xu is incorrect, you have summoned the Kraken and should file a bug report.

Mq, Lp and Nr determine whether pure rotation in pitch, roll and yaw (respectively) will damp out. It really shouldn't be possible to get them into the wrong sign without something else being unstable, but I suppose it's possible for very strange configurations.

The δe derivatives all tell you the effect of how the elevators and canards perform. If that's wrong, then somehow you've gotten your controls backwards; you want Mδe as large as possible while Xδe is as small as possible, since that means the most control authority possible with the least additional drag. Zδe is assumed to be correct for a standard tailplane design, so for canard designs it will be wrong (I'll make a change in FAR v0.13 to remove the coloring due to that reason).

Zq and Xq aren't really all that important, but they can make minor changes to the way a plane behaves under very large amounts of pitching.

Generally, Zu and Xw can be disregarded if their magnitudes are much less than the other ones. They basically consider how much additional velocity affects lift and how much additional angle of attack affects velocity, respectively; they can be the "wrong" sign at some angles of attack and Mach numbers due to Mach effects or nonlinear body drag.