**A bit of background (skip if already familiar) ...**
A bit of background (skip if already familiar) ...

Just for the sake of some lurkers or newbies getting a bit behind the aerodynamics flung around in this thread:

There is static stability and dynamic stability. A nice mental image of a statically stable situation is a ball sitting in a bowl like the picture below.

If you give the ball a bit of a nudge to either side, it will respond by returning to its original position. Now, if you were to turn the bowl upside down you'd have yourself an unstable situation:

Here, the ball is precariously balanced ontop of the bowl and any slight nudge will make it roll into the setting sun, i.e., it won't return to its original position by itself.

Returning to the original example of static stability, you'll agree with me that after the nudge the ball will roll around a bit inside the bowl until it gradually comes to rest at its original position. This is what in aerodynamic-speak is so eloquently termed a "phugoid oscillation". The picture of the ball in bowl is an example of static stability (because the ball wants to return to its original position after the nudge) as well as dynamic stability (because the rolling around in the bowl after the nudge dies down after a while and the ball comes to rest at its original position).

In the next picture I have tried to separate static and dynamic stability by adding my hand to it, which jiggles the bowl back and forth.

I had to add my hand to the picture because I wanted to create a situation that has the potential to be statically stable but dynamically unstable. Just imagine that I jiggle the bowl too much and the ball eventually jumps out of it and rolls toward the setting sun. Even though the ball always wanted to roll toward the bottom if left to its own devices, the jiggling motion makes it roll around more and more until it eventually jumps out of the bowl: statically stable, yet dynamically unstable ("divergent phugoid oscillations" is the proper term to drop at your next cocktail party).

The problem -- or shall we say "challenge" -- we face with our gyros is that the shape of the bowl is determined by a lot of parameters and even changes under different flight characteristics. You might have a deep narrow bowl (high static stability) when flying slowly with little engine power. Going really fast, however, your bowl might look more like a flat skillet. In the former, your well trained aeronautical engineer will be speaking of a "high static stability margin", whereas the skillet presents a situation of almost "neutral static stability".

So how are we to determine the shape of our flying stability bowl? One way is by looking at how vehemently the gyro wants to return to its originally trimmed attitude. This is like assessing the shape of the bowl by looking at the force with which the ball wants to roll down its sides: steep bowl -- strong returning force, shallow bowl -- weak returning force. Assessing this restoring force in actual flying conditions is not an easy task for a number of reasons I don't want to go into. But there is an easier way...

You can look at the dynamic stability to learn somthing about static stability. In other words, you can look at how much the ball rolls around in the bowl to learn how deep the bowl is. This is what Greg is suggesting. The good news is that if the ball rolls around at all, you can be sure that you're still holding the bowl right side up as can be seen in the picture below.

Here, it becomes clear that with negative static stability (inverted bowl) you can't get the ball to roll around at all. The precondition, therefore, to observe "phugoid oscillations" (i.e., the ball rolling around) in your gyro is to have positive static pitch stability.

I hope that helps, -- Chris.