# Does dynamic stability decrease with airspeed

Context: I am writing my thesis on the topic of satellite drag reduction by the means of near-specular surface scattering. The theme touches aerodynamics in some sense, but the physics are honestly quite unrelated.

I do however have a subsection where I discuss the matters of static and dynamic stability. Tldr: static stability can exist, but dynamic can not, or it would be absolutely vanishing.

I seem to recall from somewhere that dynamic stability also diminishes as airspeed increases in atmospheric aerodynamics, and had an off the cuff statement to that effect. I could not find a source later on, and removed the statement.

So: Is it true that dynamic stability diminishes as airspeed increases? The reason would be that the aerodynamic force vector becomes more and more aligned with airspeed vector, and the perpendicular damping forces shrink. Would there be a peer reviewed source for this?

(obviously, while I have worked in aerospace a while, I am not an aerodynamicist.)

## 1 Answer

Is it true that dynamic stability diminishes as airspeed increases?

Yes, when the solid body eigenmodes are concerned.

In aerodynamics, dynamic stability is mainly achieved in two ways:

1. Secondary motions (eigenmodes, flutter) induce velocities and forces which can either propel (= unstable) or dampen (= stable) those secondary motions.
2. Drag helps to let those motions die down over time.

When flying fast, the induced speeds become smaller relative to the primary motion of the airplane, so the induced forces also become smaller. This is evident in flight at high altitude, when eigenmodes like the phygoid or the dutch roll become more intense.

Your expression of the alignment of the aerodynamic force vector with the airspeed vector and the shrinking of perpendicular forces says the same, only in other words.

What also reduces damping is airframe elasticity: With the higher dynamic pressure at high speed, the induced forces cause deformations which in turn reduce these secondary forces. Again, oscillations take longer to die down. Undamped oscillations become much more dangerous: Flutter will cause almost instantaneous structural failure at high speed when the same flutter mode at low speed might still be non-destructive, with limited amplitude.

Flutter is a topic of its own: Here, you need frequency neighbourhood between a structural eigenfrequency and the frequency of aerodynamic oscillations which is proportional to true airspeed. First, increasing speed will increase damping (think of a mass-spring system, with the spring increasing in stiffness as dynamic pressure is increased), but as the aerodynamic frequency grows with speed close to the structural frequency, both mutually increase and damping rapidly becomes negative.

Any decent book on flight dynamics should cover this topic - sorry for not giving a discrete page and citation!