How does an aircraft designer increase dynamic stability?

Question

This question explains that an aircraft can be statically stable (it will seek to return to equilibrium) but dynamically unstable (the amplitude of the oscillations increase) if there isn't enough damping in the stability equation.

That's fine from a mathematical point of view, but what practical change would increase the damping and dynamic stability?

I've seen quite a few radio-control trainers that are dynamically unstable, and would love to know how to fix the problem so that they're easier for the student pilot to fly.

These planes typically pull out of a dive on their own, but then climb excessively and stall, leading to another dive. Each subsequent stall and dive is more dramatic than the last.

Answer 1

Damping is produced by drag and by large induced speeds at the tail surfaces from a given disturbance. This can be caused by long lever arms of these surfaces or by high air density.

More on the topic can be found here:

• What is aerodynamic damping?
• Will control surfaces on a plane be less efficient at a higher altitude?. The lower density at high altitude reduces the vertical or sideways speed component caused by a rotation relative to flight speed, thus reducing dynamic stability.
• Another trick is to use a conventional tail instead of a V-tail, as discussed here.
• What also helps is to shift the eigenfrequencies of the plane away from the response delay of the pilot in order to avoid PIOs. An unusual example would be the Wright Flyer.

These planes typically pull out of a dive on their own, but then climb excessively and stall …

This is the classic long period mode in longitudinal stability. Since rotation rates are low, pitch damping also is low and the most important damping contribution is from drag. A low L/D reduces the tendency to overshoot, a high trim speed reduces the tendency to stall (and shifts the motion to higher speeds with lower L/D). Reducing static stability will make the period longer such that it becomes easier for the pilot to react. However, lower stability will make the pitch response more sensitive which increases the risk of too large control inputs.

Answer 2

These planes typically pull out of a dive on their own, but then climb excessively and stall, leading to another dive.

R/C flying can be started at an early age and gives any potential pilot a huge head start in gaining experience in the all important fundamentals of flight.

A lesson in the importance of keeping CG within the specified range (and the consequences of not) is better learned at model, rather than full scale.

Not paying attention to aft CG limits (weight too far back) will reduce directional stability in pitch and yaw. It will roll 360 beautifully, but only because the tail will constantly try to drop throughout the roll, always raising the nose. In general the aircraft will be more maneuverable, but harder to control. (This is why modern military aircraft use computers to assist stability).

Among the plethora of bad things (such as stalling low and slow) that can happen, dynamic instability is another consequence of out of range CG. Especially with models, a fraction of an inch can matter.

But if you build from scratch, it is important to properly match the tail and wing. Amazingly, a horizontal "stabilizer" destabilizes pitch when a plane rises or sinks vertically. This is a very important aspect of static stability.

Rising or sinking vertically is a function of lift. Therefor, excessive lift can cause a plane to "overshoot" its correction to original flight path. An extreme example of this is a loop.

So we generally design the wing Center of Pressure to be aft of the Center of Gravity so the torque of the wing lift around the center of gravity helps control the pitching tendency when lift is increased.

The further back the center of gravity, the greater the pitching tendency will be.

For custom scratch builders, a larger tail or longer tail moment is an option, but remember, if the tail supports weight, you are essentially building a bi-plane.