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I was on a flight with a regional airline a while ago in a Bombardier airplane (if I recall correctly) where the airplane would slowly and gently rock its wings just a little bit on the whole flight. I wasn't a long flight but wasn't very short either at roughly 2 hours.

It was very comfortable and the rocking made for a very gentle cradle feeling 🙂

My question is, why would that be? Is it economical to do so for any reason? Is it possible that the airplane had no autopilot and the pilot was flying it by hand? What could cause such a behaviour?

I can give you two theories. One is it's a very very mild case of "overcontrolling" of the autopilot roll servo as it chases a perfectly wings level condition and continuously applies a teeny bit too much left, ooops, then a teeny bit too much right, oops, and back and forth.

The aileron control circuit is cables running to hydraulics at the ailerons, with a spring loaded roller in a curvy V shaped cam device that centers each side of the aileron cable circuit. The breakout force to move the control circuit out of neutral (forcing the roller from the center V of the cam) is fairly high and this can actually be a problem for pilots hand flying at higher speeds where the ailerons are quite snappy - applying enough force to break out the circuit and move the wheel left gives too much, and back the other way... too much... and back and forth you go. It can be a pain.

The autopilot servo is basically a little electric winch connected into the aileron cable circuit, doing the same thing the pilot does. It could be that something in the electronic control loop, or mechanically within the servo, can cause this back and forth oscillation on some airplanes, sometimes. It may be related to wear and backlash within the autopilot servo.

The other theory is it's more or less something similar, but in the yaw mode with the yaw damper not able to fully dampen out a dutch roll mode because the amplitude was within the yaw damper's sensitivity band. Dutch roll is rolling due to yaw, which in swept wing jets is very strong, such that it can set up continuous self energizing oscillation. It could also be related to wear and backlash in the yaw damper actuator, which is a pair of electric linear actuators (little electric screw jacks), in the push rods going to the rudder hydraulics.

If you saw the wing tip just going straight up and down, it's mostly likely the first theory. If you could see the winglet moving in a little circle (indicating rolling and yawing), it's more likely the second theory.

I can really only theorize because the issue was never fully explored on the RJ program as this phenomenon was random, very minor and not dangerous, and was never complained about by operators because only someone sitting near the wings that can look straight out at the winglet ever notices it. It was never bad enough to get anyone sick for example, at least on the RJ fleet.