How does this RC helicopter keep itself upright? I have this (cheap, beginner-level) RC helicopter:



It has 3 controls: one for climbing and descending (collective throttle), one for yawing (differential throttle), and one for pitching (the tail rotor control). There's no roll control.

This helicopter seems to have a very strong tendency to stay upright. Even if you grab it by the skids in mid-air and tilt it slightly, it will right itself (after first flying in whichever direction you tilted it in).

As shown in the picture, the helicopter has two coaxial main rotors and one tail rotor. The tail rotor is pointed vertically, so that it produces a pitching moment. The lower main rotor is fixed-pitch, but the upper rotor has cyclic pitch controlled by a weighted "balance bar". The balance bar itself is mounted about 45° ahead of the rotor. The balance bar is on a hinge so that the ends can move up and down relative to the shaft. If one end of the balance bar goes up, then the blade closer to it is automatically set to a coarser pitch; meanwhile, as the other end goes down, the blade closer to that end is set to a finer pitch.

It seems very unlikely that this helicopter has any electronic accelerometers or gyroscopes.

So, how does this helicopter keep itself upright? Here's what I can figure out myself:


Suppose that the fuselage accidentally rolls to the right while the balance bar remains upright. Then the rotor's cyclic pitch will be set so that each blade is coarsest when it's in the forward right position, and finest when it's in the rear left position. This will produce a left rolling moment, which will tend to bring the helicopter upright again. (It will also produce an up pitching moment... or maybe a down pitching moment, thanks to phase lag? Or no pitching moment at all? I don't know.)
Suppose that the fuselage and the balance bar both accidentally roll to the right. This will cause the helicopter to fly to the right... which will somehow cause it to right itself? But I don't understand the details of why this will happen.


By the way, I've noticed that the helicopter has a tendency to fly in clockwise circles, especially after being disturbed. (It doesn't yaw during this circular motion; it simply moves in a circle while maintaining a constant heading.) I bet that this tendency is caused by the balance bar somehow, but I don't know how.

(Someone may be tempted to answer, "It rights itself because the rotors are above the center of gravity." That explanation doesn't work, though, because the only way an aircraft can right itself is by means of torque. The rotors will generate this torque somehow, but they won't generate it by virtue of being located above the center of gravity.)
The rotor is gyro stabilized. The balance bar is the gyro. If the machine rolls right, the balance bar wants to stay in a level plane and generates a correction by influencing the rotor blades to go where the balance bar wants to be.

The Bell 2 blade teetering rotor system used on the '47 and the Huey used a much smaller version of the same thing, to provide a little bit of inherent stability to the rotor disc, without inhibiting pilot control.