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.)

• As a side note, it is likely that this model has electronic yaw gyro. It wouldn't be able to keep heading that well without it. Yaw is the only axis that the bar can't help with. Next time, when hovering, try to twist the body to change the heading, and you'll feel (and hear!) resistance.
– Zeus
Commented Jun 13, 2019 at 5:10
• @Zeus Well, it doesn't keep heading that well; you have to manually set a yaw trim wheel, and even after you do, the heading drifts more or less quickly. Next time I fly it, I'll try yawing it by grabbing it with my hand, and I'll see what happens. Commented Jun 13, 2019 at 5:17
• As at least one answer points out, it's gyro stabilized by the balance bar. Acting as a gyroscope, the bar probably precesses slowly, which would manifest in the rotor thrust vector doing the same, which would result in it flying slow circles. Commented Jan 31, 2020 at 3:44
• Re last paragraph-- what about the simple toy which is a propeller fixed to a dowel rod? Rub your palms together and it flies in the air-- no tendency tip over-- what is going on there? Commented May 4, 2021 at 14:30

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.

• That makes sense, but what I'm confused about is the "residual tendency to seek level". Gyroscopes don't spontaneously level themselves, so what causes this gyroscope to level? Commented May 31, 2019 at 1:32
• Residual tendency is actually a bad phrase to use. What is happening is from the fact that the when you let go, the body of the machine, being a pendulum, wants to go straight down, taking the mast with it, and this imparts a tendency of the gyro stabilizer bar to follow the mast back to vertical. The pendulous mast itself is acting a bit like the self-erecting function of a gyro instrument. Commented May 31, 2019 at 1:47
• Ah, like in the pendulum fallacy? Commented May 31, 2019 at 2:05
• "the body of the machine, being a pendulum, wants to go straight down" - But the rotors want to go straight down, too. Gravity never causes an object to rotate (ignoring tidal forces, which are insignificant here). A roly-poly toy is kept upright by the supporting force from the floor, and an airship is kept upright by buoyancy. There must be some aerodynamic force which rights the helicopter—right? Commented May 31, 2019 at 2:42
• "The body wants to swing under it unless it is accelerating laterally." That seems like a bit of a vacuous statement, since if the helicopter's attitude is disturbed, that will cause it to accelerate laterally. That seems a lot like saying, "If an airplane banks, then the occupants will feel like they're being pulled towards the lowered wing, unless the airplane turns while it's banked." That's not a false statement... but airplanes do turn while they're banked, so the statement isn't saying very much. Commented May 31, 2019 at 16:01

The top rotor is a hinge offset rotor with a very serious stabiliser bar. These rotors exert torque via the mechanism in item 1 in this answer, and the body will align itself with the top rotor. But the other way around as well: the rotor aligns itself with the shaft, it just depends on what it controlled, the rotor angle (like in a regular helicopter through cyclic pitch) or the body angle.

So top rotor and shaft will return to be perpendicular to each other after a disturbance or a control input. Torques exerted by the body are instantaneous, torques exerted by the top rotor have a time delay due to the inertia in the stabiliser bar.

The helicopter is flown by body tilt.

• Pitch direction: body tilts, upper rotor follows, in a controlled way, resulting in longitudinal movement.
• Roll direction: no control input possible. Once there is lateral movement, the helicopter can right itself if the aerodynamic drag on the rotor assembly is larger than drag on the body - if the other way around, the helicopter will speed up and tilt itself more and more until it crashes.

Notice that the pendulum fallacy does not apply to helicopters: they can align rotor thrust away from the CoG, like a hang glider does when canting the wing, and create a rolling or pitching moment that way.

On the flight in a circle without changing yaw (with the helicopter flying backwards halfway in the circle): thanks to @ZeissIkon in a comment:

The "flies in circles without changing heading after being disturbed" behavior is most likely due to precession of the balance bar. Disturb the fuselage/rotor shaft, some of that disturbance propagates into the balance bar; once the body has righted, the balance bar continues in a very slightly tilted plane, and the slight righting force from the shaft causes it to precess. – Zeiss Ikon

• Hmmmm, interesting. I don't think the top rotor teeters, though. The rotor blades are attached to the shaft by a joint which allows the blades to advance and retreat, but not to move up and down. (There is some play in the joint allowing the blades to move up and down, but if one blade moves up, that doesn't cause the other blade to move down.) The stabilizer bar does teeter, of course. If I grab the helicopter while it's flying, and tilt it, the rotors move instantly (as if the rotor disc were rigidly attached), but the stabilizer bar lags behind by a second. Commented May 31, 2019 at 3:27
• Ah so the stabiliser bar is not connected to the upper rotor? And the upper rotor blades can flap and lead/lag? Does deflecting the stabiliser change the blade pitch of the upper rotor? Commented May 31, 2019 at 3:46
• Well, the stabilizer bar is connected to the upper rotor through a linkage. Deflecting the stabilizer does change the blade pitch of the upper rotor (that's what the linkage does). When one end of the stabilizer bar goes up, the rotor blade next to it (45 degrees behind it) is tilted into a coarser pitch (so it produces more lift); meanwhile, the other end of the stabilizer bar goes down, and the rotor blade next to it (again 45 degrees behind) is tilted into a finer pitch. Commented May 31, 2019 at 4:25
• OK so it is a hinge offset rotor then. They can apply torque on the mast. Commented Jun 1, 2019 at 4:45
• centre of lift will align itself above the centre of gravity if left undisturbed This is what is confusing me about this answer. Once you hold it tilted for a few seconds the center of lift is aligned with CoG, just not vertically. I'm trying to understand how it aligns itself vertically. All my attempts at reasoning fall afoul of the pendulum fallacy. I can't seem to identify the source of any rolling moment. Commented Jun 13, 2019 at 18:06