- The position of CG in the XY plane is important. It should be centered ideally, so the controller have a full and balanced control over the attitude
- The position of CG along the Z axis does NOT affect much. Its position, together with the midpoint of the Propeller (say point M) will confine the position of the actual rotational center.
- The stability, which is our main concern, is mainly determined by the mass distribution of the whole UAV. if more mass is below, the UAV tend to level itself (when the UAV is not accelerating greatly).
- However the stability is NOT a feature actually needed. Ideally the UAV should have natural stability, and hand over all the stabilizing task to PID control, as physical stabilizing and PID stabilizing is not compatible to each other, and may cause unpredictable oscillation (heard from somewhere).
- Pixhawk should be placed somewhere between the plane of propellers and CG plane. This is where the centre of rotation lies
I hate to spoil the party but there's no such thing as a stabilizing pendulum effect when talking quads (helicopters, rockets, even planes).
One intuitively assumes that a quad is essentially a lifting device (props) and a load (the body). Like a balloon and a box attached to it. This is however a false analogy - a balloon always "thrusts" up, against gravity, even if the ballon-box system is angled sideways. Balloon acts upwards, which stabilizes the system like a pendulum. A quad, however, doesn't thrust up - it thrusts in the direction its props are aimed. If it's pitched 45�, then so is the thrust vector, and the whole system starts going forward, pitching down even more (because the props and motors aren't massless, they weigh it down).
Full scale pilots will agree that a high-wing plane has absolutely no more natural stability than a low wing plane - it's the same thing. Lift acts in the direction the wings are aimed, which is not always up into the sky.
There's a more accurate and technical explanation in the pendulum rocket fallacy article on Wiki - why do rockets have engines on the bottom instead of the top.
In multicopters this goes even deeper - you have a very precise and fast active stabilization system, so naturally you want to take full advantage of it. Introducing any external torque generating mechanisms ("natural stabilization" by offsetting the CG) will interfere with the active stabilization system and reduce the performance. That's why flat quads are preferred - the CG lying in the plane of thrust yields superior results.
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I-ve flown with battery and camera below the frame (low CG) and battery on top of the frame with camera below the frame (CG still slightly below the propellor plane, but much higher than with the lower battery postion). Of course the high battery position does also move the FC up, so that actually ends up slightly above the prop plane. You do notice a bit more sluggishness in roll and tilt responses with the lower battery position. Stability wise it doesn't seem to make to much difference otherwise.
One factor which may be more important is in fact the height of the craft. There is a university paper which has looked at this. With high landing gear and an underslung motor mount the destabilizing effects of e.g. wind increase. In addition a high, wide, landing gear puts the "skids" in the propwash which may also result in some turbulence effects around them and may transfer back as "vibration" into the FC's sensors if not isolated from vibration.
Personally I prefer the battery above the frame as it does seem to result in a slightly more responsive kopter and allows a bit more foam between camera mount plate and frame without requiring even higher landing gear. In addition the higher "cockpit" position may well compensate a bit for the underslung camera mount and high LG below the frame and thus for the destabilizing effects of wind on the vertical axis.
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Rockets with CG ahead of CP are dynamically stable. Hot air balloons are more stable with CG below CP. Of course, if you were to shoot a balloon with a gondola out of a (large) cannon, it would assume the dynamically stable configuration of gondola first (same as rocket dynamics).
Unless you are shooting quadcopters out of cannons, I think their low-speed flight dynamics resembles hot air balloons (and mars rovers) more than it does a rocket.
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Who ever said pendulums were stable? If your definition of "stable" is a mechanical system which resists external forces in maintaining a desired attitude or position in space, then the only thing "stable" about a suspended object is that gravity will tend to keep the string taught. Past that, if the end of your metaphorical pendulum is of low mass, say a toy balloon with regular air, then the slightest breeze will send it out to the limits of the mechanical tension of the string. Even moving your hand around to try to keep the balloon in one place will not accomplish much "control" in turbulent air. A weight suspended by a string appears to be stable only because it has a much higher density than the air surrounding it.
By definition, one end of a pendulum has a fixed point in space (like your hand in the above example) for which there is no aeronautical analogy. Everything about an aircraft's attitude is related to leverage about the virtual (practical) center of mass. This is complicated by the distribution of mass too, as control forces contend with inertial moments. In a very real sense, all aircraft are literally floating in a fluid of air and subject to any disturbances.
The Paul Pounds paper referenced at the beginning of this discussion has an excellent treatise on this very subject, precisely applicable to the topic. Why not avail yourself?
Conventional single rotor helicopters have the fuselage underneath the rotor disk because they would be very impractical to operate the other way around. As such, they're not very stable beasts at all; there is no "trim for straight and level" flight as you find with properly designed fixed wing craft.
(this is directed generally at Monroe's detractors)
