Center of gravity explanation?

[R_Lefebvre]

Having the camera below the frame is done out of necessity. Obviously having the camera above the frame would not work for the application. But placing everything else, including the batteries below the frame is done, I believe, because of a mis-education and lack of understanding of physics. Not the other way around. Some people think this is more stable because the weight "hangs" from the props. But this isn't true, because the props are rigidly attached to the mass. If the camera has to be below the props, then it makes sense to put the batteries above. This will get closer to a neutral CG.

There is one frame design which allows the camera to be directly in line with the props. The batteries also. This results in a low moment of inertia which benefits stability.

 

[Motopreserve]

Actually the CineTank and QAV500 seem to be designed to handle the camera and battery at least close to the plane of the props. And that is something I'm interested in, because while they are probably better for the CG from a profile view, if you look from above you now have the weight stretched out fore and aft. A whole new set of equations!!!

Now that I think of it - it's curious we've never seen a quad with platforms stretched out left and right, as well as fore and aft such as on the FPV style craft. Perhaps a tri-battery setup with a camera in front?

appreciate all your responses. I'm fascinated by this topic, but limited by my brain power!

 

[jes1111]

It's easy to overthink this subject. The academic papers that say that a slightly high CG is "more stable" are referring to the natural stability, i.e. how the craft would fly under 100% manual control. It's not really relevant to the FC in terms of the "stability" that is desirable to a camera ship. It's easier to understand the issues when thinking about a gimbal (3 DoF instead of 6). When the gimbal is perfectly balanced (the CG lies precisely at the origin of all three axes of rotation) the motors need to do the least amount of work and therefore can achieve the necessary corrections in the least amount of time. The same principle applies to the craft itself - if the craft is setup such that the CG lies precisely at the origin of all three axes of rotation then the motors need to do the minimum amount of work to restore the craft to level after a disturbance and will achieve that correction much quicker. If the CG is displaced along one axis (in this case the Z axis) then the motors need to work harder to correct an attitude error on that axis and hence will take longer to do so - the result is a craft that is apparently "less stable": it will visibly "rock" more because the corrections take longer.

This is also where the arm length comes into the picture: longer arms provide more "leverage" for the motor (the torque at the centre is dependent on the length of the lever) hence they are able to correct an attitude error quicker. So the bigger and heavier your camera/gimbal is (i.e. the further the CG is displaced down the Z axis) the longer arms you need to ensure adequate authority over that axis. In other words, if you could devise a frame that carried a Red Epic dead-centre in the frame instead of slung way down under the centre then you wouldn't need such long arms.

 

[Motopreserve]

The same principle applies to the craft itself - if the craft is setup such that the CG lies precisely at the origin of all three axes of rotation then the motors need to do the minimum amount of work to restore the craft to level after a disturbance and will achieve that correction much quicker.

This is exactly what I was talking about - except not nearly as eloquently

My initial concern with this was because it seemed that my quad was stacking up higher than many others I had seen. And without a gimbal underneath, it seemed I was building in the wrong direction. So reading these explanations calmed me about the fact that I was probably only putting 150 grams higher than looked "normal," and that in fact, more weight up might even be better.

Bottom line, It seems I had no need to worry about this fairly insignificant weight being higher. But also, since I'm using cheaper Turnigy motors, I have no reason to make them work unnecessarily, if I can achieve this with a little planning and forethought.

 

[Bartman]

jes,

rocking is a function of damping and the PID's being tuned to the weight/configuration of the heli being flown. what's so amazing about our heli's is that a lot of the design that would have been done in the past to establish stability through iterative testing and tweaking can now be done with software on a laptop so as to make many many different designs appear to fly similarly well.

there are a lot of different topics being mashed into this one thread but the original question had to do with cg and deviations along the z axis.

the "pendulum falacy" isn't such a falacy for fixed wing aircraft using both the position of the wing above the cabin and a certain amount of dihedral to make the plane dynamically stable in roll (once displaced from center its tendency is to return to center).

as for our helicopters, CG's below the plane of the props might make it harder to roll or pitch into a maneuver but will make it easier for the FC to right itself back to level. CG's above the plane of the props will help the FC to roll or pitch into a maneuver but will be working against the FC as it's trying to return to level. I'm not in a lab and I didn't stay at a Holiday Inn Express last night but what's amazing is that despite all of these theories, most FC's do just fine once a little tuning is applied to personalize the settings to the particular heli being flown. Personally I'd avoid a CG that is too far above or below the plane of the props as the motion of the FC can begin to get a little funky as it tries to roll or pitch to maintain stability about a CG that is too far above or below it's own plane. The heli will want to move about it's CG and to a FC sitting well above the CG, a roll may feel like roll and a lot of translation to one side or the other but does it really respond to a lateral acceleration along with the roll? how would it know what is really happening? Some heli gyro's used to have an offset that could be programmed so the heli could figure out how much translation was appropriate for a given roll or pitch event but I've never seen this in one of our flight controllers.

all very interesting to discuss. for a heli that is going to hang around almost still and do a lot of slow floaty types of things then a low CG might help it to resist small disturbances. If you want to rip around then a neutral or slightly high CG might help it come unstuck from level more quickly when initiating a maneuver. a lot of it is FC dependent though and the settings we have at our disposal let us do so much with whatever we happen to dream up.

 

[jes1111]

I didn't mean "rocking", as in oscillation. I meant one "rock" - away from level and back to level. This is our perceived judgement of "stability": how quickly the event passes and, hence, its magnitude for a given disturbance. Increasing the moments of inertia slows the responsiveness of the system. So a low CG may well slow the effect of the disturbance but that gain is negated by a slower subsequent correction. There is no mechanical advantage to hanging a large camera under the frame - it's there because there's nowhere else (practical) to put it, just like there's nowhere else to place the body of a single-rotor heli except under the rotor. We just have to live with the consequences. Returning to the original question - the ideal mechanical layout is coincidence of the CG and CT. Anything else slows the responsiveness. Whether the compromise is significant depends on the authority of the correction mechanism. That "authority" is the sum total of the remaining mechanical elements (arm length, motor power, frame rigidity, etc.) and the "electronic" elements (FC bandwidth, ESC bandwidth, tuning, etc.)

 

[Bartman]

yes, there are a lot of elements at play and in building a lot of different heli's, I've found that so long as you don't take any one element to any particular extreme, today's flight controls can handle the variations and fly very well.

 

[Benjamin Kenobi]

What a great topic!

 

[AirPix]

Indeed a lot of great information. And some of this CoG/balance/stability information may not be terribly intuitive, especially for an old Plank flyer.

I wonder how accurately a flight simulator models the behavior of a multirotor? For example, in AeroSim one can modify the model parameters to change the weight distribution and balance point and use the FPV or chase camera to evaluate how the aircraft reacts specific input actions. Or so it seems from my limited amount of fiddling with it.

--Bill

 

[Mav]

Hey guys I built my second multirotor yesterday after having what i think was a fly away with my 450 running naza lite. I upgraded to the M V2 and an F550. This is my first hex so I'm not sure if this is common flight characteristics of this craft but i expected it to be much more stable flight. The 550 rocks front to back on the pitch axis. Example, if i fly forward and let go of the sticks and let the flight controller stabilize, it rocks like a pendulum effect. The wind will also cause this. I do not get this on the roll axis. I am thinking it may be a gain issue on the pitch axis. But I installed the photoship one landing gear on it which has a long gimbal boom and you counterweight it with a rearward battery placement which is also on a boom, so I am thinking this could be causing the pendulum effect. The CG is dead on front to back, but it is obviously out of balance top to bottom because of the landing gear, gimbal, and battery being all on the bottom. So is this a CG problem or gain issue? Please help me get this thing to fly as good as it looks.

 

[gtranquilla]

You don't need to balance the MR's center of gravity at the center of the MR hub on the vertical, i.e., z access, only on the horizontal x/y axis. But, if I remember correctly, the FC still needs to know the vertical C of G position relative to the FC vertical position..... then also there is the vertical position of the GPS module that needs to be entered and many tend to load that value with the + versus - sign!...... it's in the documentation.

Hey guys I built my second multirotor yesterday after having what i think was a fly away with my 450 running naza lite. I upgraded to the M V2 and an F550. This is my first hex so I'm not sure if this is common flight characteristics of this craft but i expected it to be much more stable flight. The 550 rocks front to back on the pitch axis. Example, if i fly forward and let go of the sticks and let the flight controller stabilize, it rocks like a pendulum effect. The wind will also cause this. I do not get this on the roll axis. I am thinking it may be a gain issue on the pitch axis. But I installed the photoship one landing gear on it which has a long gimbal boom and you counterweight it with a rearward battery placement which is also on a boom, so I am thinking this could be causing the pendulum effect. The CG is dead on front to back, but it is obviously out of balance top to bottom because of the landing gear, gimbal, and battery being all on the bottom. So is this a CG problem or gain issue? Please help me get this thing to fly as good as it looks.

 

[Mav]

You don't need to balance the MR's center of gravity at the center of the MR hub on the vertical, i.e., z access, only on the horizontal x/y axis. But, if I remember correctly, the FC still needs to know the vertical C of G position relative to the FC vertical position..... then also there is the vertical position of the GPS module that needs to be entered and many tend to load that value with the + versus - sign!...... it's in the documentation.

I have accounted for the height of the gps in (-) but probably do not have the right amount in because i dont know where the CG for the z axis is or how to measure this.

 

[gtranquilla]

Suspend your MR from any side with your finger and see which way it tilts. Then set it down and tie a very strong cord to a position near where your finger was previously located. Adjust it back and forth until the MR hangs from one side of the hub in a completely vertical attitude. Mark that spot as the vertical center of gravity and go from there.

 

[Toymaker]

What I have found with CG's in general is you want a low center of gravity for stability. For Cars, boats, and trainer planes. This all makes them more stable. Sailboats and high wing airplanes are good examples. With airplanes as you move the CG up toward teh center oa axis, the plane becomes more agile. With multirotors it's a little different because you have an active controller. The CG needs to be as close to the center of all three axes so that the controller has as little opposing force (Gravity) to work against. If you were building a multirotor with no controller you'd need to have a low CG to make it naturally stable. This would make it hard to do any pitch or roll movement, and yaw would be no problem at all.
This comes to mind.....
View attachment 17537

 

[gtranquilla]

The original IMUs were developed by NASA with programming help from Dr. Kalman back in the mid sixties. It was first used to guide finless rockets then later to balance the LEM that landed on the moon and returned. In the case of the Saturn V, the center of gravity of the rocket is a great distance above the gimballed rocket motor thrusters. So as you already indicated, the IMU can stabilize an otherwise unstable mechanical design.... but only up to a certain point.

What I have found with CG's in general is you want a low center of gravity for stability. For Cars, boats, and trainer planes. This all makes them more stable. Sailboats and high wing airplanes are good examples. With airplanes as you move the CG up toward teh center oa axis, the plane becomes more agile. With multirotors it's a little different because you have an active controller. The CG needs to be as close to the center of all three axes so that the controller has as little opposing force (Gravity) to work against. If you were building a multirotor with no controller you'd need to have a low CG to make it naturally stable. This would make it hard to do any pitch or roll movement, and yaw would be no problem at all.
This comes to mind.....
View attachment 21629