# Pendulum rocket fallacy and the Quadcopter

Well, I don't know if this will be understood very well because it appears to be correct but my experience with rocket's tells me otherwise. I have not gotten around to doing this myself but working with rocket stabilization all the time keeps me from building a quad like this.

But! Because the quads can be built this way very easily I'd like to explain WHY I think you guy's build your quads UPSIDE DOWN! :)

The CG is supposed to be over the CP! In other words if you put all the weight ON TOP of the rotors these craft SHOULD BE MORE STABLE!

I've had a hard time proving to even some so called rocket scientist (Like the ARCA GLXP Team) you cant put the CG below the CP and get stable flight without a lot of control input. It's just harder!

Imagine a seal balancing a ball on it's noze. The amount of correction needed is very small. Now with a ball hanging from a string the amount of correction needed is much greater to balance the ball on a point.

I think the reason we still put the CG below the CP is because it looks right and helicopters pretty much have to work that way but quads DON'T!

So how about trying my theory out? :)

If you notice the Curiosity Mars Rover for example the rocket engines are BELOW the CG like they should be.

Quad rotors will be more stable with the CG on TOP!

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### Replies to This Discussion

I think that with quads the CP of the entire airframe relative to the CG is not that important, again, taking what I know from ducted fans and applying:

Most quads operate at a very low airspeed (compared to planes), and have minimal drag/lift features (i.e. do not have wings) as such the CP does not play a huge part in the design, if you were looking to make a quad for high speed flight (and as such adding a wing) then it would be good to align the CP and CG such that there is minimal moment to fight.

If you were going to add a wing to a ducted fan VTOL aircraft it would be best placed above the duct so that the combined of the "CP" from momentum drag and the CP of the wing is aligned with the center of gravity, this location will never be perfect throughout the whole flight envelope due to the change in location of momentum drag throughout the flight envelope (as stated above) and the V^2 nature of the wing's lift. Having a wing does mean that you will be able to position the CG higher than a pure ducted fan VTOL uav and as such not compromise the low speed handling as much. Hmmm, I should really grab a piece of paper as it is easier to explain with drawings... If I have some time this evening I might try.

I think that you need to go further than the no pendulum stability statement and say that quadrotors in fact have no natural stability, expanding upon that statement, the stability is mainly driven by the speed of your control system, a quad with low rotational inertia will be less naturally "stable" (faster time to double) but will respond faster to corrections from the control system, the inverse applies for a quad with high rotational inertia.

@DuctAR,  I think that I understand what you are saying. Let's see! :-)  Taking the ducted fan subject out of the discussion for a moment...  >  Case (1), if the intent is to have a small quadcopter (for example, less than 2 feet between rotor-centers) whose primary mission is to slowly reach an aerial position, hover with minimal tilting and human intervention, and slowly return home, then it would be better to move all components with significant mass (for example: the four motors, the battery(ies), a camera) as close as possible to the CG, and let the on-board control system do as well as it can to maintain a level hover (for example, in response to a gust of wind). Case (2), if the intent is to have the same small quadcopter also move very fast up and/or around obstacles, then it is not yet clear what level of flight performance improvement can be achieved by making the CP "below" the CG (and how far below).

In either Case, the faster the responses from the quadcopter's control system, the better the overall flight characteristics. And higher rotational inertia would have some impact on how a specific control system is able to perform (would need to do some testing to measure the impact). Thinking of the QR Ladybird, it does not appear to have much rotational inertia (relative to other quadcopters)!

So, has anyone come up with some solid data to prove, or not, that Monroe's rocket experience is applicable to multirotors?

Or shall we just declare open season on engineers ?

I had a friend killed in a gyrocopter, as most, if not all, gyrocopters are pushers these days, it was significant to read the eyewitness reports.

He stalled the rotor, applied power, and because it was a pusher config, the rudder had very little authority, and the airframe started to spin around the rotor axis.

Two thousand feet, and it was still too low to recover.

I'm convinced that if it was a tractor design, like the original Ciervo designs, two grand was high enough to pull the damn thing straight, in any orientation, and get air flowing over the rotor..

Those kid's toys, a dowel with a propeller on top, and you spin it between your hands, does a remarkable job of imitating a very stable low CG rotor machine.

Mmm, I'm no engineer, but I do have a Bowtech Assassin, with sights that need setting up.....

Might give it a try tomorrow,I have dowels and propellers here.

Wait, need to get my hands out the flight path, pronto !

Not arguing the math, yet, but here's the scenario :

X on the floor, you need to suspend a broomstick from your fingers, keep the bottom end in the center of the X.

X on the ceiling, same broomstick, you now need to keep the top end on the X.

I know which horse I'm going to back....

@Gustav,   Sorry to hear about your loss. Many years ago, I helped carry the coffin of a friend who died in a gyrocopter crash. It is interesting that most of the webpages that talk about such craft tend to glorify the "thrill" and downplay the risk. And the gyrocopter was being towed, not under power yet. But back to the topic of finding data that is relevant to multirotors...   :-)

John , about the Sony Nex5 .

One problem  in that camera is the video output (since if you want to shot videos you'll need to see at ground what the camera gets during flight.)

Nex5 has only an Hdmi video output, so to use an analog video transmitter if you will need a 50 USD Hdmi to analog video converter.
So consider at least 100 grams more weight and a quite large board to put somewhere plus the Hdmi cable not very flexible.

There are also some Hdmi  digital video transmitters but they cost quite a lot about 1400 USD.

Luc,  thanks! I had already ordered one of these. The cost was low enough to try some experiments. If there are severe problems with streaming NEX-5 video to ground, I will try another approach that was mentioned on this thread... attach a CCD or CMOS sensor to the shoe on top of the NEX-5 as an FPV aid, aim the sensor, and turn on the NEX-5 video record function just prior to a flight. For me, this is a hobby, not a profession, so that may be good enough. It would be ideal to see exactly what the NEX-5 sees, during a flight. (yes, a much more expensive alternative was mentioned on this thread.)  On this thread I found this 1 foot cable. Have you found a more flexible, possibly shorter cable?

The converter you found is smaller than the one I knew. :)

Forget to attach another camera , Hdmi coverters usually work well.

For the cable there might be something shorter but never found them,  low quality chinese cables may be more flexible than high quality cables (little or no shield) but you have to test it with your hands. You can cut some rubber from the final part of the connector near the cable to obtain littler angle of the cable.

But the  most important is to protect the hdmi connector of the nex5 because it is quite fragile.

You can use a 90° adapter (this is not mini but gives you an idea) that you will fix with some hot melt glue (EVA) to the body of the Nex5.

Luc,  thanks for the tips!  ( On a related subject, I do not plan to invest in one of these at \$3500 USD... way more than I need. However, you may be interested in this thread about gimbals.)

This is my fpv cam. tiny tiny tiny!

Use a second cam for recording, a 808 #16.

I used to use a bloggie, but it weighs 4x as much as these two combined, though it does have a pivoting head.

http://www.dronesvision.com/11-5x11-5mm-2gram-520tvl-0-008lux-fpv-c...

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)

I am new to the forum but not to RC aircraft. Also a physics minor in college. Think about it this way. When out multicolored pitch or roll to achieve a new acceleration vector. The whole frame shifts, not just the rotor as in a conventional helicopter. (yes i know conventional helicopter bodies pitch and roll as well, but that is a result of acceleration and inertia, not part of the operation.) Anyway, when the entire body shifts, so does anything attached to it. A mass below the frame is forced against the force of gravity. Gravity wants to pull it back down. Which does stabilize the aircraft if it remains stationary. However with every new pitch and roll movement, the motors and thrust is fighting this downward pull of gravity. Plus they are also fighting the angular momentum the "pendulum" has.

Now flip this who thing upside down. With the CG above the main source of thrust. Now instead of hindering pitch and roll movements. They are actually aiding them, allowing greater change of pitch or roll angle, with less thrust change. Granted if the CG is placed to high above the thrust line, or the Multi doesn't have enough thrust to right the mass in cases of emergency, it will topple over. That in unquestionable. But when placed slightly higher that the thrust line, the mass "assists" the motors in their job of changing the angle of the aircraft frame.

Take a look at this for instance.

This is the QAV quadcopter frame. No doubt a few of you are aware of its existence of maybe have had some experience with it. Notice how the frame is designed. There is nothing, i repeat, nothing mounted below the motors. (not saying you cant) the FCB and battery are mounted in line with the with the rotors. Ive seen these things fly, let me tell you, they are agile, and very fast in forward flight a buddy of mine has clocked 35-40mph in a no wind scenario. However, they are not unstable in any way shape or form. The fast forward flight i attribute to the "long center of gravity" and the relatively short motor arms. Also i noticed that this frame accelerates very fast with very little actually change in "cyclic" and actual pitch of the frame. All of this translates to less drag. The "long center of gravity" results in slower rotor speed by aiding the motors when they change the angle of the frame. so less rotor face is exposed, and slower rotors equals less drag.

Okay, im done now.

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