### 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!

#### Replies

• Old discussion, but two more cents:

Center of pressure only exists if there is a moving airstream.  Conceptually, it is the point at which all drag acts through.  Since drag is roughly proportional to velocity, for a hovering copter, there is no drag and no CP.  For FF or any directional flight, CP does matter and can throw off the stability while moving.  If the CP is aft of the CG, it will be stable in forward flight.  By definition, however, it will be unstable in aft flight.  However, since multicopters are meant to be able to move in any direction, the only "ideal" situation is to have the CP and CG in the same point or close.

Also note that "stable" does not mean "good."  Stability can make things wildly uncontrollable.  A stable system means  the return or centering forces are strong.  More stability means stronger centering forces.  This means higher oscillation frequencies which require faster reflexes to dampen with controls.  It may actually feel less controllable.

Mix that in with a PID controller and it could be completely unpredictable, since you have two interdependent systems--the basis for chaos theory. Either one alone will produce predictable oscillations when disturbed, but if both systems are significant, the movement will be unpredictable by definition.  Only by reducing the strength of one of the systems will it return to being (mostly) predictable.

What this means is that as long as we are using a PID controller, the system should be pretty close to neutrally stable, so that there is no stability or instability.  That means the CG and center of lift should be pretty close in hovering flight, and the CG and CP should be pretty close in translational flight.  As long as all three points are "pretty close," the stability will be small enough for the PID controller to overcome and produce predictable results.  Too much stability or too much instability in any one axis will result in chaotic movement in that axis.

• This is a really interesting discussion! It's not often that a topic gets my juices flowing.  I know from my own experiments that moving the CG lower and lower decreases stability and performance... but my own observation is that I get the best stability and aerobatic stability with the CG right at the height of the CP.  Simply because it has the least inertia and the FC can make the necessary changes quickly.  With the motors in a tractor config odviously I have to mount the batteries up a little higher.  Mounting them as pushers isn't really an option for me because I hate long landing gear and like having a low profile.

However, I will not dismiss the possibility that raising the CG higher may increase stability as you say.  The mere possibility of increasing stability and performance simply by mounting the battery a little higher... like I said, gets my juices flowing, lol.  I have a quad now that I could easily test this with... the camera and batteries sit on a tray suspended below the quad (due to a vibration isolation system) that I could unbolt, flip it over and bolt it to the top of the hub... wouldn't be useful for the camera, but I could do it as a test.  I don't have an APM so I can't do any datalogging but I can adjust the gyro gains up til it oscillates with the CG low, then try it CG high and see if I need to raise or reduce the gyro gain.

Other than that, I look forward to someone's test that provides hard data!  :)

• 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)

• 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.....

• Hi Monroe,

I work with ducted fan technology as part of my job so I thought I would just add my 10 cents worth:

With ducted fans it is very important to get the correct C.G. location because of the way in which you are redirecting the thrust from the surrounding air, if there is a lateral airspeed at the inlet of the duct (either wind or from the aircraft moving) you will be putting the airflow through an angular change to suck it through the duct, this means (due to conservation of momentum) that a force will be exerted on the aircraft in the opposite direction to your motion. This force acts in the region ranging from half a duct diameter above the duct at low sirspeeds and moving down to just below duct lip as you near horizontal flight. Now, if your C.G. is low there will be a moment which will pitch the nose of the aircraft up, if however your C.G. is optimized then you can make is moment negligible and thus greatly improve your gust response and high speed capability.

With a ducted fan this force is quite large (should be one of the biggest considerations when designing) however this force should* still be there with open rotors (quads, etc) however the force may be quite negligible. You may find that the more important between low/middle/high C.G. is the difference in rotational inertia.

It can be stated with certaincy that there is no pendulum stability with pure vectored thrust VTOL aircraft, there are forces which may have a tendency to right the aircraft in some situations however in other situations the same force may destabilize the aircraft.

If you are interested in further reading about momentum drag (or ram drag, or nose up pitching moment) try googling them (they are essentially different names for the same force).

*i say 'should' because I am taking what I know about ducted fans and trying to apply the same fundamentals to an area which I have far less knowledge about (quads, etc).
inertia.it
This domain may be for sale!
• I do not agree when you wrote

put all the weight ON TOP of the rotors these craft SHOULD BE MORE STABLE!

To achieve the maximum stability it is quite obvoious that the payload should be at the center of the mulirotor.

Putting over the CP the CG do not give any advantage.

"normal" design of multirotors with the battery under the frame and the camera under the battery is not ideal, perhaps for that reason DJ Hexa with custom camera mount for Sony Nex have motors mounted with some degrees towards the CP (loosing this way some motor effiiency).
Mounting upside down motors makes a little difference only , putting batteries  on the top of the multirotor is a better solution for improving multirotor stability.

• Well, BOOooooo, the waterjet cutter somehow mis-scaled the parts!  They're all ~5% too small!

He's going to have to recut them.  I don't know what he did.  I provided a simple 2D AutoCAD drawing, drawn with unit=mm.  He called me last week, and said "this thing is huge!", but he thought it was in inches, their machine assumes inches.  Basically the solution was simple just to rescale the drawing by 1/25.4.  How he got it wrong I have no idea.  Good thing it wasn't carbon fiber!

• Umm, on Mars Curiosity, most of the weight was far below the rockets during the lowering phase........

• Monroe, Brad, I love you guys.  Always interesting, out-of-the-box but well supported ideas.

I'm building an Octo, based on a conglomeration of Turnigy Talon and H.A.L. parts.  I'm already going to be trying out one of Brad's ideas, and will be using ~20% overlapping blades (with vertical offset, of course) on it to see if that helps efficiency.

I would love to add this idea to the mix.  However I have a problem.  It's main purpose is a camera platform.  How can I keep the motors out of the picture if the camera is above the platform?

Also, I think Trad Helis are not completely applicable to this theory, because the way the blade disk articulates.

But can you put this theory into more layman's terms Monroe?  I have a difficult time picturing it in my head.  We all know that things naturally want to hang straight down, but balancing a ball on your nose takes effort.

• So, after a quick search I found that it not only depends on the center of gravity, but also the center of pressure.

http://exploration.grc.nasa.gov/education/rocket/rktstab.html

So now the question to answer is whether the center of pressure of the quadcopter is below the center of gravity.

The test for a rocket (aside from calculus), apparently is to tie a string at the center of gravity of the rocket and then hold the other end of the string and spin the rocket around you. If the rocket aligns with the direction that you are spinning it, the rocket will see a stabilizing force.