Vertical Center of Gravity

[ctdahle]

There have been many discussions of how to find or adjust the Center of Gravity of our airplanes both laterally and forward/aft.

But one thing rarely mentioned is how high or low the CG should be relative to the wing, and how this affects stability.

Should the roll, pitch and yaw axes all intersect at the CG? or should there be variations depending on the type of plane and the desired style of flying.

Presumably a high wing trainer should have a low center of gravity so that it "pendulums" below the wing and tends toward a stable center. But contrariwise, on the club trainer, I have the servos sitting high in the fuselage so that it is easier to get my fat fingers in there to make adjustments. Maybe they would be better sitting on the floor?

On the other hand a low wing model might have a high center of gravity and thus be less stable when interupted from level flight, making it easier to kick in to spins and other maneuvers. But this could tend to make it MORE stable when inverted, and perhaps more difficult to recover from an inverted spin, for example. Should the gear be close to the "roof" of the plane, or closer to the wing?

Anyway aside from my own unproven pet theories, I don't have any strong theoretical basis for determining where the vertical center of gravity ought to be, and also no idea how to go about determining where it IS on a particular airplane.

So, what do you all think? Does finding the Vertical center of gravity matter, and if so where should you locate it and how do you measure where it is?

[jetmex]

This one got my interest also, Chris, so I asked one of my airplane engineer type friends about it. Basically, there is no measurement for a vertical CG--only laterally and longitudinally. The reason being is that equipment contained within the fuselage can't really be moved far enough up, down, left or right to affect anything. Fore and aft, or course, is whole different animal!

It's general procedure to put everything REALLY heavy down low. Engines come to mind, there are exceptions to that, such as the Boeing YC-14 and the Antonov An-72, which had the engines basically mounted above the wings. On our cargo airplanes, we try to distribute the load evenly between upper and lower decks, but it doesn't always work out that way. The MACs and CGs are always figured on fore and aft loading and fuel distribution in the wing tanks.

[ctdahle]

Well that makes sense.

But I wonder if in our small planes, it really might make a difference. For example an aerobatic plane that tended to fall off toward the belly or the canopy in knife edge flight... Might this tendency be correctable by shifting the battery pack into the top of the canopy, for example, rather than under the fuel tank?

Since our models are mostly hollow, and our gear is getting smaller all the time, couldn't it be that moving the flight gear "up" or down along the yaw axis would have far more effect on the model than it would in the full scale plane?

Anyway, it's a more interesting question than rehashing downwind turns.

[jetmex]

Chris, in the example you mentioned, moving the battery aft to beneath the canopy would probably have more effect on the fore-aft cg, since you're moving a pretty good mass quite a ways aft. It would be easy to experiment and find out, but I don't think it would make all that much difference.

I flown airplanes with servos and such located at all points vertically within the fuse, and it really doesn't seem to change anything.

Someone with more brains than either of us could probably add something to this discussion..... ;D

[ctdahle]

jetmex said:

....
Someone with more brains than either of us could probably add something to this discussion..... ;D

Yeah I figure if we toss the question back and forth enough, maybe we'll attract a response from someone who knows....

I'm thinking about pattern airplanes on the one hand which seem to have most of the gear, (batteries, fuel, servos, reciever) all clustered together as close to the CG as possible, whereas the 3d models tend to have servos out on the wing, and at the tail and the massier gear, such as the batteries nearer the firewall.

Then also, I am thinking about a baton, with weighted ends, rather than uniform mass along it's length. This makes me wonder, from a design standpoint, what the advantages are of balancing the model with mass at the nose and tail as opposed to balancing it by concentrating the massier components at the CG.

In otherwords, when you put a servo in the tail in order to simplify your linkages and reduce the potential for slop, are you giving anything up? Clearly, the pattern guys spend a lot of money and effort using their long titanium and carbon fiber elevator pushrods, when they could just put a servo right on the tail for less cost and less opportunity for slop. So they must feel there is some advantage in keeping the servos nearer the CG.

....all of which has nothing to do with the original question...

[Britbrat]

If agility is the desired outcome, then polarizing the mass will work against it. However, once you start a high-polar-moment object moving, as in a spin, it strongly resists slowing down &/or changing direction. Moving the heavy bits outboard, despite any popularity with 3D fliers, works against quick response.

[Galvin]

Should the roll, pitch and yaw axes all intersect at the CG? or should there be variations depending on the type of plane and the desired style of flying.

The pitch, roll, and yaw axes are all going to intersect at the CG no matter what you do. Controls move the airplane about the CG in all axes, period. Since the axes all intersect there, the control response in pitch and yaw can be sped up by moving the CG aft or slowed down by moving it forward. The rate of roll is not affected by the CG very much but is more affected by the size of the ailerons, their control throw, how much of their area is toward the tip, the length of the wing, taper ratio, dihedral, etc.

I wouldn't worry about how high or low relative to the aircraft reference line the CG is as much as I would worry where the thrust line of the engine is relative to the CG. ( Assuming the thrustline and the reference line are parallel to each other. If not, well, that opens up a whole newset of problems.)

In an illustration of an extreme case, I once flew a friend's antique amphibian on which the engine was mounted high above the wing. Because of this configuration it had tremendous pitch changes with power. Adding power too quickly in the air would cause the nose to drop quickly enough to really get your attention until you got used to it. One had to be careful not to add or reduce power to quickly when on the water lest a dangerous porposing condition be induced. (Fleetwings "Seabird" serial number 1. Constructed completely out of stainless steel. We called it the "SST" or "Stainless Steel Tub".)

Britbrat is right in stating that putting weight at the extremities of the aircraft makes the motion around the affected axes harder to intiate and even harder to stop once it get going. It has to do with something called "polar moment of inertia". Some aircraft are prohibited from being spun with more than a certain amount of fuel in the tip tanks for this reason.

However, fuel (or weight) out toward the tips is otherwise beneficial in many cases because it actually raises the allowable 'G' load on the wing by distrubuting the weight farther from the aircraft centerline and reducing the bending loads at the wing roots. In large transport category aircraft there is a maximum zero or no fuel weight allowable in flight because as the fuel in the wing tanks is burned, the distribution of the weight along the span tends to change, concentrating more towqrd the center of the aircraft'and increasing bending loads on the wing to dangerous levels in turbulence or if the crew get too frisky on the elevators.

Overly stable aircraft usually do not respond quickly to the controls. Because of this, modern fighters are deliberately built unstable in order to speed up the control reactions to nearly instantaneous. The F-16 and F-18, for example, are built so that the CG is often behind the center of pressure (the point on the wing chord that the wing is considered to lift from) and without very good stability augmentation devices (which work like a yaw damper but vertically instead of horizontally) they would be unflyable by mere humans.

Models are built more or less stable depending on the reactions of their pilots. If you have the reactions of a weasle on crack you can handle close coupled, small, fast aircraft. If you are like the rest of us, you will need aircraft with long moment arms, somewhat slower reactions, and a speed that will allow you to keep up with the airplane or at least get to the accident soon afterwards.

[ctdahle]

Are you sure that the axes are all going to cooincide at the CG?

Sure, if it is a baseball bat or a baton. Toss it in the air in an end over end motion and it will rotate around the CG of course. But add big fins ("wings") to one end and it will wobble around a point between the center of pressure and the CG until it reaches a stable attitude.

Don't the rotational axes exist at the point where the sum of all of the force vectors acting on the airframe are equalized? While the large forces of inertia and gravity are concentrated at the center of mass, the aerodynamic forces are concentrated at other places, so there would be differential.

But hey, It's been 24 years since I took a physics class, and obviously I became a lawyer, not an engineer.

[Britbrat]

Actually Chris, you are pretty much right on the money.

The C-of-G is an aeronautical term that really applies only to the balance point on the longitudinal axis, more specifically, on the cord line.

The center of mass does not necesarily coincide with the aeronautical C-of-G (longitudinal balance point), & the roll, pitch & yaw axes can be significantly displaced from the center of mass. Interestingly, the roll axis can change with airframe attitude. An example is found in the standard RC trainer. The center of mass is relatively low, due to the deep fuselage & low-mounted heavy components, while the center of lift is high (it can actually be above the upper surface of the wing, at the midline, if dihedral is large & the span is sufficiently great.

In horizontal flight such an aircraft will have a roll axis that is well above the center of mass and this can easily be visually observed in flight-- aileron rolls resemble barrel rolls. However, in vertical flight, the gravitational effects upon the center of mass are cancelled in the pitch plane -- in effect moving the center of mass toward the center of lift. Aileron rolls will now become visibly more axial.

[ctdahle]

Thanks, both of you guys. I'm getting a better feeling for how this all works.

I've ridden in Citabrias, Skylanes, Station Airs and Cubs, and got my wings in a Schweitzer 2-33. In all of them, the airplane felt like it was suspended from a point well over my head and that it rolled and pitched around that point, well away from the CG.

Similarly, I've ridden in Bonanzas and Cherokees, and have some solo time in a 2-32. The Bonanza and the Cherokee felt like they were balanced on top of a pivot mounted under the seats. The 2-32 felt like it yawed, rolled and pitched around a point that was in the middle of my stomache, which made it easy to maintain coordinated flight even without reference to the ball and the yaw string I might add.

Getting back to the original question then, it appears to me that it is possible to design an aircraft so that the lift, roll and yaw axes all pass through points that are not necessarily at the center of mass, and moreover, do not necessarily all three intersect at the same point.

The pitch axis could run through a point higher or lower than the roll axis, and the roll axis might be axial with a datum line through the prop hub, or displaced above or below.

If we could imagine a "mass less" airframe, flying in a zero gravity wind tunnel, it's stability and the location of it's three flight axes would be determined solely by the configuration of the airframe. They would pass through a particular theoretical point that would have nothing to do with the center of mass.

Add mass to the airframe and fling it out into the vacuum of space in zero gravity and it will rotate and tumble around the center of mass as Galvin says. Now I would concede that the airframe is going to "want" to rotate around its center of mass, but that the aerodynamics are going to make it "want" to rotate around a different center. I also think that the displacement of the center of mass from the aerodynamic rotational centers has a lot to do with the inherent stability or instability of the airplane.

Note that I am not necessarily talking about the center of pressure, but rather the point where the sum of all of the force vectors operating on an airplane cooincide.

In my mind, this raises lots of interesting questions, but maybe they are only interesting to me!

[Britbrat]

Don't back away from chewing on this topic -- it is certainly interesting to me.

[Richard]

Very intresting subject to chew on, espically when one likes to build diffrent planes including war birds and civillian aerobatic types.

[Britbrat]

It's a pleasant & usefull change from politics.

[ctdahle]

And this one, an interesting discussion even if we didn't resolve anything.

[invisible]

If any of you decide to step up to flying control Line Precision Aerobatics, you will need to have your leadout guide on a horizontal line in the vicinity the vertical CG, else your airplane will fly around with the outside wing high or low as the case may be.

[Britbrat]

I keep threatening to go back to control line flying --- but I remember the ground being pretty close

[katria]

Hi
If we could imagine a "mass less" airframe, flying in a zero gravity wind tunnel, it's stability and the location of it's three flight axes would be determined solely by the configuration of the airframe. They would pass through a particular theoretical point that would have nothing to do with the center of mass.

[Garf]

Feb 27, 2006 15:31:21 GMT -7 Britbrat said:

I keep threatening to go back to control line flying --- but I remember the ground being pretty close

If you should come back to your senses, we will be here waiting.

[Garf]

The nice thing about control line is you never need to walk more than 70 feet to collect the wreckage.