# Pendulum effect, vertical position of CG

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#### ypsilon

##### Well-Known Member
I am currently designing a tailless soaring machine (hangglider but aerodynamically controlled). I did my maths (by means of XFLR5 and OpenFoam) and realized, that the vertical position of the CG has a significant effect on the stability of the glider. Now at first sight it seems that this "pendulum effect" is easy to understand but looking at the implications regarding the dynamic stability of the wing it doesn't seem so clear.

If you have thoughts / sources of information, opinions on the vertical position, high/low wing aircraft, especially on tailless configurations, let's have a discussion about it.

I'll give it a start with an frightfully unsubstantiated perception:
While the pendulum effect (i.e. a low CG) creates a momentum towards a defined AOA, it also builds up energy when rotating (i.e. inertia) which probably make tumbling more probable and (if it happens) ferocious. Can this effect be quantified?

#### henryk

##### Well-Known Member
I'll give it a start with an frightfully unsubstantiated perception:
While the pendulum effect (i.e. a low CG) creates a momentum towards a defined AOA, it also builds up energy when rotating (i.e. inertia) which probably make tumbling more probable and (if it happens) ferocious. Can this effect be quantified?
-iff I understand You,
DYNAMIC/ STATIC stability & controll ?

f.e. KASPERWING=

(practically NO pendulum effect !)

#### mcrae0104

##### Well-Known Member
HBA Supporter
Log Member
Doubtless there will be a lot of opinions, but the heart of the matter of longitudinal static stability is straightforward. 1) The sum of the moments about the lateral axis passing through the CG must be zero. 2) The slope of Cm vs alpha must be negative. Perkins & Hage is a good source; although they don’t deal with tailless aircraft specifically, the same two rules hold true.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
I'll give it a start with an frightfully unsubstantiated perception:
While the pendulum effect (i.e. a low CG) creates a momentum towards a defined AOA, it also builds up energy when rotating (i.e. inertia) which probably make tumbling more probable and (if it happens) ferocious. Can this effect be quantified?
Let me try to help out with this whole suggestion that the CG can swing under the wing like a pendulum.

First concept to get straight is the airplane moves, both in translation and in rotation. Translation is movement in a straight line, usually defined in longitudenal, vertical, and lateral directions. Yeah, the direction the ship is pointed, the up-down direction, and the left right direction. Rotation is the classic pitch, yaw, and roll axes.

Fly the airplane and translations of the CG and rotations about the CG occur.

In steady state flight, the translations occur steadily while forces and rotation are zeroed out.

Now if you want to start accelerating the beast, you have to make one or more forces unbalanced. To accelerate in the longitudenal axis, either drag must be reduced or thrust increased, and the unbalanced Force will accelerate the mass of the ship. Equation that let's you figure out acceleration is F = m*a. If you know the unbalanced force F and mass m, do the algebra and F/m = a.

We have an equivalent equation for rotation. M = I*alpha, where M is an unbalanced moment in one of the axes, I is the mass moment of inertia about the CG, and alpha is rotational acceleration. Want to know alpha? Do the algebra, and alpha = M/I.

If this is a nose up moment, then the airplane will pitch up. As the AOA increases the lift increases and the airplane starts to describe a loop. If there is enough kinetic energy in the longitudenal direction plus enough extra energy added by thrust, the loop will proceed. But in the process, you have also put energy from someplace into rotation in the pitch axis. Here, KErot = 1/2*I*omega^2 where I is the same mass moment of inertia in pitch axis about the CG, omega is rotation rate in radians/sec. you also have rotation momentum, MOMrot = I*omega.

How do we get that pitching moment and rotation? If you slowly add nose up elevator, the airplane will slowly increase nose-up angle and slow down, and approach stall. If instead we move the controls vigorously to the stop for pitch up, we can get some rotation speed and the nose could go through the stall AOA, and perhaps get into deep stall. Do this fast with a footfull of rudder and it snap rolls. This is all very normal.

One other thing is going on. If the controls, applied slowly and smoothly and then held at a position would have produced a particular attitude and AOA of the airplane, the airplane would have been balanced at that attitude. If you somehow dynamically got it to overshoot the stable spot, most of the time there is now restoring moment resulting that is trying to slow rotation and return the airplane to its stable spot for this state of the controls. If instead of returning toward the original stable position, we get rotate on through to a deep stall or a spin that stays without rudder inputs, that is bad. Enough rudder and elevator to stop yaw rotation and then break the stall is required to get back out of this case.

Can it be quantified? You bet. You do a time step integration of the state of the airplane in three translation and rotation axes (both positions and accelerations), with wing and control surface characteristics, and masses and mass moments of inertia included and you can simulate all of this. The Control and Stability texts get into all of this stuff.

Now where does this "pendulum" come in? The CG is translating and then the airplane is rotating about the CG. A high wing airplane with the CG below the wing is then moving the mass of the wing aft, any object ahead is moving up, and objects behind are moving down, and the mass of the landing gear is moving forward. If this is what you meant by a pendulum, well, let's use the established nomenclature for mass moment of inertia, rotational velocity, rotational momentum and, rotational kinetic energy.

And if that is not what you were attempting to describe, well, maybe a little more effort to explain all of this is needed.

Billski

#### Aesquire

##### Well-Known Member
Vertical position of the CG is more often a powered plane issue, when the thrust line is high ( Or low, but that's rare ) in relation to the CG.

In a glider, the stability forces in pitch act through the fulcrum of the center of lift on the wing, and the tail. On a tailless plane. It's often said there is a tail, but you don't see it, when the airfoil is reflexed, it's the reflexed area, swept with twist, the tips. Sorta.

If the center of mass is below that line, and fixed, ( not swinging like in a weight shift craft ) then it "resists" pitching just by inertia, then resists stopping, ditto. The math is mentioned above. ( thanks! ) The greater the vertical lever arm, the more inertia moment. The gravity doesn't change, just the angles.

So in oversimplified terms, the greater the distance, the harder it is to pitch, AND stop pitching.

Things get weird when the mass isn't fixed. In a paraglider, with those long "strings", it's a hazard to stall, ( duh) but the problem is when the wing surges ahead on reinflation, and can dive in front of the pilot, ( it is constrained to fly in an arc by the risers ) and yanking the pilot forward, lines can go slack and in worse case the pilot ballistic arcs into his own wing. ( the soft connection can only pull, not push )

A weight shift hang glider with a "soft" connection that can go slack & let the pilot float ( no control until suspension takes the load again ) or worse hit the wing from below, ( imparting a force to rotate the wing around it's own CG ) is usually not a crisis, unless the pilot lets go of the frame and is creating a far aft unstable CG position. Like I said, weird.

In a weight shift trike with a hinged, but fixed distance connection between high wing/low mass, It's the same as a fixed mass, but you have to calculate the moments at the limits of pitch and roll. ( more math!!!! )

#### Hot Wings

##### Grumpy Cynic
HBA Supporter
Log Member
So in oversimplified terms, the greater the distance, the harder it is to pitch, AND stop pitching.
And why FWs tend to have more pitch related problems than conventional planes. The damping factor of the equation is limited. The Spratt method has the advantage of having a well damped fuselage hung under the pivot.

#### ypsilon

##### Well-Known Member
Thanks for all the responses. I see there is need for some more clarification, what I was actually talking about:

If you consider a CG much lower than the wing, and you project both center of lift and cg onto a horizontal plane, then as you increase the AOA the horizontal distance between (the projection of) CG and COL will increase thus the nose-down moment induced by this pair of forces will increase. Now once there is a rotation established Aesquire's statement (the greater the distance, the harder it is to pitch, AND stop pitching) comes into play, although it's not really about the vertical distance between CG and wing, but about the distribution of the mass around the rotational centre (which happens to be the CG).

Now in practical terms: Did ever lowering the CG fix any issues a concept had before? I gather that Howard Long flew his Mitchell Wing as a Hangglider from "inside" the wing, while later Mitchelwing HG-Pilots would build some fuselage under the wing, thus lowering the CG. Or Jim Marske's Monarch mounts the pilot significantly below the wing (as opposed to the Pioneer). I just wonder if those developments are to be explained by practical reasons rather than aerodynamic ones, or if indeed lowering the CG may improve the handling of such aircraft.

#### TFF

##### Well-Known Member
It will up the stability and degrade the maneuverability. It would be pretty easy to build a chunk glider model. Build it to glide and then add up elevator and see how it reacts when thrown

You don’t ride at the top of a parachute or balloon. Hanging below is about as stables can be if lift is above.

The control will be like doing curls in the gym. Pitch or roll any direction and you have to lift that weight around the CG point. Little movements would be not to noticeable, but something extreme like a loop where the pitch control will have to muscle the weight over the top and without enough speed, the moment inertia will just flip it upright as it goes over the top.

You might not be looping, but to avoid a bird or spiral down to look at something, you will fighting the thing trying to be stable. Its going to want to go straight. It’s all going to matter how heavy above is to what is below.

#### henryk

##### Well-Known Member
You don’t ride at the top of a parachute or balloon.
=?

De Lackner HZ-1 Aerocycle

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#### TFF

##### Well-Known Member
You make my point. Those are the most unstable craft and are over maneuverable.

#### Aesquire

##### Well-Known Member
...while later Mitchelwing HG-Pilots would build some fuselage under the wing...
That's more a matter of simplicity of construction, keeping a clean wing center section ( without gaps or bulges ) and putting the variable weight, the pilot, in the right spot. than a vertical distance.

Paragliders, balloons, and other flying things that have a flexible connection to the lifting gizmo are a different critter and don't apply here.

Fortunately, there's an easy way to observe the effects. Make a small free flight glider. Paper airplane works. Then mount a vertical spar you can put a weight on, right at the fore & aft CG. A splinter of wood from a disposable chopstick ( or an entire stick for a larger model ) and a lump of modeling clay.

Get it flying nicely, with the "mass lump" right against the wing, then move it down and fly again.

My recommended model design is the Barnaby Special, which glides very nicely, and can do loops and is very stable.

I have made thousands of these, and lost many rising out of sight in ridge lift and thermals. One trick I do is tweaking the symmetry so I can launch it sideways, and it will make a circle and return to my hand. I would have entire conversations with people tossing the model in a circle around them & catching it, repeatedly.

#### Aesquire

##### Well-Known Member
I preferred supine under the bar to prone harnesses for hang gliding for 3 reasons. Never liked supine over the bar. ( suprone... silly name but does give a distinction ) That's 2-3 feet lower than "normal" .

Comfort. Easier on the neck, than prone, but you need a headrest on the supine harness for multi-hour flights for real lounge chair effect. I often tossed a rope over a branch and napped in mine while waiting for conditions to improve.

Better roll authority. Important when most of your flying may be turning flight and turn reversals.

Turbulence.
When experiencing zero and negative g loads, instead of my heels hitting the wing, as with prone, my lap would hit the bar. ( triangle base tube. Called a control bar, it's actually just a handle, and structure, not a control actuator ) With my feet in a stirrup, I just assume the "dead bug" position with knees in front of bar, and torso behind, locked into a "well over max L/D, but not diving" weight shift position, which gives a mostly automatic recovery from unusual attitudes. "Over the falls" rotations past vertical dive to inverted dive, or sudden zero visibility punching through heavy Virga, that was my trained reaction. Once visibility returns, or the lift/weight relationship allows control, then I'd do what was needed to avoid or return to course.

The downside is you need to hold the wing higher with usually more awkward leverage on take off, and when you get a rapid pitch disturbance the momentum is higher, so theoretically you rotate more, but I never had experience with that for certain, and the increased ( by just a few feet ) lever arm made roll control better, especially in stiff, competition gliders or with the variable geometry cranked to max.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
OK, let's get a little further in.

If the masses around the airframe are in fixed positions relative to the flying surfaces, the spots on the airframe that are CG and Neutral Point are fixed relative to the flying surfaces too. With the wing above the CG, increasing AOA of the airframe swings the wing and the Neutral Point aft, most likely increasing your static margin, increasing your reserve pitch stability and driving more nose down moment... Pitching down will swing the Neutral point forward, reducing reserve pitch stability and drive less nose down moment through the same mechanism. Pitching up will be strongly stabilizing, but if your stability is modest, it could become neutral or unstable with big negative AOA.

If you get some velocity in the pitch axis as you are pitching up, you will have stability increasing and nose down moment increasing - to overwhelm this with some rotational momentum is possible. Overshooting the stable spot is more likely if you get some momentum in the nose down direction, as the restoring moment is decreasing...

If you start moving a major mass around while you change AOA, the whole question then becomes how did you move the relationship of CG to Neutral Point?

Have fun.

Billski