CG and Stability

[uwochris]

Hey guys,

I have a question in regards to CG and its effects on stability. I have been reading the Jep Comm-Inst manual and the Jep Multi Manual, along with some other stuff, and there seems to be some conflicting views.

This is how I see the situation; if I am misunderstood, please let me know:

If the CG is farther aft, it will be located closer to the Centre of Pressure, shortening the arm between the CG and the CP. With a shorter arm, the airplane will be able to fly at a lower AOA, reducing lift and hence induced drag as compared to a forward CG. Also, since the CG and CP are located closer together, the airplane will be more responsive to pitch changes, and less control inputs will be necessary to change the position on the airplane; however, because of this increased controllability, it is possible to overcontrol the airplane, thus making it more unstable. Also, because the CG is located closer to the tail, there will be increased tail down force, which will be difficult for the tail to counteract.

I got confused because some authors state that an aft CG will make the aircraft more controllable and sensitive to pitch, while other people state that an aft CG makes the airplane less sensitive to pitch.

It seems to me that if the arm between the CG and the CP is lower, more force will be required to disturb your position; however, this also implies that more force will be required to return to your intial position once you are hit by a gust, implying greater instability. With a forward CG, the arm between the CG and CP is slightly longer, so it seems to me that because of this, it will take less force to disturb your position, and hence the airplane will constantly be trying (and be able) to correct itself for tiny disturbances.

My logic here is based on a fact my brother (an engineer) told me. He said that it takes less force to move something if that force is applied across a distance. For example, if you try to close a door by pushing on the area near the hinges, it will be more difficult (and take a greater force) than if you pushed against the door near the door knob.

So, since the arm between the CG and CP is longer with a forward CG than with an aft CG, should this not imply that the aircraft is more sensitive to pitch movements (ie. takes less force to move)? Or, is it that because the airplane can constantly correct itself with a more forward CG (ie. more stable), this makes it harder to maintain a position other than one in equilibrium, and more control inputs will be required to offset this increased stability?

I hope I got my point across. This is a difficult area for me to understand, so I hope someone can shed some light on the situation.

 

[Andy Neill]

I think you were right on the money for the first half of the post. Where your point fades is when you suppose that the shorter the distance between CG and CP, the greater the force needed to control pitch. Remember that the elevator (well aft of CP adn CG) is what is controlling the pitch.

Consider the extreme case where the CG and CP are conincidental. It would take zero force to alter the pitch and every bump and deviation would have an immediate (and impressive!) effect on pitch. The further CG moves from the CP, the greater the force will be to disturb the pitch and hence the greater force required of the elevator.

CG placement is a battle between efficiency and stability. With a very forward CG, the elevator must apply a lot of downward force to counteract the moment of the CG about the CP. This is very inefficient (since much of the lift of the main wing is being spent overcoming the downward force of the elevator) but the aircraft is as stable as you might want - perhaps so stable it cant even lift off the runway. As the CG moves aft, less force is required of the elevator and the efficiency is improved as less and less force is required from the elevator to alter the pitch. Stability is lessened as efficiency improves. Finally, we get to the point previously mentioned where the elevator is using zero downward force (best efficiency) but the aircraft is unflyable because it is so twitchy in pitch.

 

[Sphincter Boy]

The way I always understood it was that the more aft the CG, the less downforce required by the horizontal stablilizer to counteract the nose down tendency. This unloading the tail allows the airplane to acheive better performance than a foward CG.

I agree with the above post as for as the stability is concerned.

 

[Andy Neill]

The way I always understood it was that the more aft the CG, the less downforce required by the horizontal stablilizer to counteract the nose down tendency. This unloading the tail allows the airplane to acheive better performance than a foward CG.

That is precisely what I intended to say. Sorry if it didn't come through that way and thanks for the clarification.

 

[Cardinal]

For further reading on this and other subjects try http://www.av8n.com/how/htm/aoastab.html#sec-too-far-forward. The ideas aren't always conveyed as clearly as they could be, but it's at least well illustrated.

 

[tarp]

Yeah -

You messed yourself up with the Door example. You're not working with a door but with a "see-saw" (i.e. lever and fulcrum).

In the door example, all the weight is distributed on the same side as the lever. The fulcrum point (CP) is the hinge. This would make a very bad airplane - since the tail would now be required to provide lift and a stall (or loss of lift on the tail) would create an unrecoverable situation. This is NOT how airplanes work.

In a "see saw" or lever and fulcrum, the weight is opposite the lever and now we just apply some simple physics to "balance" the equation. To be in balanced flight the force on one side of the CP must equal the force on the other. Force equals mass x acceleration and acceleration is a factor of speed (distance and time).

If the weight of the airplane (let's say 1200 lbs) is one foot (12") from the fulcrum (CP) then we could say that it is exerting 1200 ft-lbs of force. The tail now has to exert 1200 ft lbs at the other side. So let's build an airplane where the tail is aproximately 12' (12 feet or 144") from the approximate Center of Pressure (CP). Then we have to exert 100 lbs of down force to keep the plane level or balanced.

1200 ft-lbs (weight and arm) = 1200ft-lbs (downforce and arm)

Now, let's move our weight to within one inch of the fulcrum (CP) - the moment is now 1/12th of what is was, so the value of the force is only 100 foot lbs. The very same tail that was designed to move 1200 ft. lbs now only has to deal with 100 ft-lbs. This means that a very small elevator movement will basically fling that weight around. If we tried to fly the aft CG the same way we flew the normal CG we'd be overcorrecting like crazy. Think of a see-saw when you are see-sawing with someone exactly your same weight. Then, a 3-yr old child at 45 lbs gets on. You suddenly become a giant. Likewise, any trim setting we put in to stabilize the situation would become immediately upset by turbulence. Less stability.

Obviously if we move the weight further forward, let's move it two feet from the fulcrum (CP). Now the 1200 lb weight is exerting 2400 ft-lbs of force. But the tail is again designed for moving 1200 lbs. We will have to work extra hard (i.e. apply more force to the elevator to move all that extra weight. Instead of 100 lbs of downforce, we have to apply 200 lbs of downforce. This is a doubling or significant work! The airplane is very stable since there is a large amount of weight offset by a large amount of force to a relatively small arm.

Did that help?

 

[VNugget]

A related question that I was asking myself earlier in my learning was "Why can't you have an inverted see-saw with the CP in front of the CG, and thus having the tail provide lift and wasting no efficiency fighting downforce?"

Well, this was answered by a very good site with animations. I don't have it bookmarked because I'm at work -- but google for "aerodynamics1" and it's in the first several results. But basically, let's say that a gust caused an increase of AOA... increased AOA means more lift, and since the wing is in front of the CG (around which the whole plane rotates), it would move up increasing the AoA even more, thus magnifying the reaction further and further.

But with a CP behind the CG, as in most planes, the increased lift from the gust would again move the wing up, but it would decrease the AOA because the wing would "rotate" upward around the CG and point down. This AOA decrease would, of course, return the plane back to the trimmed state.

edit: I'm back home now, here is that particular section:

 

[bobbysamd]

CG

I like Tarp's explanation.

Let's try a practical application. Nearly everyone I've known has agreed that a 182 with only two people in front is an SOB to land because it wants to land flat. It's hard to raise the nose of that airplane into the proper landing attitude with only a pilot and front pax. However, with one or two pax in the back the airplane lands just fine. That is because the CG has moved aft, perhaps because, as Andy noted, the AOA, less downward elevator force is needed to raise the nose. Also, a 182 flies better with an aft CG.

Hope that furthers the discussion.

 

[metrodriver]

OK,here is the way I explained it. If you have a forward CG, there is a very long arm between the elevators (or rudder, think spins, see later), and so a little deflection of the elevators will make a big pitch change . This is a very stable condition, not much input is required to correct an unwanted situation. To keep the nose of your airplane level, the tail needs to have a high taildown force, resulting in more toatal lift required, resulting in a higher angle of attack and thus a higher stall speed.
At an aft cg, the arm is very short, and a big deflection of the controls will result in a small attitude change. This is an unstable situation, it will take a large amount of control input to make corrections and these corrections will be slow. In case of the elevators they will have to provide very little down force, so total lift required is lower and the angle of attack is smaller, giving you a lower stall speed.
Now about the spin. If you're aft of cg, you happen to let your plane stall, pushing the elevator forward results in not enough force to break it and in the meantime one of your wings stalls a little more and here you go in a spin. With the arm between your rudder and the cg too short to provide enough force to stop rotation the airplane will keep on spinning till it makes a large hole in the ground.
Hope this is clear for you

 

[tarp]

Bobby's 182 example is the corollary to your original problem.

The 182 is a fairly weighty airplane compared to the C-172. The engineers took a Continental 530/540 engine (big six cylinder) and hung it way out front - hence natural CG in the C-182 is pretty far forward.

To offset the big engine, there is a pretty good size and again weighty elevator at the back.

In a normal flight envelop with pretty good speed the C-182 is a nice firm "stable" airplane. But when landing, in slow flight and near stall, the downforce of that big elevator is diminished and now the pilot's hands/arms/shoulders have to make bigger corrections. This makes for the "flat" landings and the plethora of nose wheel landings and failures that this plane has a reputation for.

Back to my original science - The elevator developed force as a by-product of speed - the faster the airfoil (elevator) flies through the air - the more effective it is at producing a downforce.

When the aircraft slows, this same airfoil gets mushy and less effective - now pilot technique (knowing that greater control forces will be needed) kicks in. If you don't make these large corrections, the plane will "nose over" or land flat.

Now, take two friends along and put them in the back seat and the CG arm moves further back (towards the CP). Now, the pilot doesn't have to work so hard on landing - the weight moving back has reduced the stability of the airplane (in this case, the C-182 had too much stability). The CG moving aft makes the elevator more effective even at slower speeds. The only cost of this was two people bound and gagged in the back seat and the fact that in normal cruise flight you may find yourself playing with the trim wheel a bit more than usual (again, you made the airplane less stable by adding weight to the back).

Uwo -

just remember that all of this is highly simplified stuff. We are making huge assumptions about a simple wing with a pretty consistent CP, etc, etc.

You had mentioned about authors talking about more or less stability - one thing I had to learn in the Jets was that swept wings, moving CP's, speed, W&B all mess the whole thing up. I fly a CRJ now and this airplane is a bear to land light and just about perfect fully loaded but for just the opposite of the C-182. At light loads, the supercritical wing in ground effect changes the whole dynamic of the landing - the airplane is light and squirrelly (highly scientific terms). Heavily loaded, the wing is less overpowering and the tail force to weight seems normal.

Good luck with the rest of your Aerodynamics - they are fun!

 

[uwochris]

Hey guys, thanks a lot for the help.

Thinking about it as a teeter-totter helped clarify it, as opposed to thinking about it as a door. I can see then that as the arm between the CG and CP increases, more force will be required by the elevators to counteract the nose heaviness; also, as the the CG and CP move closer together (as with an aft CG), the responsiveness of the controls will be improved as less inputs will be necessary to make pitch changes- however, this implies that the airplane will be less stable and more succeptible to gusts.

One thing, however... it seems that Andy Neil's original post and Metro Driver's posts are in conflict... Andy says a more forward CG will require lots of tail down force to counteract the nose heaviness. It was also mentionned that as the CG and CP get closer together, the control inputs for pitch become more responsive.

MetroDriver, however, says that with a forward CG, the arm between the CG and CP is longer, so less control inputs will be required to cause a pitch change.

Am I misinterpreting the posts??

Thanks again.

 

[metrodriver]

this is what I wrote:
If you have a forward CG, there is a very long arm between the elevators (or rudder, think spins, see later), and so a little deflection of the elevators will make a big pitch change . This is a very stable condition, not much input is required to correct an unwanted situation. To keep the nose of your airplane level, the tail needs to have a high taildown force, resulting in more total lift required, resulting in a higher angle of attack and thus a higher stall speed.

So it says that you need a high taildown force (bottom 4 lines).
it also says small control movements make big pitch changes (top 3 lines). This is because the long arm.
In the teeter totter principle see the change of weight at the end of the arm as a control deflection. Forward cg: You got a 400lb guy (cp)at 1 foot from the fulcrum (cg) and you put a 100lb girl at 4ft (elevator). You hand here a 6 pack of beer (small control input). She will sink and the fat guy is almost launched of his seat (pitch change).
With an aft cg the guy now weighs 100 lbs at 4 ft from the cg and the girl gained weight and is now 400lbs at 1 foot. You give the girl the same 6pack of beer (small control input) and nothing happens. you give her a case, little happens. Another case (by now a large control input)and slowly she will sink and the little guy goes up slowly (aircraft pitch change).

The strong taildown force does not effect a trimmed airplane in the way control forces act, it does however effect your total lift that's required and the consequent increase in stall speed.
Remember here that everything that is pulling down, weight acting through the cg and in addition to that the tail down force, has to be compensated by lift to stay in level flight.

When I was teaching I would draw a little airplane with a fixed cp and put in the different cg positions, the effect it has on the taildown force, the change in angle of attack and what that does to the stall speed (the more lift required, the higher the angle of attack required for level flight. Wing stalls at 15 degrees angle of attack, so the more more lift you need, the smaller the margin in angle of attack so you reach the 15 degree limit at a higher airspeed. It also showed what kind of control inputs were needed to make things move.
It's a simple way, without any technical terms and everyone understood it, including people that had not completed high school.

Disclaimer: if you want to get a guys attention or explain something to him it either has to involve beer, woman or sex, but preferably all of them. Wise words from an old groundschool instructor / check airman

 

[Mickey]

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[Skaz]

stop stop.....you guys gave me a headache by making it so bloody difficult to understand.
its like warp field dynamics...pretty simple really, ahem....

right, the average a/c has two wings (not counting fin or props thanks). with me so far ?

the front wing (the wing) and the rear wing (the horizontal stabilizer)

the centre of pressure on the wing is usually aft, at straight and level flight. This means that the LE will tend to pitch down uncontrollably.....if the a/c has only the main wing. Now the function of the horizontal stabilizer is to prevent the wing and thus a/c from pitching nose down and fluttering outta the sky like a leaf. It does this by exerting a downward force, or you can say it generates lift the opposite way to the main wing, i.e. downward. Imagine a see-saw with the pivot point 1/2 way between main wing and horizontal stabilizer.

What is the overall effect of the downforce produced by the tailplane/horizontal stabilizer.......................anybody?


ok ok, t increases the overall weight of the a/c.

no really, it does, by adding downforce to the total aerodynamic equasion. (spelling?)

So.....if you have a forward CoG, then the tailplane has to produce a Greater down force to counteract. THis has a number of effects. Firstly it increases the overall 'aerodynamic' weight of the a/c. This results in a higher stalling speed as well., and methinks.........results in a smaller stalling angle because of increased effective AoA.

Now.....what happens if you move pax or cargo rearward? The CoG moves aft, of course. An aft CoG, within limits naturally, will result in LESS downforce needed by the tailplane, thus less aerodynamic weight added to a/c & so reduces the stalling speed. Once again, talking under correction, but methinks it should then increases stalling angle (bigger) because of decreased effective AoA.

simple heh.....what was the question again?

 

[midlifeflyer]

stop stop.....you guys gave me a headache by making it so bloody difficult to understand.

I just know I'm going to get in trouble with this one. I once got completely taken apart, chewed up and spit out for even suggesting it:

Start with definitions. Like any field that has it's own language ("terms of art"), there are common words that have very specific aviation meanings. In aviation terms,

stability: the tendency to return to a desired condition when disturbed
controllability: how easily the body responds to control inputs. (Not how easy it is to maintain control)
maneuverability: the ability of the body to withstand the stresses of being pushed around. (Not how easy it is to maneuver something)

I mention these because these are not necessarily the way these words are used outside aviation. For example, something can be highly "controllable" because it responds too easily to control movements. If it is also unstable, though, it will be very, very difficult to "control" in the lay sense.

I sometimes use a skiing analogy. Let's stick to the flat blue runs. There is an ideal part of the ski for your weight to be centered. Essentially, it's the CG that gives you the best balance between the ability to turn (controllability) and yet prevents you from losing control completely as the skis fly off on their own (stability).

Sit too far back on your skis and the skis become very "controllable" in the aviation sense. The smallest movement of your foot will make the ski fly of in another direction. Unfortunately, the ski's aft CG also makes it very, very unstable. Not only does the slightest foot movement send the ski in a new direction, but the instability magnifies the movement.

Move your weight forward, and the ski becomes very stable. Put it on track and it will tend to stay there. But have your weight too far forward, and it suddenly becomes more difficult to turn.

Not a very aerodynamic explanation and, unlike an airplane, skiers can constantly shift their CG to handle changing conditions. But a useful analogy for some.

 

[metrodriver]

the computer still has one major shortcoming: you can't draw the picture that tells a thousand words on the screen, I know there are programs that try to come close, but still. You got to translate the whole thing in words and that ain't easy. So maybe here is a way to make a million bucks in aviation: make something that allows you to draw a picture on the screen for use in groundschool and on aviation message boards.

 

[midlifeflyer]

the computer still has one major shortcoming: you can't draw the picture that tells a thousand words on the screen, I know there are programs that try to come close, but still. You got to translate the whole thing in words and that ain't easy. So maybe here is a way to make a million bucks in aviation: make something that allows you to draw a picture on the screen for use in groundschool and on aviation message boards.

http://www.groupboard.com/demo/

 

[flywithastick]

A related question that I was asking myself earlier in my learning was "Why can't you have an inverted see-saw with the CP in front of the CG, and thus having the tail provide lift and wasting no efficiency fighting downforce?"

You can - it's called a Long EZ, Vari-EZ, Starship... but the CP is still behind the CG. otherwise, it'd be unstable and fly about as well as a shoe.