CG, COL, COP and all things complicated

I have a couple of questions I hope someone can explain to me in plain language. I get confused easily

1) When speaking of wings and airfoils, does "center of pressure" and "center of lift" mean the same thing?
2) how does CG position in relation to COL(center of lift) relfect on plane's behavior? My initial reaction is that if CG is ahead of COL, at high AOA, the plane will tend to rotate back towards lower AOA. If CG is behind the AOA, the plane will tend to overrotate. Of course, I assume all other variable being equal. Does position of CG in relation to COL have ANY affect on plane's tendencies?

This is a follow on question to questions one and two:
3) how does one go about figuring out position of COL?

>I have a couple of questions I hope someone can explain to
>me in plain language. I get confused easily
>
>1) When speaking of wings and airfoils, does "center of
>pressure" and "center of lift" mean the same thing?

Dont know on this one.

>2) how does CG position in relation to COL(center of lift)
>relfect on plane's behavior? My initial reaction is that if
>CG is ahead of COL, at high AOA, the plane will tend to
>rotate back towards lower AOA. If CG is behind the AOA, the
>plane will tend to overrotate. Of course, I assume all other
>variable being equal. Does position of CG in relation to COL
>have ANY affect on plane's tendencies?

The way iy was explained to me was that the COL will always be behind the CG. This will be the case on all airplanes real or models. If the CG is to close or behind the COL then the plane becomes unsatble and will not be flyable.

>
>This is a follow on question to questions one and two:
>3) how does one go about figuring out position of COL?
>

I have asked that many times and no one has been able to tell me how. They have told me that it is really insignificant. I think they are right. Where it falls on the airframe really means nothing. If you add more lift in the tail you will move the COL back and the CG comes back also. And vice versa should you add more in the wing and leave the tail section alone. All you really need to worry about is the placement of the CG.

>
>Steven Yampolsky
>Webmaster for www.control-line.org

At low mach numbers and our model's typical reynolds numbers, I would have to say Doug is right. No worries on the COL. Also he flies well. And you have done a great job on the PAMPA website! Thankyou!

LAST EDITED ON May-11-04 AT 11:29 PM (CDT)
 

As far as I know the notion of "centre of lift" is not part of full scale aerodynamics.
Airfoil polars(?) are plots of lift, drag and pitching moment about the 1/4 chord vs angle of attack. The forces on a wing section form a "couple". They can't in general be reduced to a single force acting at one point. There will be a torque trying to twist the wing as well. This torque is independent of the lift coefficient and for lifting sections is nose down. The quarter chord point is sometimes referred to as the "Aerodynamic centre".
Symmetrical sections are a special case, and at the 1/4 chord there is no pitching moment. In this case you could say the lift was centred at the 1/4 chord. The plot of Cmc/4 is a flat line. The shape of the section, L.E. radius, where the maximum thickness is, has no effect on this.

This is based on both theory and measurements.**

Pat MacKenzie

** Theory of Wing Sections, Abbott and Von Doenhoff.

>As far as I know the notion of "centre of lift" is not part of full scale aerodynamics.

It used to be. The problem was that the calculated center of lift could - and often did - move off the wing entirely, even to infinity. The moment about the quarter-chord point was felt to be a more useful concept, especially for comparisons.

The longitudinal (fore-aft) position of the quarter-chord point of the mean aerodynamic chord is, in my opinion, an important place to know. For instance, George Aldrich would have had more success with his "Magnum", had he positioned c.g. and leadouts relative to this point. As Pat says, lift will be considered to be centered here, until flaps are deflected. Then it moves aft.

SK

LAST EDITED ON May-13-04 AT 05:07 AM (CDT)
 
>>>The longitudinal (fore-aft) position of the quarter-chord point of the mean aerodynamic chord is, in my opinion, an important place to know.<<<

Yes, that is aerodynamic center (AC) where are all aerodynamic forces referenced. The lift vector is positioned there and oriented up, the drag vector is pointed there a oriented back and the moment vector is pointed on begin of mean aerodynamic chord (MAC), it is oriented up and makes moment to the AC – means the arm is 1/4 MAC.

The center of lift (CL) is positioned on place where you can “load” the wing without any pitching moment. You can find its place from knowing the lift and the pitching moment. If the pitching moment is zero, the CL is at AC. If you have some pitching moment – it is typically negative – meaning nose down – you must move the “load point” chord wise aft to make counter moment equal to the pitching moment of the same value.

It means the pitching force from pitching moment coefficient cm multiplied by 1/4 MAC arm must be equal to lift from lift coefficient cl multiplied by distance between AC and CL:

{moment} x {1/4 MAC} = lift x {CL shift}

means the distance from CL to AC is:

{CL shift} = {moment} x {1/4 MAC} / lift

The moment is typically independent on lift and thus it can really easy to be of higher value than lift and thus at low lift the CL can be really far away from MAC. That is why we use AC instead of CL.

If you sum all pitching moments:

1/ CG moment as ({gravity} x {lift}) x {CG from AC arm}

2/ lift of tail as {tail lift} x {AC tail from AC wing arm}

3/ {wing cm moment} x {1/4 MAC of wing} plus {tail cm moment} x {1/4 MAC of tail}

4/ mass inertia moment (if accelerated pitching)

then you have all pitching moments which are always balanced and the sum is ZERO, and it allows you to recalculate unknown value from those known. For example from position of CG you can recalculate necessary tail lift.

It also allows extracting much simpler way for stability. There is something called neutral point (NP) what is point on AC of wing to AC of tail line. It is point, which divide that line in reversed value of wing to tail area. If the CG is front of that point, the model is stable. That is called static stability. But it ignores pitching moments and so if the CG is very close to NP it can be stable but also unstable. So we have something called “reserve of static stability. It has percentual value how far is CG from NP compared to the distance AC of wing to AC of tail. Higher value means more statically stable vehicle.

(I promise it is all true …… if I did not miss something … please check or ask if something unclear)