Barbell effects in the pitch axis.

[Ted Fancher]

In the "Brain Dead" thread Eric V. asked me a question that sort of begs a separate thread.  Thought I'd start fresh on the subject.

Eric's post was: "Thanks for the most thorough reply Ted! I really do appreciate your thoughts. As long as your in the mood to type, if I may be so bold to post one follow on hypothetical question.

Let's say you had a plane that exhibits the barbell effect, say it came out tail heavy due to the nose is too short, so you add a bunch of lead to the nose and now it balances well on the CG, grooves well, corners sharp enough, but is hard to stop and start the turn consistently. If the airframe is still reasonably light at this point, could adding weight to the CG reduce the barbell effect? Am I making any sense?
Thanks!

EricV"

First of all,   I gotta make it clear.  I don't necessarily advocate adding weight to an airplane for its own sake.  Sparky and I can at least agree with the basic principle that airplanes have to have a reasonable wing loading to do the stuff we do.  We just disagree on how high or low that loading has to be to be competitive.

Eric's question, though, is a good one and something like it was actually begging to be asked as we worked through the numerous threads started or continued at length based on Sparky's design philosophies and his concern about motor mass and MOI.  That, in fact, is the underlying aerodynamic question asked by Eric above; in essence, requesting an in depth discussion of what the effects of weight masses at the ends of the barbell are in the pitch axis.

In theory, the simple answer to Eric’s question is, yes, increasing the overall weight of the airplane will reduce the MOI of a given concentrated mass at the end/s of a given “barbell”. 

Is that a good idea?  Better yet, are you apt to encounter the problem Eric postulates in the first place?

I think the second question is the one that needs to be answered first.  Let me give a real life, empirical, example and then expound on what the experience might teach us.

Back in the ‘70s I built and published the Imitation, a “complex” profile – if there is such a thing.  Among other adjustable features built into the ship was the ability to switch engines easily, using an RC style engine mount on a flat firewall mounted to the nose.  I did, in fact, try about six or seven different engines (this was just about the start of the use of schnerle ported stuff in stunt), the last of which was a rear intake Enya .46 four cycle.  This was by far the heaviest of the engines used and, because of the rear intake etc. had to be located further forward than any of the lighter two strokes.  That, of course, required adding lead to the tail to bring the airplane back to the preferred CG location.

In other words, I did exactly what Eric was postulating.  The overall weight of the airplane was then around 62-3 oz, by far the heaviest wing loading of its long career; and it had a lot more weight in the nose and tail than originally envisioned.
 
To make a long story short, it was by far my favorite set-up for the airplane and the only configuration I recall actually flying in a contest environment.  There was no noticeable effect of the added weight at both ends of the longitudinal barbell.  If anything, the pitch response seemed just a bit more controllable and easier to start and stop “reliably”, the key word being reliably (as opposed to "quickly").

And, no, in response to Eric’s ultimate question,there was obviously no reason to add weight to the CG to battle any ill effects of the increased barbells.

The following discussion may be a bit controversial to those who embrace long standing convention.  I certainly understand that there might well be some rebuttal to the following theory.  I look forward to reading it. 

To be specific, I’m going to take exception to Bob Gialdini’s suggestion that we actively minimize barbell effect in the pitch axis; a concept that became stunt gospel almost instantly upon publication of his excellent Olympic article published in American Aircraft Modeler back in 1963.  This convention is, of course, at the heart of much of the differences between Sparky and me.

As Eric’s question suggests, the concern of Bob (Gialdini) -- and most every stunt flyer since -- has been that concentrated weight in the nose and tail will act like concentrated weights at the end of a barbell and make pitch changes harder to start as well as harder to stop once they are started.  The theory is, of course, true.  The question becomes one of degree.  How much of the barbell effect will there be and what will be the consequence of it.

Let’s look at an obvious barbell effect that doesn’t really concern us a lot in a controlline airplane but is a very big deal with free flying ones.  That is the barbell effect of concentrated masses at the wing tips on the roll axis.  Then we can compare what happens there to what happens in the pitch axis and see how they are different and how any difference may modify our concern about it.

Mass at the tips of the wing (like tip tanks) when accelerated acts about a “fixed axis of rotation”.  If you do a complete roll there will 360 degrees of rotation around that axis in whatever time it takes to complete the roll.  The greater the concentration of weight at the ends of the rotating mass the greater will be the control forced necessary to both start and stop it.  All the while the roll is taking place it is occurring about that fixed axis running from the nose to the tail.  Almost like spinning a bicycle wheel while holding onto the axle. 

No matter what we do with that axis, the weight spinning about it will act in the same manner (there will be other effects, like gyroscopic precession of course, but that will have no effect on the ease or difficulty of starting and stopping the “roll about the longitudinal axis”).  The affects are large and they are real.

IMHO, the barbell effects in the pitch axis are only a small fraction of those encountered in the roll.  This is for the simple reason that the actual “rotation of the ends of the barbell” about their axis of  rotation – from wingtip to wingtip in this case – is only a matter of a few degrees.  The airplane's rotation about the pitch axis is quite literally only enough to establish the angle of attack required to develop the lift necessary to support the “g” loads in the pitch maneuver being performed.  Once that angle of attack is achieved, "rotation" stops and there will be no further “rotation of the concentrated masses” about the spanwise axis.  Thus, no sustained barbell effect.

Once the airplane achieves that necessary condition it simply tracks around the circumference of the desired maneuver arc.  The CG now becomes the only mass of concern, primarily in terms of where it is relative to where the lift which supports it is developed.  Once again, if the CG and that “center of lift” are separated by a significant amount the amount of control input necessary to maintain the desired rate of turn may change BUT there will be little or no change of the angle of attack that results.  You still are looking for the same amount of lift which will require roughly the same angle of attack around the loop (for instance).


There is actually some school of thought that says a flapped airplane doesn’t even need to change the body angle to achieve the A of A necessary to maneuver.  That the mere deflection of the flaps increases the angle of attack to that required without ever “pitching the airplane around the pitch axis”.  If that point of view is accurate (and, in theory in could be) there would be NO barbell effect whatsoever in the pitch axis.

To the extent that barbell effect in the pitch axis  is real in a stunt ship, I think (as in the Imitation example above) it could, within reason, be beneficial to performing maneuvers that get good scores.  Given the modest amount of pitch rotation necessary to achieve the necessary angle of attack, it is safe to say that any reasonably competent stunter would have the control effectiveness necessary to achieve that AofA.  It might take a bit more input if there is a “larger” MOI, but it would almost certainly be well within the ability of both the pilot and the airframe.  (This is part of the reason that many modern designers advocate the use of larger axis control systems, four inch B/C and long horns, for instance).

Were you to minimize the MOI in the pitch axis to zero (mount the engine, etc. at the desired CG, like the Bell Aircobra), for instance, pitch inputs would be instantaneously effective (no dampener) and very difficult to start and stop at a precise 90 or 120 degrees which is essential to flying high scoring maneuvers.  I don’t think that would be desirable for a stunt ship.

An increase in MOI due to a modestly greater barbell effect could (and likely does) act sort of like a shock absorber in corners, allowing (requiring, really) more positive control input by the pilot and, therefore, a more controllable pitch change.  This is another example of dampening not unlike the discussion of pitching moment from flaps and the slightly out of trim conditions used by the Blue Angels, Thunderbirds, etc. to allow greater precision in flight track.

Eric, that’s my “take” on this stuff.  I know it is somewhat heretical and could generate some opposing opinion and theory (maybe even some actual facts from some of our more competent contributors.

Ted

[Eric Viglione]

Wowsers!  

That's gonna take a minute to absorb... but I think I get the gist. Yeah, I didn't really foresee a practical situation for application, but the theory intrigued me and the question begged to be asked. One of my follow on questions I was holding back was a "what if" where you spread the weight added to the CG over a larger central area in order to avoid creating a "fulcrum"  for lack of a better word, or somehow making the very situation we are trying to fix worse somehow. I know I've heard theories on multi engine semi scale stunt planes that stated putting the engine pods on the leading edge of the wing was a good way to reduce the control forces needed to turn and a reduction in barbell. But it would seem you are saying the center of lift distance from the C/G already would essentially spread the "fulcrum" ?

I may have spoke too soon and need to re-read your post, which I will. Thanks again, this has been a treat.

EricV

[Dick Fowler]

Worth being returned to the top for additional exposure.

[Alan Hahn]

A couple of comments--from a physics perspective.

First, adding weight to the COG will have no impact at all on the moment of inertia around that axis. After all the moment of inertia is calculated by multiplying the mass x the square of the distance from the COG. "Obviously" if the mass is at zero distance, there is no contribution to the moment.

Secondly I wasn't able to follow Ted's argument about rotation around the pitch axis. It seems to me that since the nose of the airplane does a 360 degree rotation in a loop that something is making it rotate. It is true that it is the lift (and other forces acting along the control lines,aka the centripetal force) which provide the overall force which makes the entire plane move through the path of the loop. But it is the elevator which keeps the angle of attack positive to provide the force (and keeps the nose pointed in the right direction. Admittedly the rotation rate is pretty small for a standard loop, but in a square maneuver, the rotation through 90 degrees in a corner is pretty fast. In this case a lowering of the moment of inertia  should keep the elevator motion smaller (less torque is needed to accelerate plane about the pitch axis to give a positive AoA).

Anyway that's how it looks to me.

[Eric Viglione]

Yeah, I know what you are saying, but I can't help but think  what you describe is more of a static object scenario. I keep picturing going down the highway in my car with my hand out the window playing with the wind... Once the wind catches the flat of my hand, or in our case the flat of our wing past the highpoint, the thing is going to complete the rotation almost by itself. It would seem to me the hardest part is to start the turn, or break away from the direction we are headed. The tail would seem to do this by being knocked down when the elevator goes up, and also leveraging against some imaginary fulcrum near the center of lift and CG, hence lifting the nose. At least, in laymens terms, that appears to be what's happening to me. The trick would seem to change AOA without loosing flow and causeing seperation and a stall, and also without inducing too much drag. I would think where the barbell effect would come in, is it would start as drag going into the turn, and act as inertia when  trying to stop the turn. But then again, I'm probably out to lunch. 
EricV

[Dick Fowler]

A couple of comments--from a physics perspective.

First, adding weight to the COG will have no impact at all on the moment of inertia around that axis. After all the moment of inertia is calculated by multiplying the mass x the square of the distance from the COG. "Obviously" if the mass is at zero distance, there is no contribution to the moment.

Secondly I wasn't able to follow Ted's argument about rotation around the pitch axis. It seems to me that since the nose of the airplane does a 360 degree rotation in a loop that something is making it rotate. It is true that it is the lift (and other forces acting along the control lines,aka the centripetal force) which provide the overall force which makes the entire plane move through the path of the loop. But it is the elevator which keeps the angle of attack positive to provide the force (and keeps the nose pointed in the right direction. Admittedly the rotation rate is pretty small for a standard loop, but in a square maneuver, the rotation through 90 degrees in a corner is pretty fast. In this case a lowering of the moment of inertia  should keep the elevator motion smaller (less torque is needed to accelerate plane about the pitch axis to give a positive AoA).


Anyway that's how it looks to me.

That's funny Alan, because I went through the exact same though process regarding the 360 deg. of rotation in one loop. I think Ted mentions somewhere in his post about Newton's First Law which covers what's happening. The plane is rotating about the CG at a relatively uniform rate. Inertia only becomes an issue when the object is accelerated. By definition an acceleration is a change in velocity but the rotational velocity of the plane is constant through the loop, therefore no inertia effects, no barbells.

By the way, that section within Ted's post is a real nugget and explains why beginners with safe set-ups, do a lot of figure nines until they learn to loop.

[don Burke]

"A couple of comments--from a physics perspective.

First, adding weight to the COG will have no impact at all on the moment of inertia around that axis. After all the moment of inertia is calculated by multiplying the mass x the square of the distance from the COG. "Obviously" if the mass is at zero distance, there is no contribution to the moment.

......."

I have to disagree with your first statement.  The total MOI is the sum of the MOI of the individual elements about their own neutral axis, plus the sums of their individual masses times their distance from the CG, squared.  Weight added at the CG will not have any contribution to the overall MOI only if it is a massless concentration of weight.  Since most weights do have physical dimensions there is some contribution, but it is very small in comparison to masses at some moment arm, the engine for example. If one assumes a rectangular blob at the CG that is symmetrical about the CG, it's MOI contribution in the pitch axis will be it's mass times 1/4 it's length in the fore aft direction squared, that is it's physical MOI about it's neutral axis in pitch.  That is, it's two butt-joined barbell blobs.

What this has to do with the general discussion is probably insignificant.  It's just a point I felt needed to be made.   


don Burke

[phil c]

"There is actually some school of thought that says a flapped airplane doesn’t even need to change the body angle to achieve the A of A necessary to maneuver.  That the mere deflection of the flaps increases the angle of attack to that required without ever “pitching the airplane around the pitch axis”.  If that point of view is accurate (and, in theory in could be) there would be NO barbell effect whatsoever in the pitch axis.

To the extent that barbell effect in the pitch axis  is real in a stunt ship, I think (as in the Imitation example above) it could, within reason, be beneficial to performing maneuvers that get good scores.  Given the modest amount of pitch rotation necessary to achieve the necessary angle of attack, it is safe to say that any reasonably competent stunter would have the control effectiveness necessary to achieve that AofA.  It might take a bit more input if there is a “larger” MOI, but it would almost certainly be well within the ability of both the pilot and the airframe.  (This is part of the reason that many modern designers advocate the use of larger axis control systems, four inch B/C and long horns, for instance).

Were you to minimize the MOI in the pitch axis to zero (mount the engine, etc. at the desired CG, like the Bell Aircobra), for instance, pitch inputs would be instantaneously effective (no dampener) and very difficult to start and stop at a precise 90 or 120 degrees which is essential to flying high scoring maneuvers.  I don’t think that would be desirable for a stunt ship.

An increase in MOI due to a modestly greater barbell effect could (and likely does) act sort of like a shock absorber in corners, allowing (requiring, really) more positive control input by the pilot and, therefore, a more controllable pitch change.  This is another example of dampening not unlike the discussion of pitching moment from flaps and the slightly out of trim conditions used by the Blue Angels, Thunderbirds, etc. to allow greater precision in flight track.

Eric, that’s my “take” on this stuff.  I know it is somewhat heretical and could generate some opposing opinion and theory (maybe even some actual facts from some of our more competent contributors.

Ted"

Got some physics problems here.  The barbell effect comes from the rotation of mass about an axis.  Whether flapped or unflapped, the plane is moving about the center of rotation of the turn, whether it is a big loop(small effect) or a "square" corner(more effect).  Once you start the rotation the MOI of the plane wants to continue at the same rate.  It takes another force to stop the rotation.  This comes from neutralizing the elevator(removing the downforce), allowing the CG to do its thing and drag the plane back onto a straight path.

Damping- the barbell effect always accentuates what happens in the maneuver.  It's a main cause of overturning or "hopping" in square corners.  The plane wants to keep turning and goes past the desired angle because the pilot can't move his hand fast enough to stop it.  Any "damping" the pilot observes is reduced control response due to it taking extra effort to start the plane turning and to stop it turning.  The only thing that stops the turn is the aerodynamic effect of returning the elevator to neutral.  This comes from the tail volume and the location of the balance point.  If the plane has severe barbell problems it may even take some reverse control to effectively stop the turn quickly enough.  This is visible in some of the videos I've seen.