Yaw and leadouts on pictures after all

I see my texts are not very clear, so I did some pictures. Hope this will show what I mean. I do not know if my ability to make self explaining pictures is better than my English, but I hope all together will be enough to understand what I mean after all.

So first of all usual understanding what is happening here.

I assume:

1/ Model is tangent to the circle
2/ fuselage & engine has no side aerodynamic forces
3/ lines are outside of wing
4/ bellcrank (BC) is at (CG)

Here is Ted’s visualization from "Bellcranks and CGs redux":

We have dragy lines and moving mass point CG at end of them. Centrifugal force of CG makes tension in lines, so they tend to be straight, but drag makes its usual curvature.

So let’s call the centripetal force Fc. The line drag of lines Fd. It is clear, that stable situation is, if the angle makes another force Fy which is in size equivalent to Fd but with opposite orientation. All is on pic1.

[photo not recovered: 41b07e8a68e375b0.jpg]

Static (flat) theory tells us where to put lines in leadouts to keep tangent position of fuselage.

So we know the shape and we can convert the CG point to real model and fix lines on place, which will match actual position of lines. Nothing happens. Line drag is counterbalanced by centrifugal force of CG to LO position and forces are balanced. Pic2.

[photo not recovered: 41b07e93690541a8.jpg]

Now assume that we have the same model and we fly overhead. The shape of lines curve is different, because the force FC is less gravity FG. The drag is the same. It means lines are more round. Pic3.

[photo not recovered: 41b07e9b6944e532.jpg]

Therefore if LO is in wing fixed on the same place, the nose will yaw inwards. That is happening because CG position is not aligned with LO position and therefore any change in that force leads to yawing. Pic4.

[photo not recovered: 41b07ea269527a9d.jpg]

Such a model is not flyable, so “flat” theory cannot work for aerobatic model. … at least at those conditions over.

Now another try.

Assume that we have little bit functioning rudder and it makes constant force Fr on tail. Tail is of the same length as wing. So that force is permanently yawing nose out and thus inboard tip forward. Just opposite than the line drag Fd is. Pic5.

[photo not recovered: 41b07eab696dd574.jpg]

It means that it is the force, which counterbalances line drag instead of CG position. If we want reach no friction in LO, we must put BC far forward, but we know that BC position has no effect to yaw and thus we can live it in CG.

Both line drag and also force on rudder are aerodynamic forces and every change in speed has proportional effect to both of them, so they are in balance at every speed. It means that CG can stay aligned with LO not making any yaw.

As the CG is aligned with LO and not making yaw, then also variation in line tension does not make any VARIATION in that nonexistent yaw. Aerodynamic forces are still in balance, thus also if curvature of lines is different, the resulting stable orientation of fuselage still tangent. Pic6.

[photo not recovered: 41b07eb369d25c55.jpg]

We can fly overhead or strongly pull handle and model will still keep its angle.

It is not only CG or (exclusively) only rudder what can balance the line drag. They can work together. Assume the rudder is little smaller and its effect is too small for line drag. Its force is not enough, model tends to yaw in, but we can put lines little back and give CG chance to balance the rest. No problem, but it will make lower line tension overhead.

Opposite situation – if rudder is stronger than necessary, it will lead to opposite situation. We will move leadouts FRONT, CG will fall aft of LO thus not allow outboard yaw caused by excessive rudder force (Fr>Fd) and we are still at tangent position. But lack of line tension will point nose OUT … Dick, are you watching? No gismo, no screws, no tricks, just simply proper design/trim. It means LO moved forward will improve line tension overhead – sounds familiar?

I am not calling for any change. We are able trim models and they fly well. I am only explaining what is happening here. So if we use calculation in hope that “flat” theory is proper and works also for our stunt models, then we simply get situation on pic 2. But we fly on circular path and that makes forces permanently yawing out. The CG can in that case fall to in-flight level of LO, or front of or aft of LO. That situation is on Pic 7.

[photo not recovered: 41b07ebd6a2d685a.jpg]

So the rudder, LO position can very effectively place CG on proper place making that proper response not allowing too much yaw, but also keeping good tension overhead. Pic 8 shows detailed configuration. Fvr is variation of line tension and it gives idea what is its effect on yaw.

Quote - "Opposite situation – if rudder is stronger than necessary, it will lead to opposite situation. We will move leadouts FRONT, CG will fall aft of LO thus not allow outboard yaw caused by excessive rudder force (Fr>Fd) and we are still at tangent position. But lack of line tension will point nose OUT … Dick, are you watching? No gismo, no screws, no tricks, just simply proper design/trim. It means LO moved forward will improve line tension overhead – sounds familiar? "

Interesting.... One question. When the model changes speed (slows down) doesn't Fd increase (Z+) but Fr decreases (Z-) so it should still yaw nose in? Are you suggesting a coupled rudder of sorts. I didn't think so.

So I take it that the old timers were right when they built models with rudder offset.

Problem with your idea is that it isn't as much fun as mine! Where's the challenge? We all know that the more things to tweak the more fun we have.

What you drew was what I thought you were talking about way back in the begining. Nice work.... solid illustrations. Welcome to the 21st century!

No, line drag and also rudder lift depends on square of speed.

May be there are some minor differences in line drag coefficient, but for this example we can assume it is constant. In this example are ignored much stronger influences. … like line weight if nose pointed up, or even line swinging.

I see you are another gentleman not judging my ability ... only little bit telling me about my inability

>No, line drag and also rudder lift depends on square of
>speed.

Got it - Failed to consider that when tension is reduced (slow down or wingover) and the angle of the line entering the wing increases the drag on the line is reduced so the resultant torques from Fd and Fr both get smaller. Still a zero sum game.

Igor,

BEAUTIFUL!

Only one little thing still nags at my thoughts... And it is why I spoke in terms of misalignment of 'pull' force from CG.

From both our spreadhseets, the actual value of line drag is too small to have that much effect on yaw - IF we consider it as acting as a 'drag tab' effect at the leadout guide position. Or did I foul up on units translation again <g>.

The rest of the pretty strong force needed can be provided by the torque of pull's line of action NOT passing through the CG when the yaw changes.

Of course, curvature of the lines changes with height: static weight (mass) picks up an inward component along the lines when the lines are ABOVE perpendicular to gravity's direction. Gravity and lines are only perpendicular in level flight.

Speed also decays in high flight and maneuvers, and c-force has only the terms: mass, radius and speed.

As you show so well and clearly, to account for the changing "line rake" effects, we use a trim condition that on purpose is not ideal for level steady flight. We can also use other techniques, which, again you showed very clearly.

Thanks for the great work!

>>>From both our spreadhseets, the actual value of line drag is too small<<<

First of all I do not know how precise is that calculated drag. I found some disproportions to Pete Soule's program. It will really need go foot by foot, check proper drag coefficient from RE number, for used line type, consider lines induced drag if they are close or behind …

That my worksheet is not program so it only estimates drag in some not known precision. It must work on field in PDA, that is the key. I crashed in Muncie and I had to retrim another model to my hand. I have no idea how I could do it without that spread sheet successfully.

>>>to have that much effect on yaw - IF we consider it as acting as a 'drag tab' effect at the leadout guide position. Or did I foul up on units translation again <g>.<<<

Simplest way is to use that “flat” theory and get line drag from CG offset. If it is one inch front of the LO, if the weight is 50oz, if the CF acceleration is 4G, you know the line drag effect on wing. If I fill it with data of my model, then the force on tip is ~2.8N that makes ~10oz and it is enough I think.

Anyyway, if this my new theory is proper, then that piece of spread sheet is bull ##### … I must repair it … but I still do not know how to calculate fuselage yawing moment, it looks I have enough fun for Christmas

Thanks, that was very useful.
I appreciate your efforts with both the text and illustrations.

Thanx, looks like "picture" letters works better for me .

Igor,

Your drawings and analysis are great. You have done a splendid job in describing the unique attributes of control line flight.

A question - what would you predict if your Assumption #2 is not zero?

I've always thought that the fuselage had a knife-edge flight characteristic (as in RC). This is due to the geometry and the circular flight resulting in an angle of attack sufficient to cause some lift along the length of the fuselage. Of course, as in RC flight, the rudder also has the effect of increasing the angle of attack until sufficient lift is obtained to maintain level flight (on its side).

The propwash and engine torque may also exert a force in opposition to the rudder, and probably at the rudder. This force will vary with the speed of the engine, not the airspeed.

Both effects may be small enough that they can be ignored, but the first one is certainly enough to lift an entire plane for sustained flight under the right circumstances.

Am curious to hear your view ... thanks.

This looks like a pretty good review of Bill Netzeband's article in the July 1966 issue of American Modeler, the Rosetta stone of control line dogma.

Igor VERY nice, I think I am beginning to understand! On combat models, with no side area to speak of, we just move the leadouts back and yaw out the plane as there is only a small effect on the drag. Stunt trim is not that simple!

>>>Stunt trim is not that simple!<<<

I think that really this is the point. Another model needs another tricks. I have no idea how to design / trim combat, but I think you must have similar situation. Did you try longer inboard panel? I think it will not work well. You do not have rudder, but you have high speed model and short lines and thus large effective engine offset. At that high speed, prop makes relatively large thrust and on long arm to the AC of wing makes outboard moment. And here we are - aerodynamic moment against aerodynamic drag. The same trick.

Yes Tom, the fuselage does lift. But opposite - toward the circle. At least if it is tangent. Therefore I think it is better to have little yaw out - small, but positive - at least to keep it at zero lift.

Regarding those "small components", they could be small, but all of them together makes clearly visible effect. The fuselage is not very small ... may be not very large, and if it should be wing, then also aspect ratio is small ... however if I remember then I feel wind on my handle very well