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Leadout position for overhead fuselage tangency?

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Peter Germann:
Thanks for establishing the engineering board, I really appreciate, and enjoy, this very much.

Here is a question for you:

When using lineIII to define leadout position the result shows a number valid for horizontal flight with x amount of fuel. Nice.
However, would it not be at least equally important to avoid yaw when flying overhead?  Therefore, what shall I do to calculate the leadout position leading to accurate fuselage tangency when flying through the top of the hemisphere with approx. 1/4 of fuel on board, such as when flying the top segment of the hourglass manoeuvre?

regards

Alan Hahn:
I don't have the formulae, but when you are overhead I have to believe (my data recorder with airspeed from ~1.5 years ago supports it) that the airspeed is slower. So line drag also should be less (and I think gravity when the plane is above 45 degrees tends to be along the line direction). This would argue for leadouts more forward. How much of course is your question.

I am not sure what exactly LineIII is calculating--the optimum position for level flight, or does it have a built in fudge factor to account for the overhead difference.

Dick Fowler:
Posted on SSW By Igor Berger. A rather interesting approach and runs contrary to some people's opinion.


 http://www.clstunt.com/htdocs/dc/dcboard.php?az=show_topic&forum=103&topic_id=130453&mesg_id=130453&listing_type=search

Yaw and leadouts on pictures after all"
Fri Dec-03-04 03:55 AM

           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.



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.





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.





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.




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.





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.





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.





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.









  
 

Peter Germann:

--- Quote from: Alan Hahn on June 24, 2009, 03:13:09 PM ---I don't have the formulae, but when you are overhead I have to believe (my data recorder with airspeed from ~1.5 years ago supports it) that the airspeed is slower. So line drag also should be less (and I think gravity when the plane is above 45 degrees tends to be along the line direction). This would argue for leadouts more forward. How much of course is your question.
I
--- End quote ---

Interesting, Alan. What exactly did your airspeed recorder indicate? I thought that my PA .75 adds sufficient power when I go overhead to maintain airspeed. If this would be so, then line drag would remain constant while line tension will be minus one G. I therefore believe, if speed is maintained and relative to the LineIII level flight setting, leadouts must go to the rear to get tangency while flying throught the zenith of the hemiphere.

Alan Hahn:
Peter,
Here is a link to a post I made. The first post has a plot of airspeed, altitude, watts input, and derived tangential acceleration (just subtracting adjacent airspeed points). I note that the airspeed magnitude is off based upon my lap times (indicated 54mph whereas the indicator gave ~45mph. But I think the variations are correct. I note that I run a governor on the prop and as I recall the rpm is somewhere in the 8000 rpm range (I think I mention it in the text).

http://stunthanger.com/smf/index.php?topic=7574.0

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