I was contemplating the question of what would be the results of combining the log rhythmic flap bellcrank and the exponential bellcrank for primary control input? As a result I was trolling around reading bellcrank posts trying to find a post by Howard where he showed some photos of 3D printed bellcranks he made as I'm working on creating one or several by my favorite method, plagiarism. When I read a post which stated longitudinal position of the bellcrank with respect to the CG makes no difference only the position of the lead outs. To this I have to take exception and challenge the individual(s) to produce a free body diagram showing how this can be. While it is true that if we hung the airplane by its wingtip leadout guides it would take a position as expected or stated. However, this is not how the cable running through the model works.

At the wing tip there is a force which is generated by the bend of the cables passing through the leadout guides. That force, in turn, creates a moment that must be reacted by a shift in position of the CG or cant of the model. The shift in cant can be calculated or diagramed. Certainly for small displacements it surely doesn't make a huge difference however the carte blanche statement that is makes no difference is, in fact, incorrect.

Sorry guys but this is Statics 101.

   It is indeed. Without going through this all again, just make up some examples and see.

         Brett

Such as the free body diagram I drew? or is this an agreement?

   It is indeed statics 101, you have missed something.  On your drawing, I don't see the forces drawn in, or at least not all the vector components. I just don't want to rehash something that was conclusively proven in all possible ways 20 years ago*.

    Brett

p.s. or to be picky, 500 years ago.

Sorry guys but this is Statics 101.

If you took "Statics 101" it was at a really high-class university (MIT maybe?)  Usually statics as a separate subject is taught at the 200 level in mechanical engineering programs, and in 200-level general physics classes.  So let's assume that "Statics 101" means "everything you should know about statics except the course number":

Statics 101 says that if you attach a hinged joint to a weight, and suspend the weight from that hinged joint, then the center of gravity of the weight will hang directly below the joint.

Statics 101 doesn't say anything at all about cables, except in the example and homework problems where it says "assume the cable is infinitely flexible"  Such a cable that's affixed to some point inside a weight and exits through a hole will act like a perfect hinge.  So, go back to my first statement.

Common sense, and an incredibly small amount of time spent looking at how leadouts behave when you're tugging them with far less tension than they're subjected to in flight, says that any deviation between normal leadout behavior and that idealized infinitely flexible cable is vanishingly small.  This is assuming that you have normal-sized leadouts, e.g. .027" for a big stunter.  The offset between the real exit point and the virtual one due to cable bending won't be more than 1/32" (I'm going from memory here -- you're welcome to test and document).  And where there is such a deviation, the degree of its effect will be subsumed under all of the other varying effects on an airplane, and will be taken up when you trim the thing.

If there's a lateral force on the cable where it bends, then to the extent that it's infinitely flexible -- who cares?  That force is internal to a rigid body -- and Statics 101 starts by saying "pay no attention to internal forces on a rigid body".  You don't start paying attention to internal forces until you take Strength of Materials, which you cannot enroll in unless you've passed Statics -- whether 101 or 200 or 201, or whatever the course number is.  If you absolutely must pay attention to that lateral force, then -- as a remedial exercise because you obviously did not pay attention to the first chapter of your Statics book -- I suggest that you calculate all of the forces and moments being exerted on a rigid body by a cable that is hinged at its point of exit from that body.  Pay attention to the forces at the hinge and at the attachment point.  Try it for various locations of the attachment point, or better yet let the attachment point be at some arbitrary position (x, y).  Then -- because you know Statics so well -- do the math.  You'll find that the location of the attachment point within the body drops out of the reckoning, leaving only the position of the exit point as having any bearing on torques and forces.

When you guys finish thrashing this one out please give us the answer in a form us non-engineers can understand  I read that years ago too and my reaction was "Bull****".  The point of attachment of the lines to the plane is the bellcrank, not the leadout guide and it seems strange they are not trying to align themselves in flight.

Ken

Grab a 1x6, maybe two feet long.  Drive a pair of finish nails into one end, centered on the board and maybe 1" in (so it won't split).  Better yet, use the smallest screw-eye you can find.  Now drive about half a dozen nails into the board, in various positions.  Make sure that a few of them are good "bellcrank" positions.

Grab a piece of string.  Tie a loop in the end.  Thread it through your screw-eye, and over one of the nails in the interior of the board.  Look at how the board hangs.  Move the loop to one of the other interior nails, look at how it hangs again.  Repeat until convinced.

Note that an effect that does happen (and that Mike Alimov mentioned while I was typing) is that if the bend is too sharp then friction will go up.  That is an issue - but it's not a problem with a 4 or 5 inch bellcrank in a 60" span wing, with the bellcrank located as forward as you can get it while still enjoying free movement.

If you don't want to go through the logic -- stop here, and go pound some nails into wood.

Basically, yes, the leadouts and the bellcrank are trying to align themselves in flight.  But the leadout guide is in the way, and forces a bend in the cable.  When the plane is hanging straight out from the leadout, the force needed to make that bend, and the torque that it imparts on the airframe, is exactly matched by the torque imparted on the airframe by the bellcrank.  Internal to the airframe, the bellcrank is trying to torque the airframe so that the cable is straight -- but this torque is exactly matched by the torque from the leadout riding on the leadout guide.

Mark,

The "pull" force passes to the model's structure by means of flexible 'cable(s?)' - the flying lines. The lines curve aft due to air drag and sag vertically downward (weight.)They do not form the straight theoretical vector from handle to CG.

The drag curvature ends at the leadout guides, where the leadouts go inside the wing. Exterior leadouts produce drag, but they are short and have little, if any, effect.   LINE*** apps estimate the curve. If a curved, flexible cable applies force in a direction not within its diameter, that creates a torque in yaw. Ideally, (CG to leadouts spanwise and lengthwise) the lines should not do this;  each should  practically 'float' in its guide, not applying force across either leadout...

The angle aft of CG-to-handle vector should  meet the angle of  curvature where the lines reach the leadout guides. That will 'aim' pull force through the leadout guides to the CG When flying level (equal force on each line.) Maneuvering requires more pull on one line - and less on the other - to move the control surfaces into the airflow to do the maneuvers.

Total Pull remains pretty much the same. Maneuvering does shift the 'aim point' through the leadouts within the distance between guides. That's why we think UP-line forward.  (Models (in CCW flight with CCW prop rotation try to nose-out on "inside" turns - and nose-in on "outsides.") Corners can make a strong prop procession moment in yaw, the shift of pull aim to the CG can help counter that ( to resolve the 'couple?'.)

Just read Ken's comment: Good stuff. The alignment of the hardware inside the model can have some effect. If the leadouts have a definite 'trail angle' from a bellcrank pivoted at the CG, it may be corrected by shifting the span of the bellcrank so that the span is perpendicular to it, we should avoid the "differential aileron" linkage situation. However, the pushrod linkages should be correct. If neutral means linkages move equally for equal angles from neutral both ways, e.g., Bellcrank to 'flap' horn should be square to model length and span, not any angle BC leadout  span has to equalize response angles.

Say wha-at? Try to picture this: BC Pushrod-flap hole squarely spanwise; BC leadout hole 'span' rotated, say, 5° CCW to  be perpendicular to leadout trail mid-angle.

I really like the way I manage to stir you guys up... Man, I just rub guys the wrong way. Thanks for being informative and descriptive in your replies. I spose I just need to go away and stop driving you crazy.. So, I figured this out on my way back from the airport. Summing the moments around the CG M1 from the tip to the CG is (L x Cos(theta)) x (T x sine(theta)) and the moment from the CG M2 to the attachment point is (L x sine(theta)) x (T x cos(theta))

Mttl = L x T x cos(theta) x sine(theta) - L x T x sin(theta) x cos(theta)

By observation both terms are identical Therefore the system is balanced. An interesting result I never thought fully through. I don't need a test piece to solve this one a bit of quiet time.

I guess I should have just been quiet. But now you have the correct mathematical solution which is easy.

Have a nice day.

Ok, Tim I am buying your explanation but I was looking at the overall question of where to place it and there are two very good reasons to put it as close to the CG as possible.  First is the angle that leadouts would form making it nearly impossible to make control equal with out designing a really strange crank or using a circular.  The other is the excessive pressure/rubbing on the leadouts which will introduce some yaw.

Ken

Those are good reasons to have things as centered as possible -- just as long as you understand why you're doing it.  My bottom line is that small deviations from "perfect" don't seem to screw things up -- this is one of those things that you can start obsessing on one detail of stunt design, then compromise everything else in favor of that one thing and suddenly you have a dog -- but a dog with really free and symmetrical controls.

Those are good reasons to have things as centered as possible -- just as long as you understand why you're doing it.  My bottom line is that small deviations from "perfect" don't seem to screw things up -- this is one of those things that you can start obsessing on one detail of stunt design, then compromise everything else in favor of that one thing and suddenly you have a dog -- but a dog with really free and symmetrical controls.

Tim, you nailed it.  I do what works.  I will try most anything but I end up doing what works.  Sometimes we do get stuck trying to make things to .0005 += 1/4".

Ken

     But, in any case, you are doing and thinking about interesting things, by all means, keep it up!

     Brett

Thanks Brett

I'm perfectly aware that at times my communication approach "lacks some finesse". Just ask my bosses. It wasn't and never is my intent to stir people up causing the dragons breath reaction. So, it's been hammered out many times in the past, new people don't know that. Perhaps a more understanding response would be appropriate. I'm often wrong when I shoot from the hip like I did on this one. However, you gotta admit, the mathematical proof is interesting and if'n that would have been the response, smoother communication would ensue. There's likely a day when our paths cross in person and creating hard feelings in a forum won't bode well in that event.

Thanks Brett

I'm perfectly aware that at times my communication approach "lacks some finesse". Just ask my bosses. It wasn't and never is my intent to stir people up causing the dragons breath reaction. So, it's been hammered out many times in the past, new people don't know that. Perhaps a more understanding response would be appropriate. I'm often wrong when I shoot from the hip like I did on this one. However, you gotta admit, the mathematical proof is interesting and if'n that would have been the response, smoother communication would ensue. There's likely a day when our paths cross in person and creating hard feelings in a forum won't bode well in that event.

  Well, again, you aren't creating "hard feelings" and I sure hope I am not. You have done nothing to offend anyone, at most a minor lack of tact, and you have nothing at all to apologize for.

   Just like anything else, posting to internet forums takes practice, you get better the more you do it, and the more you see how people react.

     Brett

     This makes me think of an OTS model that had a rearward bell crank location. The Gyrator?? I was thinking of the "other" Ringmaster" but that may not be correct. We're talking 60 years ago or more so more proof that there really are no new problems!!
     Type at you later,
     Dan McEntee

Dan,

You are correct about the Harry Williamson Gyrator (Man, Oct 52) that showed the bellcrank mounted where it just cleared the TE shear webbing and the lead outs swept back to near the TE.  I built two of these things and they flew quite well with the older OS Max .25, placing in the top five at several VSC's.  Builds light, Williamson's was powered by a Fox .35 and weighed 25 oz.  This is what he wrote about the rearward position of the bellcrank/leadouts:

"Notice the location of the bellcrank on the drawings.  Now, before you go tell the modeling world that Williamson has flipped his lid, leave us explain!  Locating the B.C. here was done for a dual purpose: to keep the ship tight on the lines through any maneuver and to provide a greater looping couple.  This can be seen by noticing its location with respect to the CG and the center of lift.  Unfortunately, this idea is not original -- all credit should go , we think, to Hank Cole who had it on one of his ships some years back.  It's a swell idea, though and again contributes largely to the Gyrator's performance."

Williamson suggested to notice the BC/leadout location "with respect to the C.G and the center of lift".  The plans do not show where the CG is and the article does not explain where it is.

The two I built had the BC/leadouts in a more "standard" location, like as near to the 25% CG as structurally practicable as allowed by our OTS rules.  Nice airplane.  In my opinion it is in the class of good Barnstormer.

Williamson made reference to a Henry (Hank) Cole design that used a rearward located bellcrank.  Cole published plans for his Super Looper (FM Jun 48), the fuselage was a sheeted crutch with the bellcrank mounted on the bottom of the fuselage, below the wing where the rear leadout was at the wing TE.  Cole makes no mention of the bellcrank/leadout location.  Described as a "stunt model trainer for any maneuver in the book."  Charlie Reeves flew one successfully at several VSC's.

(At that time, Henry Cole was a "Scientific Leader" for the AMA.  Reference his Arrowhead construction article in Air Trails, Oct 47.  This was a 40" swept back flying wing design with the bellcrank located near the CG.)

Keith

... That's why you don't necessarily want a 6" bellcrank in your Lil' Jumpin' Bean.

   Brett

Aw crap.  Well, if y'all will excuse me, I need to go rework a little bitty plane.

My egghead engineering side keeps wanting to visualize pulleys at the leadout positions, to allow for a ginormous bellcrank and get rid of that pesky friction.  I'm trying to keep it suppressed.

Aw crap.  Well, if y'all will excuse me, I need to go rework a little bitty plane.

My egghead engineering side keeps wanting to visualize pulleys at the leadout positions, to allow for a ginormous bellcrank and get rid of that pesky friction.  I'm trying to keep it suppressed.

No, keep thinking.   How about putting the bellcrank on the inside wingtip?

I am witness to two examples of what not to do with the leadouts.

1.  I have a 1/2A swept wing profile scale model where the CG is behind the wing root TE.  I did not want to have an exposed bellcrank which meant that I buried the bellcrank inside the thick part of the wing root which dictated that the leadouts had to follow the wing sweep to their proper exit from the wing LE relative to the CG which required a significant angular change in the leadouts at that position.  Using 1/2A leadout cables, I thought that the cables were flexible enough so that 1/8" dia steel pins at the leadout positions to guide the leadouts would allow leadout movement with little drag or friction.  The system worked.  I had control of the elevators as well as the throttle control through a Roberts type bellcrank.  The airplane had been flown probably fewer than 20 times when one of the lines failed the pull test.  One of the leadouts failed where it had to flex around one of those internally mounted steel pins.  At least, the model was not destroyed by an in-flight line failure and is now a nice wall ornament.

Conclusion:  The thing needed rollers or some sort of bearings for those leadouts to flex without rubbing anything.  (Or, the bellcrank could have been mounted in the inboard wing at the leadout position, but there was not enough room for it.)

2.  I was standing by a top 20 finalist at a Nats when he was pull testing his model for an official flight when one of the leadouts failed inside of the wing.  The failure was determined to be where it had rubbed against a landing gear wire.

Conclusion:  Do not let leadouts rub against anything, particularly steel wire, inside the wing.

Observation:  Evidently brass or nylon eyelets at the leadout guide do not have the same deleterious effect on flexible leadout cables as do steel pins constantly wearing on leadouts.

Interesting?

Keith

Conclusion:  The thing needed rollers or some sort of bearings for those leadouts to flex without rubbing anything.  (Or, the bellcrank could have been mounted in the inboard wing at the leadout position, but there was not enough room for it.)

I suspect that brass tubing with a much larger bend radius would have worked -- but the only way to tell would be to try it, and see how long the plane lasts.

No, keep thinking.   How about putting the bellcrank on the inside wingtip?

    That has been done also. Enter the Comet "Lil Schmoe", and neat little twin boom 1/2A model. I bought one as a kid because it was the cheapest thing at Schaefer's Hobby Shop. It had the bell crank at the inboard wing tip, and it drove a push rod wire that ran through some small aluminum tubing that arched back to the elevator. If I remember correctly, the bell crank wasn't a typical bell crank, and was asymmetrical, I think, with the rear arm longer that the front. The pushrod attached to the longer arm between the pivot and the rear lead out. It wasn't a stunt model by any measure, but it did fly and handled OK for me at the time. All balsa, tricycle landing gear, and a single rudder. If anything it was fast! I can't remember what I had on it for power, either a Cox .049 or a Wen=Mac/Testors, but for me it really hauled the mail for a 10 or 11 year old!
   Type at you later,
    Dan McEntee

     PS; I meant to add that in later years , long after the model was gone, I found pictures of it in old model magazines, and it was around the mid 1950's when the Walker patent was still in effect. They probably came up with that tube system to get around the Walker patent. Comet did other odd ball stuff like the Whizzer, that just had flaps on the wing with no elevators, and it was controled by some sort of "unique" bell crank.

Keith,

There were probably two factors involved in your leadout failure:

1. The recommended bend radius for even very small cable (I assume you used something like 1x7 .015" stainless) is much larger than the .062" radius provided by a 1/8" steel pin. From cable manufacturer's literature, which they cautiously state is a starting point for testing, you might want a 3/8" radius or more. One source gives a rule of thumb starting at 100x the cable diameter. The goal here is to reduce the bending stress in the individual wires to below the yield point. As a cable bends sharply, some of the wires are stressed more highly than others and can fail after even a small number of cycles.

2. The wires in the cable may also be damaged by rubbing against the guide pin. The fretting there reduces the cross section making them more susceptible to failure, and the cable "unzips," failing wire by wire. Lubrication can help here, but a better material combination is always desirable. There are tables available that show the contact force required between various metal combinations to cause galling. Some combinations are particularly bad. The use of a "self lubricating" material like UHMW Polyethylene is particularly good around lightly loaded (transverse) cable guides.

3. There is always the potential for high cycle fatigue due to engine vibrations. But even at 18,000 rpm, your 20 flights should not have come close to the fatigue limit.

For only 20 flights, and assuming there was no hanger damage, you must have been done in by so-called low cycle fatigue. (Item 1 above.) The wires bent far enough to yield in throughout the control range meaning the individual wires had to yield around the pin and the point of yielding moved up and down the cable. Repeatedly. Ping. Ping, ping. Less likely is that the wire rubbed enough material off to compromise the strength. This can be misleading in a post-failure analysis since wire under tension (yield) will elongate causing it to neck down and look thinner.

Very glad you caught it in pull test. You avoided an accident and could always rework the guide...and have one more plane to fly.

A few other thoughts: On F2C racers, guys have used tight-wound coil springs as a guide, which protruded from the wingtip. The spring prevented very sharp bends in the lines during catches. I have also seen a lot of plastic tubing. It seemed like UHMW, but might have been teflon?

Makes me wonder what's inside the wing of Kirk's Corsair....?

Dave

FWIW...

Too late to the party again. This is my demo model hanging with the lines attached to a bellcrank mounted at the tail. I'm sure someone has already remarked that valid statements on longitudinal bellcrank placement usually include recommendations to avoid excessive bending of the leadouts at the tip.

SK

Mark,

There are different conversations going on here. The photo with the strand failures at a wrapped termination is a different case than what Keith was talking about. The failure at terminations has been exhaustively discussed....but the failure at the point of "redirected" routing of the 1/2A leadouts inside Keith's swept-wing scale job is of interest to me because of a potentially similar problem with a 1/2A scale plane I have in work.

Dave

Having the bellcrank at the CG has always worked well enough.   That minimizes the force and wear on the leadouts & leadout guide.

You need a really BIG leadout guide to get it right, but that's the nature of a swept wing.

If you're good at physics and higher math you can plot the leadout positions as handed down in The Bible according to Wild Bill Netzeband, or else drill a line of holes.

Having flown in hurricanes ( singular ) one can faithfully say , The TETHER POINT ( we assume the center of the bellcrank )  tends to be DOWNWIND of the LEADOUT ' When its Blowing !

Of course one could use the offset / stagger , as a steering device !

If the drag from the wind is say 4 times the weight , the ' function ' of the alignment is quite apparent .
Later things I flew in WIND more recently , Varied - according to the ship .
But if youre kicking your heels in ( 70 Oz Plane ) and leaning WAY back and needing to use both hands to hang on ,

im quite sure thats more load than say holding four of them .  280 Oz . ! or is it ? 17.5 Stone . Now thats ' hanging on .  Id say 14 stone ish max .  224 Oz ! = 3.2 x mass ( 70 ) wind drag / inirtia / wind up .
Though flat laps too . For a ' drag / load figure . 3.2 G'
 drag OUT !
Not so much upwind . 

Therefore ! the tendancy to fly ( IF the center of area was at the bellcrank point ) cacked would be overwhelming of a ' its the leadout point that counts ' approach .
Lead Out Rake , Side Area Center , ( How you figure the side C / L airbornes up to you ) & C G , need to be ' factored .

Easier to estimate C G posn & fix pivot near aft of that , at the ' where do I put it ' point .

Sheeks 262 going that way has the leadouts a few inch in from the end , on the L E  ( gathered to 1/2 sep ish ) , rear line straight to rear bellcrank arm . just about .

( A vertical wind tunnel , plane hanging way down , ( on its lines ) , and ' switch er on ' , would give a vauge guess at whats going on ! )

But in a windy area , i think the bellcrank pivot even just aft of C G is needed , 20 & 25 even 30 N M ( Knot ) for the 3.2 . Actually , the 25 or gusting . big long steady ones . not at 20 even .
Great fun if your not to worried about planting it . ( not for your best engines , Eh !  )