Having vacated another discussion about a design/engineering question on the main board, I'd like to aim at some understanding of one of the points that was brought up, but apparently not appreciated. This often happens, when something is brought up with the expectation of non-scientific answers to engineering propositions. So I bring it here, where it belongs. Yes, this is another bellcrank-position observation, but it is a useful one that has not been acknowledged except by a couple of us.

On the other forum, it was argued that re-positioning the bellcrank changes the feel of the model and that this supposedly invalidates the statement that bellcrank position is irrelevant to aerodynamic effects on the airplane and to the other dynamics of the plane as a whole. It does not invalidate this basic idea. That structural considerations and friction/wear at the leadout exits are rightly considered as relevant to bellcrank placement was mentioned over and over by most participants. The one thing that seemed to be misunderstood or ignored by most was the idea that moving the bellcrank relative to the flap horn could change the behavior of the control surfaces relative to control input at the handle. That's what I'd like to bring up; as Tim said, this is possibly why a change in feel might take place. While it is still not counter to the basic principle of the bellcrank's independence of placement, it's still real and worth examining.

First though, note that when we discuss moving the bellcrank, it is to be assumed that all of these effects - potentially changed structural strength, wandering c.g., etc. - are compensated so that the bellcrank in its new position is functioning in a plane with the same aerodynamics, weight distribution (stability margins and moments of inertia), and weight as always. Then all we have is the bend angle and thus friction/wear of the leadouts at the tip....

AND the control geometry. The control action must be maintained, or a new feel can indeed be injected into the mix. Fortunately, from playing around with the mathematics of the control system, I've found this to be pretty easily adjusted. I posted some of this stuff more generally several years ago, after trying out data in a spreadsheet created by A.J. Herbon in 2000 and forwarded to me by Larry Cunningham. I think that it must be pretty much what Howard also developed. I'd like to apply it to the specific question at hand, to point out how easy it can be to readjust control geometry to adjust for when one moves it closer or further from the flap horn.

The adjustment boils down mostly to just re-angling the flap horn as, for instance, the bellcrank is moved forward or aft - a very simple design move that doesn't complicate construction. Adjustments for lateral or up-down bellcrank moves are much the same. One thing to remember is that bellcranks as generally installed already are a minor mess regarding symmetry. So we get used to what we have and probably don't like anything different, even when it is more symmetrical. Second, within reasonable design limits, control asymmetry is fairly low, perhaps barely noticable by the best pilots. I'll let them decide that. Third, FWIW, the effects of flap-elevator linkages are significant, often not so well configured, but not relevant here.

OK, I trust these results fairly well, since they seem consistent and conform to my common-sense expectations. The first picture is a diagram showing the control set-up and symbols. Below it is a set of data, showing measurements that give a "delta alpha" value of zero, meaning that there is no difference in up and down control input amounts to achieve equal up and down flap deflections (in this case +/- 35 degrees). With this spreadsheet, you just keep changing the flap horn angle with the vertical, until the bellcrank deflection is the same for equal up and down flap deflection of some chosen amount.

Most top stunters are equipped with flap horns that angle forward to meet the control rod from the bellcrank arm at more of a right angle at neutral. It turns out, perhaps surprisingly to some, that the right angle is far from the best angle. Also what is not obvious is that whatever flap angle you choose for control symmetry, for smaller and larger angles, control symmetry is lost, but we'll look at that later. Most realize that the further forward the bellcrank is moved ahead of the flap horn, the more horizontal it becomes at neutral, and the less horn lean is needed. The spreadsheet bears this out.

Suppose you have a smallish stunter with a bellcrank arm of 13/16" and a flap horn arm length of 1.0" (from hinge to bellcrank-rod hole). Here are some example figures (I've changed mm to inches and removed intermediate values) for various horn angles that give control symmetry for different locations of the bellcrank (I've arbitrarily chosen a flap-deflection value of +/- 35^o, which I think is ordinary, but too high. So, if "D" is the longitudinal distance the bellcrank arm is ahead of the hole in the flap horn, and "b" is the angle from vertical made by the line from the flap hinge axis to the connector hole in the horn arm, then these are values of "b" in order for equal +/- flap deflections to require equal bellcrank deflections:

D = 5.0"   =>  b = 8.33^o
D = 5.5"   =>  b = 7.62^o
D = 6.0"   =>  b = 7.02^o
D = 6.5"   =>  b = 6.51^o
D = 7.0"   =>  b = 6.06^o

So, all that is needed to maintain close to the same control symmetry is to cange the control horn angle, as you move the bellcrank. The spreadsheet I've used also accounts effects for lateral bellcrank movement, and they are much the same, with the same solutions. You can pretty easily decide what to do for vertical movements.

So here's the "bad" - maybe really good - news. Our control systems are already so screwed up that we may not really know what's good anyway. We are used to flying with line rake that makes input to the bellcrank non-linear anyway. Our fancy angled flap horns are only approximations, and, if you've taken time to make your bellcrank rods perpendicular to your flap horns, then you've overshot it and may be no better off or even worse than angled stock horns, because perpendicular doesn't make it. The good news is that these aberrations aren't necessarily huge - often in fractions or very low numbers of degrees.

The graph compares what happens when you choose various flap angles as your goal for control symmetry. You can choose one flap deflection angle where equal bellcrank deflections provide equal flap deflections; there will be varying amounts of deviation from symmetry for all other angles (except zero). Here's how you read the graph. The distance above or below the horizontal axis is how many more degrees you must deflect the bellcrank one way than the other to get the flap deflection written on the horizontal scale. The vertical scale is in degrees too and tells you this deviation. There are ten curves, each representing one value of flap horn angle (as measured at neutral). These values are (from bottom to top) 0^o, 2^o, 4^o, 6^o, 7^o, 8^o, 9^o, 10^o, 10.911^o, and 12^o. The red line is the angle for the bellcrank arm to be perpendicular to the horn arm at neutral. You can see that it is not the best. Where each line crosses the horizontal axis, that is the value for which its horn angle leads to control symmetry. Before and after that point, for each line (horn angle) there will be differences in control inputs. When the lines are below the axis, you'll need more down than up, by the amount indicated. When a line is above the axis, you need more up than down to get the same deflection.

Here are some examples of things you can see on the graph. First, for values of horn tilt of less than about 4^o, control is never symmetrical. This plane, fitted with the vertical flap horn of our standard fun stunters already needs more than four degrees more down than up for flaps at 30^o in an ever wider divergence; fortunately we don't need that many degrees of flap and fly happily on - I think! For a horn angle of 8^o on this particular plane, we have control symmetry for the flaps at 35^o deflection, and less than half a degree of asymmetry for all smaller deflections, where a bit more down is needed. For greater deflections, the amount of extra up needed increases rapidly. The red line, signifying about 11 degrees of horn tilt is the dividing line between horns that deliver symmetry somewhere and those that do not. It just needs increasingly more up input, until past 30^o of flap, the up required quickly increases from one degree more than down. What you should see from this is that control asymmetry is ever present, but not really of much concern for most of us. Anyone concerned about moving a bellcrank can just probably make a pretty good gustimate of how to adjust the horn tilt and not be significantly different, even in this respect from most others. For instance, for standard models with vertical flap horns, moving the bellcrank forward has to improve control symmetry anyway. I rather doubt that many top stunters know how close or far off they are anyway. We have a few here who do though.

So to design a control system that has symmetrical responses to your satisfaction, you must choose a horn angle whose symmetry satisfies you in the areas of your choice. Note that for some of these angles, the deviations from neutral on out remain below 1.0^o over a reasonable range. But if you really want this symmetry of control, you'll also have to design a bellcrank whose control arm is at neutral when the lead-out arms are angled perpendicular to the lines. I'm not sure that everyone would even like control symmetry, since...

a) They don't fly with control symmetry now.
b) No planes are symmetrical dynamically anyway.

But if you want control symmetry, there are ways to get pretty close, and no more changes would be required than would be required just to change a common design to have control symmetry now. So, if you're worried about moving the bell crank, just change the flap horn angle. If you want to get it entirely right, you'll need the spreadsheet or some math acumen. Rule of thumb: Bellcrank forward, decreased horn angle, and vice versa.

OK - that was a couple or more hours of effort. So do me a favor please. If you are not pleased with my efforts, constructive criticism/corrctions are appreciated. The other stuff is not merited. I may be back to correct or edit things later. Thanks.

SK

I thought this looked familiar.  Searching a little, I found http://stunthanger.com/smf/index.php?topic=19875.0 .

Howard - I knew I'd used this before and remember your efforts. Your graph is quite to the point. I've also posted more of these elsewhere, although one former "regular" who probably should have made some effort to understand replied then with a simple "Huh?" I think I got an early version of your spreadsheet, but not the final one. It was during a very busy time here. Thanks for the very cogent input.

Bill - Thanks for highliting that aspect. I should have emphasized it more. it's mentioned in there, but not analyzed.

You're certainly right that the vertical position is important. Intuitively it would appear that lifting the bellcrank would also tend to lessen the desired forward tilt (or increase rearward tilt) of the flap horn too. My post was mostly directed at showing that moving the bellcrank can be compensated for without resorting to any structural complications.   Compensation for vertical movement could have been built into this spreadsheet, but wasn't. Without modifying the spreadsheet, I'd probably opt for superimposing a vertical-plane adjustment to it's answer as a close enough approximation.

For now though, I've been more interested in demonstrating that, regarding moving the bellcrank,...

1) The flap arm tilt is a key to making sure that the plane the newly-positioned bellcrank handles is the same plane that it handled in the old position.

2) The final effects of moving without compensating may be small.

3) Without doing this analysis on the existing ('preferred"?) plane, there's no way to know whether it is "better" as it stands; moving the bellcrank forward without compensation, for instance, might actually improve control symmetry.

4) We fly some pretty asymmetrical equipment and like it anyway; we may not even like an improved control movement. Preferences vary, and familiarity is relevant. Asymmetry of stunters themselves may often make absolute control symmetry undesirable.

Like you, I wouldn't be satisfied without some vertical position adjustment, but life sort of gets in the way of some interesting things. For now, I just wanted to put to rest the thought that bellcrank position in truly equivalent planes makes any difference in feel.

SK

4) We fly some pretty asymmetrical equipment and like it anyway; we may not even like an improved control movement. Preferences vary, and familiarity is relevant. Asymmetry of stunters themselves may often make absolute control symmetry undesirable.

And asymmetry of the stunt pattern.  Having a control system that gives a little extra leverage at the top of the hourglass may be OK. 

Like this?  http://www.netax.sk/hexoft/stunt/the_max_ii.htm .  Good idea.  I'm putting it in the new plane.

That is not what I described.

The drawing, at that link, is something I wouldn't put in my plane.

Charles

yeah ,, doesn't make sense to put the drawing in the plane,, however I beleive that the devise depicted is pretty much what the last world champ and nationals champs had in theirs

Howard,, I was attempting to avoid a "piling on" penalty,,( hey its football Sunday,, and after the Hawks game,, it was a concern)

How many tilt the BC (side view) so that pushrod is parallel to the BC arms?

I did that in combat planes half a century (literally) ago --wow, I'm old-- to make the pushrod straight and minimize the exit hole from the wing.  I did it in the last stunter, but fiddling with the program, it looks like it doesn't do much.

How many set the neutral with the BC "square" (top view) to the theoretical leadout location, and the pushrod square to the BC pivot?

This is a big deal, I think, in F2D, where the line drag is big relative to the airplane weight.  It results in an offset output arm, which does affect linearity a lot.  You really gotta fiddle with these parameters in 3D to see what happens.

I looked at Igor's device, and I'm wondering if there are any construction drawings? I'm just assuming that the "roller" is a ball race? How to make the rest? What materials?

Stop by the laboratory.

How many tilt the BC (side view) so that pushrod is parallel to the BC arms? How many set the neutral with the BC "square" (top view) to the theoretical leadout location, and the pushrod square to the BC pivot? Together with the flaphorn square to the BC/Flap pushrod, that should go a long way toward getting "the feel" we're looking for.

I looked at Igor's device, and I'm wondering if there are any construction drawings? I'm just assuming that the "roller" is a ball race? How to make the rest? What materials?  Steve

I always try to have BC arms paralel to flap pushrod, not only because of linearirity, but especially because of bending forces on BC arm and bushing

more details of that devoce are in this thread ... it is slovak, but you will understand also slovak pictures 

http://www.rcmania.cz/viewtopic.php?f=123&t=49486

installation in fuselage is here:

http://www.rcmania.cz/viewtopic.php?f=123&t=49537

material is 1mm steel sheet, the pivot is 10mm ball bearing

Looks like this program recognizes the problem to be 3D, which is something you gotta do.  That makes it difficult.  I couldn't figure out how to do it closed-form, so I used a silly iterative method.  It works a treat. 

 3-dimensionality is definitely the issue. John Miller and Larry Cunningham did some interesting work, mostly with graphical methods, and published it in SN a long time ago. Tilting the bellcrank helps the geometry issue but you also have to leave enough clearance for the leadout fittings, pushrod, etc, and you don't want the pushrod sitting way up above the plane of the bellcrank because that can make the play in the pivot show up in free play in the controls. That's why my bellcrank design has a very long tube as the bearing, which leads to an issue with it binding under load if the pivot rod bends, which leads to making the pivot rod very large. Weight considerations of a 2 1/2" long 3/16 pivot rod led me to make it out of titanium.

      Mine is not tilted but it the important bit (ball link) is well above center to minimize the 3-dimensional variation without running out of clearance.

      Brett

I would really like to fly a plane with that control system.