I am doing some work on a 40 size profile 3d plane and I'm interested in the arguments for thrust line arrangements. Some planes have the wing dropped from the trust line... Some drop or raise the horizontal stab from the thrust line.

What are the trade offs?

I presume -you are making a straght (no dihedral)wing--
for strictly a 3d setup - somewhere close to wing is best-
I prefer along the top of the airfoil curve -easy to build and no bad effects.
the stab also goes on this line .
everything 0-0-0 add right thrust to taste - 0-2 degrees.
arguments
The CAP layout works well especially for tumbles but I again presume you will make short nosed long tail setup - which typically are easiest to fly in the thrust vectored mode.
Lousy for anything else but great for that--
If you use a more balanced lateral area (and totally more side area - the plane will do better roll transitions - again- all in what you want.

Okay... Thanks for that…

Here the issue: I'm setting up a 40 size profile with a fully symmetrical wing. The top, bottom, leading edge and trail edge will all taper. I'm looking for a plane that will do 3d maneuvers…. I'm thinking I'll set up the wing on the engine thrust line. I'm also thinking that the horizontal stab should be set either above or below the thrust line to get "clean" air….. I want to be able to knife edge for days….

Here's what I’m comparing it to… I've flown a profile plane with the wing on the trust line and the stab 1/2" down from the thrust line… I've also flown a plane with the wing dropped 1" from the thrust line and the stab was on the thrust line…. Both had fully symmetrical tapered wings with no dihedral. Both knife edged really well…. I've flown another design that had the wing dropped 1" and the stab raised 1". The wing was built flat upside down… so the top of the wing did not taper but the bottom, leading edge and trailing edge did taper. This plane did not knife edge near as well. The wing seamed to wobble in high alpha and didn't want to stay locked in like the other birds.

What I'm looking for is something aerodynamic to explain these behaviors. Why did the other knife well? Why did the last plane knife poorly? I'm wanting to design something with a little more that the trial and error approach…

Thanks for your help.

Unfortunately - you have too many differences to pick out a fault in either setup -
some of the best knife edge designs have a low wing -high thrust line !
But try this - use lots of side area on the fuselage-keep it pretty well balanced in area that is don't go for a very long tail moment arm - but if you must , then--add lots of forward lateral area
the trick is this:
for best knife edge -- the plane --when rolled to it's side - is now flying on the fuselage - obvious .right?
The center of lateral fuselage/fin area should be close to the TE of the wing. (SWAG)
go too far forward in area and the plane will be unstable in yaw - BUT-in a profile -- you can really push this .
get it right and the plane will loop in knife edge - do fantastic flat, tight turns etc..
the downside is that is not quite as good in hovering forever --
go for it - hell- that's what it's all about!

Thanks Dick for your help!! I'm not an aeronautical engineer.. but I want to learn more...

If I'm understanding you correctly, you're saying to try to keep the fuse area balanced on either side of the thrust line. That makes sense since your flying on the "fuse" both sides should be equal to provide an equal amount of lift for stable knife edge.

On your second comment on centering the lateral fuselage area I'm a little unclear... Are you saying to try to keep the fuse area forward of the TE of the wing roughly equal to the area behind the TE? Sounds good, but what is the logic behind this arrangement?

The fuselage -on it's side-- becomes the lifting surface
It's "CG" should be a sclose as possible to the wing's CG.
IF- all of the area is AFT-- the plane will try to drop -nose first during knife edge flite .

too many models have way too much area aft the cg - an they require huge rudders and that produced HUGE drag.
If the areas are more balanced - the plane easily holds AOA (on it's side ) needed for flight- with minimal rudder.
This makes all maneuvers smoother as the plane stays on line much better.
The
"tricky" part is balancing the correct amount of forward -vs aft lateral area .
cut an try - it's only a model - find out the real limits --

Dick, I think I understand what you are getting at regarding the CG's of all the lifting surfaces. Essentially, as you design a plane to fly on the wing, the planform of the wing, the airfoil and the moments/areas come together to define a CG for the plane to use during 'level' flight (lots of websites that can help calculate this).
When extending the design parameters to knife edge flight, you have to figure up the CG of the plane as it uses the fuselage sides/rudder as a lifting surface. The CG of the 'fuselage lifting surface' would be affected by area distribution front to back coupled with the area and moments of the rudder.
I am then reading into your statement that it might be advantageous to have the two CG's (Horizontal Flight and Knife Edge) in the same location in the airplane.

Then you add into the parameters the balance of fuselage area above and below the centerline created by the engine thrust line, the centerline of the wing and the centerline of the tail. (of course all of this is easier if all the center/thrust lines are common)

Over the past year or so, I have designed several airframes to test these thoughts, and they have proven what I think you have said. Am I on the right track?

The result of my experiments was/is a little profile called a Half-Wit. The plane has a Hershey bar wing with a thick airfoil. The wing, engine and tailgroup all ride on a common centerline (or at least extremely close to it). Fuse and rudder area are very balanced above and below this center line. The tail moment is rather long and the majority of the fuse side area is quite a bit forward and somewhat centered over the 'flying' CG.
This plane is easily the cleanest knife edge flyer I have ever flown- very little pitch or roll coupling in knife edge and the performance is very much the same on either side (either tip down). It also does a fairly clean High-Alpha knife edge, but will start to wobble occasionally.

yes- as long a it is still stable in yaw- -it doesn't matter how you do it -
On pattern planes -long ago - variou guys noted that adding area to the front (chin) made knife edge better.
simply - the plane flew at a lower fuselage AOA (in knife).
The thick wing is better in that it is very piutch insensitive - actually does not snap nearly a well as say- 10% but it all depends on whatcha want.
The real aerodynamic rule for making all thiswork. is really simple:
do anything necessary to make the plane fly at the lowest angles of attack.

Does that still hold true for 3d flight? If I want the plane to be stable at a relatively high angle of attach... how would these design parameters change?

well- that is a little different - -you really don't need decent side area for that -
basically just lotsa control ability and very short wings - longest moment arm from prop to elev and rudder .
The plane is really doing most flying using thrust and the flight surfaces are simply holding angle.
It is a compromise but what is best for hovering about is not best for good aerobatics
bipes are good - short wings -relative to overall fuselage --in a monoplane just use 3.5 -1 aprox wing planform - airfoil is not important -
thicker will be stronger but anywhere from flat to 20% works .
The lighter you get -the less the thickness matters .

Thanks for the good stuff Dick, Paul are you working on the burrito 2 or the Enchilada?
I've been working on a small .25 size profile with a thin and very blunt airfoil, picture a symmetrical balsa SPA3D wing, will have pics of it later, all that is left is the ailerons.
as for the fuse area, how I look at it is that you have a fuse with a length of say 48", that is now a 48" cord when in KE. so to get good lift and stability in KE the cg of the lifting surface should be about at about 25% of the cord, but really even 15% would be ok because now we are talking about a flying wing/ lifting body,
the trial and error part could be lessoned with some careful area calculations, finding the % of fuse side area that you are looking for 15% or whatever and then move the wing accordingly so that the wing and fuse cg line up...did i just repeat what you said Dick? sorry, of course a simple fuse profile makes this all easier. But I think Dick is right on that this might kill how well it hovers, although the Extra is close to perfect, Quique said that his Yak is close also, long nose and still hovers well
If you look at George Hicks bipe design you can see the results of this, he has a very small rudder and the plane KE at just slightly less than wing level AOA.

Paul, you could ask George for input, he is a Bro
good to see some people do their homework

Matchlessaero, have we seen the half-wit?

here is my latest as of 5 min ago the thrust line is abit below the wing because the tank will be tucked under the wing, not much choice, the thin wing with the blunt LE is an experiment. we will see... as of now i'm calling it the Razor, i know there is another razor out there, but it's not a profile,
my hope is that harriers and elevators like a SPA3D, but flies more predictable and lighter... anythoughts?