I started thinking about almost fully symmetrical stunt plane, in which the vertical stabilizer and the under-the-fuselage end vertical fin will have the same size.
Also, the wings and the horizontal stabilizer will be on the same level w/r to the fuselage horizontal plane of symmetry.

Fuselage will also be symmetrical w/r to its own axis.

The only elements that will not be symmetrical: cabin and the main landing gear.

Such plane should have the normal and inverted aerodynamic properties almost the same, especially when the cabin drag will match the drag of the main landing gear.

It is relatively easy to measure the drag of both shapes using the kitchen scale.

Regards,
M

Unfortunately, nothing else about the plane is "symmetrical." For instance, there are prop P-factor, down- and up-wash, engine torque, and gyroscopic precession from flying the plane around the flight circle as well as in maneuvers. I don't think that you can get gear drag to balance the cabin drag. My last plane is pretty symmetrical with thrust line, wing chord, and tail chord aligned together, but I did this only for comparison with a certain other plane and NOT with the intention of getting symmetrical responses. There are advantages in raising the stabilizer above the wing, some relating to these other asymmetries. Regardless of what you try, the plane will present a bundle of balances and compromises. Here's hoping that your plane comes out well and that you are able to trim for the unavoidable asymmetries that all CL planes present.

SK

Swirly air from the prop is significant. I was surprised to find that it has a bigger effect than engine torque.

The Yatsenko Shark has engine, wing, and tail in line.  It's a tad harder to land than usual stunters because the gear has to be long to provide prop clearance. 

Igor's plane has some vertical stabilizer on the bottom. 

You probably won't notice the drag difference in those parts, but you can balance them by referring to Hoerner's drag book.

Hmm, tandem undercarriage with tip skids come to mind here.

Cant remember the name of the Russian model that tried this system though.

Sirotkin Akrobat maybe? :   http://www.outerzone.co.uk/plan_details.asp?ID=1154

This too may be the model you remember. I think that the best thing to say about symmetrical models is that models with thrust line above the wing chord and stabilizer above the thrust line are more symmetrical with respect to aero, inertial, and other forces than in-line planes, because the l.g. are shorter, and there is more upper drag to balance the l.g. drag and precession forces, etc. You should be able to trim your plane well, but trimming amounts may be greater in some cases. Some people report hunting problems. My semi-educated guess is to give the model some positive incidence in the stabilizer (1-2 degrees) and/or some down thrust (same).

SK

To eliminate gear drag my in-line "Symmetria" model is equipped with a retractable landing gear. Furthermore, as I am running a (lightweight, low RPM) left turning prop I have installed the bellcrank with up-line rear for  better compensation of yaw, induced by gyro-effect and p-factor, in corners. So far, the airplane tracks fine and, following a minor elevator adjustment of 1/16 up, turns equal both ways. For specs see  "List your Setup"

Peter G.

p.s. due to unsafe ground handling, the originally installed monowheel design has meanhwile been replaced by a conventional two legs fuselage mounted retractable landing gear. Total weight of this folding back gear assembly (servos, legs, wheels and Y-cable) is 103 Grams or 3.6 oz.

One observes that earlier today a symmetrical (or nearly so) stunter won the World Championship.

Good point. There are several well-flying "symmetrical" designs out there, but I don't think they have any advantage. I was going to take my own in-line plane out today, but woke to sleet, hail, rain, and 13 kt winds here in Cleveberg. It'll have to wait. I used the last of my CF landing gear legs, but if I use a 10" prop, I'll be mowing grass or fitting even more ungainly legs. Thats not a particular recommendation either.

SK

One of the reasons for raising the stabilizer above the wing is to simplify the control geometry and reduce possible pushrod/stabilizer LE conflicts (without kinks in the pushrod). Reason for raising the thrust line is to get engine weight better centered on the leadouts, while also giving needed ground clearance with a shorter LG and less tendency to tip over on landing. This has been working quite well for many decades. 0-0-0 setups are not new, but they're still not dominating.   Steve