We know that the shape and position of the tail unit in every aircraft is affecting on the aircraft stability and control but what is the optimum case and why? assuming conventional aircraft type.
Dear Ahmed Shandookh
There is no general rule over such an optimum design. For the case of any aircraft, the aerodynamic shape of the fuselage and the wings (including tail-wing) are interconnected, while they affect the stability and maneuver performance of the aircraft. For civil aviation, transport or military fighter aircrafts, the problem is different. Even for various conventional civil aviation passenger aircrafts, such an optimum design is not unique. Moreover, for subsonic, supersonic, and hypersonic flight regimes, the shape of fuselage, wing and empennage is different.
For missiles, the shape of the fins, are more critical. Please see:
https://www.researchgate.net/post/Which_aerodynamic_surface_control_setup_the_file_attached_is_more_suitable_for_a_spinning_missile
The best way to calculare the position vs. wing and the dimensions of vertical & horizontal tail is described in these two books: Fluid dynamic Drag, and Fluid Dynamic Lift, by Sighard F. Hoerner. Also if aged, nothing more has been invented in Aerodynamics that is not mentioned in these books, just the computer use of the formulas and graphics there contained. In any case, there is a very good software for aircraft design than has been developed by Prof. Jan Roskam of the University of Kansas. If I remember this s/w is named AAA (Advanced Aircraft Design) and is sold by DAR Corporation. In the past I have been using it with very good results.
I'm a bit late to this party, but seems there is no too much consensus on this. For positive stability, the tail moment should increase faster than the main wing moment with regard to AoA increase, and that creates a pitch down moment with a perturbation that increases AoA. Usually this is done by having the tail flying at a lower AoA than the main wing. Se a pertinent explanation here: http://www.av8n.com/how/htm/aoastab.html
The tail can produce a small positive lift, neutral, or negative lift, but as the main wing is generally more efficient at producing lift (it has larger aspect ratio) the optimum would be neutral lift on the tail, and as Omid Habibi mentioned, as small as possible.
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