Well - no-
three different cats
basically it has to do with speed /power differing
The trainer:
designed to fly at a low speed and to then climb (recover)as speed increases
The sport:
fly a little faster and still recover (climb) as speed increases
The pattern :
Ideally is fairly neutal and so has cg placement and various thrust/drag angles setup so that speed changes offer little pitch difference.
IF- you setup a Seniorita (basic trainer) to be neutral- you won't like it and the character designed into it will be gone.
Let's get airfoils sorted out
the first shapes used were draggy things designed to work at low speeds ( these were undercambered_
the next step were thicker shapes -usually flat bottomed and were stronger because they were thicker - they also were less sensitive to angles of attack
The streamline shape (sym)used in current fighter craft and on pattern planes flies at very low AOA and may use movable surfaces to work better at low speeds
Now - the opposing angles designed into the trainer -will fight you getting a "nuetral" dive - if you keep sliding the weights back-to move cg back- the plane will become weird and very sensitive and speed sensitive
ALL cg/power settings are compromises- No exceptions
You have to come to grips with
type of flying desired
speed range desired
Also maueverability desired
which brings up wing loading requirements for speed range
(more compromises.) After all this is digested - you may want to look up formulas and graphs which are simply models representing how these things interact.
I don't know any math so I don't use em.