Precise modeling the aerodynamic forces is very difficult indeed.
Aerodynamic forces and moments are complex functions of the airplane's
state and control variables, and the local environment. The important
state and control variables are the airspeed along body axes
(
*u*_{a},*v*_{a},*w*_{a}), the angular velocity components (*p*,*q*,*r*), and the
control deflections (
). Aerodynamic interactions between
different components of the airplane (wing and stabilizer, for
example) can complicate the relationships. External interactions such
as ground effect complicate these relationships even more.

There are many models for the aerodynamic forces and moments. Most aerodynamic models are accurate only in a restricted domain. The very simplest models, for example, are accurate only near a certain trim condition. More sophisticated models are accurate for normal flight conditions, but not for post-stall situations or other unusual situations. Very detailed simulations can be accurate for almost the entire flight envelope.

The rest of this section describes three general models: polynomial models, multipoint models, and tabular models.