Domain of Accuracy Checking

Every polynomial model has a domain in which it is accurate. (The domain of accuracy could be the set of possible flight conditions, but probably is not.) Because polynomials generally approach infinity, the model can yield ridiculous values for the force and moment coefficients when outside its domain of accuracy. It is therefore important to detect when the aircraft exceeds the model's domain of accuracy, especially with variables involved in high-order terms.

Depending on its purpose, the simulator may choose to abort or reset the simulation, informing the user that the airplane encountered a flight condition that the simulator could not handle. Or, the simulator could choose to use reasonable values for the force and moment coefficients, perhaps by setting them to an upper or lower bound, or perhaps by setting them to zero.

Flight conditions outside of the domain of accuracy often happen unexpectedly. For example, suppose an airplane is sitting on a runway, heading north, while a breeze crosses the airplane in a direction one degree north of east. Relative to the wind, the airplane's angle of sideslip is . Because of terms such as $C_{L_\beta}\beta$ and $C_{Y_\beta}\beta$, large forces and moments can result from this small breeze, especially when $\beta$ appears in higher powers.