STRATEGIES FOR SIMPLIFICATION

Some of the simplification techniques used to get workable models for flight data analysis are (1) choice of coordinate systems, (2) linearization of model equations, (3) simplification using measured data, (4) use of decoupled models, (5) neglecting small terms, and (6) restricting excursions during maneuvers to permit the use of simplified models. Some of these simplification techniques are briefly discussed here.

5.2.1 Choice of Coordinate Systems

The selection of appropriate coordinate systems for EOMs plays an important role in simplification of EOM. The following are some of the important points to be considered [1]: (1) Body axis system is most suitable for defining rotational degrees of freedom. It is a normal practice to include the angular rates and the Euler angles in the aircraft state model, and the equations in body axis, under certain assumptions, can be considerably simplified; (2) Either of the polar or rectangular coordinate systems can be used for translational degrees of freedom; and (3) The polar axis system uses the (a, b, V) form, which involves wind axis coefficients CL and CD.

The wind axis coefficients introduce nonlinearities because of the way they are related to the body-axis force coefficients CX, CY, and CZ. However, a, b, and V are commonly measured quantities, which encourages the use of a polar coordinate system. The expressions for a, b, and V in observation equations are simple if polar coordinates are used for data analysis.

Linear accelerations are normally defined in terms of CX, CY, CZ, which suggests the use of u, v, w form of state equations. This form is particularly useful in the case of rotorcraft where the (a, b, V) form may lead to singularities. With the differential equations for u, v, w in the state model, the (a, b, V) expressions in the observation model will be nonlinear.