Simplification Using Measured Data

In this approach, we do away with some of the differential equations from the state model and work with a reduced set of equations. However, since the eliminated variables will mostly appear in other equations, measured values of these variables from flight data are used. A very good example is that of the model equations used to analyze data generated from longitudinal short period (SP) maneuver. It is well known that during an SP pitch stick maneuver, there is only marginal change in velocity, implying that the longitudinal SP modes are more or less independent of velocity. Therefore, in the a, b, V form of equations, the V equation can be omitted from SP data analysis. Instead, the measured value of V can be used in the model equations without any loss of accuracy. The measured data for the variables used in this manner are sometimes referred to as ‘‘pseudo control inputs.’’

It is clear from the above discussion that the use of this approach would require measurements of the motion variables omitted from analysis. The disadvantage of this approach is that it is sensitive to the noise in the data.

Since most aircraft can be assumed to be symmetric about the XZ plane and fly at small sideslip angles, further simplification is possible by separating the 6DOF coupled equations into nearly independent sets: longitudinal and lateral-directional. Each set has nearly half the number of differential equations in the state model compared to the full coupled nonlinear 6DOF state equations. The simplified nondimensional and dimensional models normally used for longitudinal and lateral-directional flight data analysis are discussed next.