Scaling Laws Applied to a Modal Formulation of the Aeroservoelastic Equations

A method of scaling is described that easily converts the aeroelastic equations of motion of a full-sized aircraft into ones of a wind-tunnel model. To implement the method, a set of rules is provided for the conversion process involving matrix operations with scale factors. In addition, a technique for analytically incorporating a spring mounting system into the aeroelastic equations is also presented. As an example problem, a finite element model of a full-sized aircraft is introduced from the High Speed Research (HSR) program to exercise the scaling method. With a set of scale factor values, a brief outline is given of a procedure to generate the first-order aeroservoelastic analytical model representing the wind-tunnel model. To verify the scaling process as applied to the example problem, the root-locus patterns from the full-sized vehicle and the wind-tunnel model are compared to see if the root magnitudes scale with the frequency scale factor value. Selected time-history results are given from a numerical simulation of an active-controlled wind-tunnel model to demonstrate the utility of the scaling process.