## Deficiency Lift Function Theodorsen

Figure 4.7 Comparison between p and p-k methods of flutter analysis for a twin-jet transport airplane. From Hassig (1971) Fig. 2, used by permission.

one can compute [A(ifei)]. Using this new matrix in Eq. (4.75) leads to another set of ps, so that k2 - |3(p)|, Y2 - -7^. (4.77)

Continual updating of the aerodynamic matrix in this way provides an iterative scheme that is convergent for each of the roots, with negative y being a measure of the modal damping. The earliest presentation of this technique was offered by Irwin and Guyett in 1965.

Hassig applied the p-k method to the configuration of Fig. 4.6. As illustrated by Fig. 4.7 (which is his Fig. 2), the p-k method appears to yield approximately the same result as the p method. This, of course, simply validates the convergence of the scheme. Its greatest advantage is that it can utilize airloads that have been formulated for simple harmonic motion. Another comparison offered by Hassig was between the widely used k method and the p—k method for a horizontal stabilizer/elevator configuration. This example of a strongly coupled system provided the results given in Fig. 4.8 (which is his Fig. 3). Here again, as in the k versus p comparison of Fig. 4.6, widely differing conclusions can be drawn regarding the modal coupling. In addition to the easily interpreted frequency and damping plots versus airspeed for strongly coupled systems, a second advantage is offered by the p-k method regarding computational effort. The k method requires numerous computer runs at constant density to ensure matching the Mach number with airspeed and altitude. The p—k method does not have this requirement.

The accuracy of the p-k method depends on the level of damping in any particular mode. It is left as an exercise to the reader (see Problem 13) to show that the p-k method damping is only a good approximation for the damping in lightly damped modes. Fortunately, these are the modes about which we care the most.

Figure 4.8 Comparison between p—k and k methods of flutter analysis for a horizontal stabilizer with elevator. From Hassig (1971) Fig. 3, used by permission.

Figure 4.8 Comparison between p—k and k methods of flutter analysis for a horizontal stabilizer with elevator. From Hassig (1971) Fig. 3, used by permission.