Development of an analytical model of wing rock for slender delta wings

Three analytical models of the subsonic wing-rock phenomenon for slender delta wings mounted on free-toroll stings are compared. The first model was developed earlier by other investigators, the second is a version of the first model that has been modified in the present paper, and the third was developed in an earlier paper by the authors. The differences among the three models lie in the assumed nonlinear form of the roll moment as a function of the roll angle and its derivative. The numerical values of the coefficients in the moment expressions are obtained by fitting them to moments obtained in an earlier numerical simulation. It is shown that the original model, which contains only quadratic terms, does not predict roll divergence. The model is modified by the addition of a cubic term, and the modified version does predict roll divergence. An asymptotic approximation to the solution of the equation of motion is obtained for the modified model, and it is shown that the solution reduces to the one given when the cubic term is dropped. Finally, the two models are compared with a third model developed earlier by the authors. The periods and amplitudes predicted by the asymptotic analysis for all three models are in close agreement with the numerical simulations, which were found in an earlier work to be in good agreement with experimental data. It appears that the authors' model is slightly more accurate and easier to analyze than either the earliest model or the modified version of that model.