Fluctuations of an airplane with aerodynamic wingtip «At winglets» - Melikov, E. (Science-based technologies, 2018)
By the method of equations of steady rectangular horizontal flight the effect of the aerodynamic wingtips "AT winglets" on the lateral oscillating stability of the aircraft is investigated. This method calculates the expressions for the coefficients of the roll and yaw moments for a wing with wingtips, which are used here to obtain an approximate equation for the lateral oscillatory motion of the aircraft. The forward and backward arrangements of the centers of pressure of the tips with respect to the vertical plane passing through the lateral coordinate axis are considered. The derivatives of the coefficients of the roll and yaw moment coefficients for the slip angle for the wing with the tips that enter the equation for the lateral oscillation of the aircraft are determined. The correspondence between the derivatives of the coefficients of the moments of roll and yaw for the wings without the tips and with the tips for the slip angle is established. Using this correspondence, from the known differential equation of the lateral oscillation of an aircraft with a wing without an wingtip, the corresponding equation of lateral oscillation of the airplane is obtained for the aircraft for aircraft with a wing with wingtips. A study is made of the solution of this equation in terms of stability, depwingtip on the ratio of the attenuation coefficient and the coefficient of dynamic stability of the aircraft in yaw . The study showed that for a stable lateral oscillation of an airplane, the numbers and must be negative and, in addition, still should be less than a negative number, i.e . It is shown that, in the case of steady lateral oscillations, the presence of wing tips leads to an increase in the oscillation frequency and amplitude decay factor as compared to the wing without the wingtips.