Influence of at winglets wingtips on the inductive reactance of the wing

In this article by the method of equations of steady horizontal flight the impact of AT winglets wingtips on the inductive reactance of the wing is explored. The total aerodynamic force, created by all four parts of the wingtips is determined. The vector of the total aerodynamic force of the wingtips is represented in the form of components of a linked coordinate system. Equilibrium equations for the steady motion of an aircraft with AT winglets wingtips in a horizontal flight are recorded. From these equations it is obtained that, in the direction of motion, the longitudinal component of the vector of the total aerodynamic force of the tips reduces the inductive drag of the wing, the vertical component is added to the lifting force of the wing, and the lateral component, due to symmetry, is zero. It is shown that the lifting force created by the AT winglets wingtips is larger compared to the same ones created by the upper tips. An important consequence is that the distribution of the lifting force over the wing span with double tips is more even in comparison with the wing without a tip or with a wing with the upper wingtip. The expression for the effective aspect ratio of the wing with the tips is determined, which is greater than the inductive drag of the wing without the tip. An interesting result is obtained: for identical aircraft weights, the product of effective aspect ratio of the wings with double and only upper wingtips on their coefficients of inductive resistance is equal to the product of the wing aspect ratio without a tip on its coefficient of inductive resistance. This law can also be formulated as follows: at the constant weight of the aircraft, the effective aspect ratio of the wing with the tips by its coefficient of inductive resistance is a constant value, independent of the form of wingtips.