Theoretical Study of the Low-Aspect-Ratio Wing in Uniform Shear Flow : The Case of the Free Stream Velocity Varying in the Spanwise Direction

Abstract

The characteristics of the finite low-aspect-ratio wing in uniform shear flow is analized on the basis of the assumption that the disturbance velocities are small in comparison with the undisturbed flow velocity and that the width of the wing increases gradually in the chordwise direction. This assumption is analogous to that in the Jones' theory for the low-aspect-ratio wing in uniform potential flow. As the result, it is found that the aerodynamic forces acting on the wing are strongly influenced by the velocity gradient of the free shear flow; when the zero-velocity point of the free shear flow comes infinitely closer to the wing tip, the total lift and total drag coefficients become about 20 percent smaller than the values of the wing in uniform potential flow. If the free stream velocity gradient tends to zero (uniform velocity distribution), the present theory agrees perfectly with the Jones' one.