The Theory of Lattice Composed of Airfoils of Arbitrary Profile Form

Abstract. Many people belieye that the How through a system of an infmite number of identiairfoils is very, similar to the flow through blades of a propeller or a turbine, if the flow is as-sumed to be constrained to a cylindrical surface coaxial with the axis of revolution, and that the aerodynamic interference of blades may be solved by such a latticed airfoil theory. But, in the first place, the distance of two points in the field with latticed airfoils corresponds to the distance alohg the cylindrical surface in the case of a propeller or a turbine. The influence of a blade does not extend in such a way, but straightly through the liquid, as in the case of a vortex, where the influence exerts according to Biot-Savart's law, in which the-distance is measured along a straight line, not along a cylindrical surface. In the second place, if the num ber of blades of a propeller or a turbine be n, the section of a blade repeatedly appears infinitely many times in every n profiles in the two-dimensional field with the lattice. Therefore the influence of a blade on any point, in the two-dimensional field, reckoned infinitely many, times along different paths, which, in the actual field; correspond to the paths on the cylindrical surface different one another by the complete turns of the cylinder. In fact, such a process of influencing can not be imag ined to occur. The correspondency of a flow along a _cylindrical surface with the flow through a lattice in two dimensional field is discrepant in these two points. However, the tendency of the pressure distribution over the profile being altered from that of a monoplane, and of the stream lines separating can be shown by the latticed airfoil theory, particularly in the case of large number of blades. For this purpose, the theory of latticed airfoils of arbitrary profile form is necessary, which is here developed.