Section 2 Optimization

**Chapter 4**

**Abstract**

*Vladimir Frolov*

diameter of fuselage equal to approximately 0.2.

2D potential cross-flow model, optimization

**1. Introduction**

modern aircraft.

**81**

Optimization of Lift-Curve Slope

for Wing-Fuselage Combination

The paper presents results obtained by the author for wing-body interference. The lift-curve slopes of the wing-body combinations are considered. A 2D potential model for cross-flow around the fuselage and a discrete vortex method (DVM) are used. Flat wings of various forms and the circular and elliptical cross sections of the fuselage are considered. It was found that the value of the lift-curve slopes of the wing-body combinations may exceed the same value for an isolated wing. An experimental and theoretical data obtained by other authors earlier confirm this result. Investigations to optimize the wing-body combination were carried within the framework of the proposed model. It was revealed that the maximums of the lift-curve slopes for the optimal midwing configuration with elliptical cross-section body had a sufficiently large relative width (more than 30% of the span wing). The advantage of the wing-fuselage combination with a circular cross section over an isolated wing for wing aspect ratio greater than 6 can reach 7.5% at the relative

**Keywords:** wing-fuselage combination, lift-curve slope, discrete vortex method,

An analysis of a lift-curve slope for wing-fuselage combinations currently plays

an important role in studies of aerodynamics and the preliminary design of a

Since the aircraft occurrence aircraft designers have been interested in the problems of the wing-body interference in aviation and missile technology. Initially, research is focused on the experimental study of specific wing-body combinations [1–6]. First mathematical models of the wing-fuselage interference were offered later. The solution of the linearized problem of the ideal incompressible flow around arbitrary shape wings in the presence of the fuselage is a difficult task since it is necessary to solve the three-dimensional Laplace equation for the velocity potential which satisfies the boundary conditions on the surface of the wing-body combination and the boundary conditions at infinity. One of the few exact solutions was obtained by Golubinsky in the article [7]. The first theoretical calculations were based on the inversion of discrete vortices inside the cross-section body [8], on the solution of integral equations [9], on the application the thin body theory [10–21] or the strip method [14, 15, 22], and on the application of the velocity potential [23–26] or the stream function [27] written in the Trefftz's plane. The application of
