**4. The formulation of the optimization problem**

Note that in some theoretical and experimental papers devoted to the wing-body interference revealed a maximum dependence *<sup>∂</sup>CL=∂<sup>α</sup>* <sup>¼</sup> *f df <sup>=</sup><sup>b</sup> :* Our calculations on the above mathematical model also confirm this fact. It was found that the maximums of lift-curve slopes for a wing-body combination depends on the shape of the wing and the cross-section shape of the fuselage. The paper presents solutions to the optimization problem for the wing-body combinations with unswept trapezoidal wings and circular or elliptical cross sections.

*Optimization of Lift-Curve Slope for Wing-Fuselage Combination DOI: http://dx.doi.org/10.5772/intechopen.89056*

**Figure 16.** *Theoretical and experimental results for lift-curve slopes vs. relative diameter of the fuselage.*

We will use the formulation of the optimization problem as a nonlinear programming problem as follows:

$$
\max \quad \mathbf{C}\_{L\_aW\_bB}(\mathbf{X}), \quad \mathbf{X} \in E^n,\tag{9}
$$

where **<sup>X</sup>** <sup>¼</sup> ½ � *<sup>x</sup>*1*, x*2*,* <sup>0</sup> <sup>T</sup> is a vector of the project parameters connected with geometrical characteristics of the wing-body configuration by formulates

$$\overline{D} = \frac{d\_f}{b} = \frac{1}{\varkappa\_1^2 + 1}, \quad \frac{1}{\lambda} = \frac{1}{\varkappa\_2^2 + 1}, \tag{10}$$

where *x*1*x*<sup>2</sup> are auxiliary variables. The problems Eq. (9) and (Eq. (10) are a problem of unconditional optimization, for which there are *D* ∈½ � 0*;*1 *,* ð Þ 1*=λ* ∈½ � 0*;*1 and *x*<sup>1</sup> ∈½ � �∞*;* þ∞ *, x*<sup>2</sup> ∈½ � �∞*;* þ∞ .
