**5. Results of the optimization problem for lift-curve slope for midwing-body monoplane configuration**

**Figures 17** and **18** show results of the optimization problem for lift-curve slope for midwing-body monoplane configuration with circular cross-section fuselage vs. the aspect ratio of the rectangle wing. In **Figure 16**, the notation is used:

$$
\overline{K}\_{\Sigma} = \frac{C\_{L\_a W, B}}{\overline{C}\_{L\_a W}},
$$

where *CL<sup>α</sup> W, <sup>B</sup>* is the lift-curve slope of the wing-body combination the same as in Eq. (9) and *CLα<sup>W</sup>* is a lift-curve slope of the isolated wing in which it is included part of the occupied fuselage.

**Figure 18** shows the results of the solution of the optimization problem for liftcurve slopes for midwing-body monoplane configuration with elliptical crosssection fuselage. Maximum values of the lift-curve slopes depend on the aspect ratio of the rectangular wing and the ratio of the axes of the ellipse. **Figure 18** shows that the advantage of the wing-fuselage combination over an isolated wing is enhanced

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

**Figure 14.**

*Aerodynamics*

**Figure 15.**

**90**

zoidal wings and circular or elliptical cross sections.

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 trape-

*Calculation results of lift-curve slopes vs. Mach number for case high-wing monoplane combination.*

*Calculation results of lift-curve slopes vs. Mach number for case midwing monoplane combination.*

#### **Figure 17.**

*The optimal relative diameter of the fuselage with circular cross-section body for the midwing configuration vs. the aspect ratio of the rectangular wing.*

model for cross-flow around the fuselage and the discrete vortex method for the wing were 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 also confirms this result. Investigations to optimize the wing-body combination were carried within the framework of the proposed model. The proposed mathematical model for the solution optimization problem for the wing-body combination allows selecting the optimal geometric parameters for configuration to maximize the

It was revealed that the maximums of the lift-curve slopes for the optimal midwing configuration with elliptical cross-section body reach their values at sufficiently large relative width of the body (more than 30% of the span wing!). The advantage of the wing-fuselage combination with a circular cross section over an isolated wing at the wing aspect ratio greater than 6 can reach 7.5% at the relative diameter of fuselage equal to approximately 0.2. The advantage of the wingfuselage combination with the elliptical cross section with the ratio of axes of the body equal to 2.5 over an isolated wing with aspect ratio equal to 12 is that it can

values of the lift-curve slopes of the wing-body combination.

*Effect compressibility on the solution of the optimization problem.*

*Optimization of Lift-Curve Slope for Wing-Fuselage Combination*

*DOI: http://dx.doi.org/10.5772/intechopen.89056*

reach 29% at relative width of fuselage equal approximately to 0.35!

NACA National Advisory Committee for Aeronautics

ARC CP Aeronautical Research Council Current Papers

AGARD Advisory Group for Aerospace Research and Development

The author declares no conflict of interest.

ZFF Zeitschrift für Flugwissenschaften TsAGI Central Aerohydrodynamic Institute

J. Aeron. Sc. Journal of the Aeronautical Sciences

**Conflict of interest**

**93**

**Figure 19.**

**Acronyms and abbreviations**

J. Aircraft Journal of Aircraft R&M Reports and Memoranda

#### **Figure 18.**

*Maximums of the lift-curve slopes for the optimal midwing configuration with elliptical cross-section body vs. the aspect ratio of the rectangular wing.*

with increasing the aspect ratio of the rectangular wing and with increasing the ratio of the axes of the cross-section fuselage. The optimal ratio of the width of the body to the span of the wing can reach 30% and more!

**Figure 19a** shows the effect of the compressibility and the statistics for modern aircraft also (**Figure 19b**). Red color point shows the project of fifth-generation aircraft (project M-60, Russia). The feature of the project M-60 is a wide fuselage. As can be seen from **Figure 19b**, with the aspect ratio wing equal to 15, the optimal ratio of the width of the circular cross section to the wingspan can reach 20%!
