# THE WING-FUSELAGE SYSTEM. IN INCOMPRESSIBLE FLOW

6- 2-1 Fluid Mechanical Fundamentals of the Wing-Fuselage Interference

In the next section the quantitative computation of the interactions between wing and fuselage will be discussed, but a few physical explanations will be given here first. When putting together a wing and a fuselage, a flow about the wing-fuselage system results, with the fuselage lying in the flow field of the wing and the wing in the flow field of the fuselage. Thus, an aerodynamic interference exists between the fuselage and the wing, in that the presence of the fuselage changes the flow about the wing and the presence of the wing changes the flow about the fuselage. Consequently, the computation of the flow about a wing-fuselage system can be accomplished by first computing the flows about the wing and fuselage separately, and then adding the interference effects of the wing on the fuselage and the

fuselage on the wing. These interference effects are obtained by satisfying the

kinematic flow condition (zero normal component of the velocity on the surface of the wing-fuselage system).

The, flow field of a wing-fuselage system at subsonic velocity in symmetric incident flow (angle of sideslip /3=0) is illustrated in Fig. 6-5. Figure 6-5a shows the flow about the fuselage as affected by the wing. Along the fuselage axis, additive velocities normal to the fuselage axis are induced by the wing, which are

directed upward before the wing and downward behind it. In the range of the

wing-fuselage penetration, the flow is parallel to the wing chord, corresponding to a constant downwash velocity along the wing chord. The fuselage is therefore in a curved flow with an angle-of-attack distribution сфс) varying along the fuselage axis as shown in Fig. 6-5a. This angle-of-attack distribution, induced by the wing, shows that the fuselage is subjected to an additive nose-up pitching moment.

The effect of the fuselage on the flow about the wing is sketched in Fig. 6-5b. The component of the incident flow velocity normal to the fuselage axis Uoc sin Qoc ~ U0„а» generates additive upwash velocities in the vicinity of the fuselage. The effect on the wing of these induced velocities normal to the plane of the wing is equivalent to an additive symmetric angle-of-attack distribution over the wing span (twist angle).

The flow field of a wing-fuselage system at asymmetric incident flow is shown schematically in Fig. 6-6. The flow about the wing-fuselage system with the angle of sideslip /3 can be thought to be divided into an incident flow parallel to the plane of symmetry of the velocity Um cos @ ~ and an incident flow normal to the plane of symmetry of the velocity £/«, sin j3 ~ С/«Д The latter component of the incident flow generates a cross flow over the fuselage as illustrated in Fig. 6-6b, c, and d for a high-wing, a mid-wing, and a low-wing system, respectively. This cross flow over the fuselage results in an additive antimetric* distribution of the normal velocities along the span that is equivalent to an antimetric angle-of-attack distribution a(y).

 Figure 6-5 Symmetric flow about a wing-fuselage system (schematic), (a) Flow in the airplane plane of symmetry and angle-of-attaek distribution

The lift distributions over the wing span generated by this angle-of-attack distribution have reversed signs for high-wing and low-wing airplanes. The rolling moment (rolling moment due to sideslip), as affected by this antimetric lift distribution, is zero for the mid-wing airplane, positive for the high-wing airplane, and negative for the low-wing airplane. These findings are confirmed by the test results of Fig. 6-4, which show that the rolling moment due to sideslip ЬсМх/д& of a high-wing airplane is larger than for the wing alone.

The effect of the fuselage on the wing in yawing motion may be interpreted, therefore, as the effect of a positive dihedral of the wing on the high-wing airplane, and as that of a negative dihedral on the low-wing airplane.

Figure 6-6 Asymmetric flow over a wing-fuselage system (schematic), (a) Wing planform.

(b) High-wing airplane with angle-of-attack distribution a(y).

(c) Mid-wing airplane. (d) Low – wing airplane with angle-of – attack distribution a(y).