# Effect of the Wing-Fuselage System on the Vertical Tail

Fundamentals As has been shown in Sec. 7-2-2, the effect of the wing on the horizontal tail at symmetric incident flow lies essentially in the downwash of the

wing. The fuselage and the relative position of wing and fuselage (wing high position) contribute little to the interference. In all cases, however, the effectiveness of the horizontal tail is reduced by the wing and fuselage.

Considerably different conditions prevail for the effect of the wing and fuselage on vertical tads at asymmetric incident flow. Schlichting and Frenz [35, 36] showed that vertical tails are markedly affected only by a combination of wing and fuselage. This interference results in an increase or in a reduction of the effectiveness of the vertical tail, depending on the high position of the wing. This influence on the vertical tail is caused physically by the quite asymmetric circulation distribution over the span of wing-fuselage systems. This asymmetry, explained by Fig. 6-6, causes a rolling moment due to sideslip. This fact has been discussed in Sec. 6-2-3. In Fig. 7-38, this antimetric circulation distribution along the span is illustrated for a sideslipping high-wing airplane. The lift increase of the leading wing-half and the lift decrease of the trailing wing-half generate a pressure drop on the upper side of the wing toward the advancing wing-half. This pressure drop leads to an induced flow, as explained in Fig. 7-38, which revolves around the wing. This velocity induced at the wing is effective at the vertical tail as an induced

Figure 7-38 Evolution of induced side-wash of a wing-fuselage system in yawed flight, (a), (b) Geometry (high-wing airplane), (c) r(y) = circula­tion distribution, Tg(y) = circulation distribution at symmetric incident flow, (d) Induced velocity field at the location of the vertical tail.

lateral velocity of about the same magnitude. Figure 7-38<7 shows immediately that, for conventional positions of the vertical tail, the incident flow angle of the vertical tail is decreased by the lateral velocity v, that is, that the effectiveness of the vertical tail is reduced. As in Fig. 6-6d, the sign of the induced lateral velocity is reversed for the low-wing airplane from that of the high-wing airplane. This results, for the same relative positions of fuselage and vertical tail, in an increased effectiveness of the vertical tail. In consequence of its evolution, the lateral velocity induced by the fuselage-wing interference is proportional to the sideslip angle 0 and independent of the angle of attack a. Thus the resultant velocity in the у direction at the location of the vertical tail is

Vy — {3 Uc0 4- vg – f Ug

where j3C/co is the lateral velocity due to the sideslip angle, vg is the induced lateral velocity at symmetric incident flow, and fivp is the additional induced lateral velocity due to sideslip as in Fig. 1-3M. The effective sideslip angle of the vertical tail is

Hence the efficiency factor of the vertical tail is

(7-61)

because vg is independent of j3. Because = d(3v/d@, Eq. (7-61) is identical to

required to determine the efficiency factor of the vertical tail.

For an experimental confirmation of the above considerations, a few test results on the efficiency factor are plotted in Fig. 7-39b for the wing-fuselage-vertical tail system of Fig. 7-39a. From measurements of the yawing moment due to sideslip with (yvV) and without (oV) vertical tail, a mean efficiency factor of the vertical tail has been established by Jacobs [14] in the form

where (dcMzld@)y is the contribution of the vertical tail to the yawing moment.* This experimentally determined efficiency factor is given in Fig. 7-39b as a function of the high position of the vertical tail. The result is

for the low-wing airplane:

1 (stabilizing)

*This has been determined as the difference of the measurements on fuselage and vertical tad and of the fuselage alone.

and for the high-wing airplane:

< 1 (destabilizing) dp