# The Wing-Fuselage System in Transonic Incident Flow

The following discussions on the interference in wing-fuselage systems in transonic flow will be restricted mainly to the drag problem. The drag of wing-fuselage systems near Ma„ = 1 is generally larger than the sum of the drags of the wing

alone and the fuselage alone. Here the wave drag at zero lift is the major factor.

Figure 6-37 shows drag measurements by Whitcomb [50] on wing-fuselage systems in the Mach number range from Max — 0.85 to Mz« = 1.1 with Ci = 0. The tested models are shown in Fig. 6-37a, their total drag in Fig. 6-376, and the drag remaining after subtraction of the friction drag in Fig. 6-37c. The curve for the fuselage alone (model 1) shows a strong drag rise near Mr» = 1. The simple combination of wing and fuselage (model 2) produces a particularly large drag in the transonic range. Whitcomb [50] showed that by contracting the fuselage within the wing range, the drag in the transonic range may be greatly reduced (model 3). ‘ This contraction of the fuselage has to be chosen such that the wing-fuselage system and the original fuselage (model 1) have approximately equal distributions of the cross-sectional areas normal to the fuselage axis. This rule for the distribution of cross-sectional areas of a wing-fuselage system is called the “area rule.” Figure 6-38 shows the application of this rule to an airplane, where Fig. 6-38<з gives the plan view of the airplane, Fig. 6-386 the contour of an axisymmetric body of equal cross-sectional area distribution Ap(x), and Fig. 6-38c the variation of this cross-sectional area along the fuselage axis dAp/dx. In Fig. 6-38c, the case without

Figure 6-37 Drag coefficients of wing- fuselage systems and axisymmetric fuselages in the transonic Mach number range, from Whitcomb. (a) Geometry. (b) Total drag coefficients Cjj at zero lift, (c) Coefficients of wave drag.

Figure 6-38 The area rule for transonic flow, (a) Airplane planform. (b) Distribution of the cross sections Ap{x) of the equivalent body of revolution, (c) Variation of the cross-sectional area distribution along the fuselage dAp/dx.

area contraction is drawn as a solid line, the case with area contraction as a dashed line. The fuselage area contraction has been chosen for as smooth a dApjdx variation as possible.

For the experimental proof, Whitcomb [50] also tested a fuselage whose cross-sectional area distribution is equal to that of the wing-fuselage system without contraction (model 4 of Fig. 6-37). This model indeed has the same drag rise as model 2 in the transonic range. The theoretical basis of this phenomenon has been studied by Jones [18] and Oswatitsch [35], as well as by Keune and Schmidt [19]. Finally, it may be seen in Fig. 6-39 that the advantage of the area rule is limited to

the transonic Mach number range. This figure gives the drag coefficients of 3 wing-fuselage systems in the Mach number range from = 0.8 to Max = 1.4. Model 1 is the fuselage without contraction, whereas models 2 and 3 are fuselages with two different contractions. The contraction of model 2 has been chosen for largest drag reduction at Mz*, = 1, whereas that of model 3 is for lowest drag at MZoo = 1.2. These tests show that contraction according to the area rule yields favorable results only in the transonic range. In the supersonic range, the results are even less favorable than for fuselages without contraction.

In this connection, the comprehensive experimental studies should be mentioned that Schneider [42] conducted on wing-fuselage systems with three different wings (rectangular, swept-back, and delta wings). A computation of the pressure distribution on wing-fuselage systems at an incident flow of Max = 1 and a comparison with measurements have been conducted by Spreiter and Stahara [45]. Compare also the computational methods in [20].

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