Inclined Wing at Transonic Incident Flow

It has been shown in Sec. 4-34 that the aerodynamic coefficients of a wing profile undergo strong changes during transition from subsonic to supersonic flow, that is, at transonic flow. The linear approximation methods for incident flows of subsonic and supersonic velocities for the airfoil of infinite span fail when sonic velocity, /kfoco 1, is approached (see Fig. 4-33). For wings of finite span, however, physically plausible results may be obtained at = 1. In this case, the same limiting values are obtained for the lift-related coefficients (see, e. g., Fig. 4-82), by approaching Max = 1 both from subsonic and from supersonic incident flow.

Now, for the lift problem at Max = 1, a few results will be presented that have been obtained according to the method of Truckenbrodt [95]; compare also the publications of Mangier [58], Mangier and Randall [58], and Spreiter [85].

For tapered swept-back wings, the lift slope and the neutral-point position are shown in Fig. 449 as functions of the geometric parameter cyfa for several values of crla0. The wing geometry is seen in Fig. 449a, the lift slope in Fig. 4-49b, and the neutral-point position in Fig. 449c. It is noteworthy that for crja > 1 [i. e., when the trailing edge of the inner (root) section lies farther back than the leading edge of the outer (tip) section], the lift slope is equal to 7тЛ/2 for all wing shapes in agreement with Eq. (4-75c). For cr/a < 1 (i. e., when the trailing edge of the root section lies farther upstream than the leading edge of the tip section), the lift slope is smaller than тгЛ/2. The neutral point for cr/a> 1 lies at xNja = (see Fig.

4- 49c). For delta wings (a0 = a = cr), xNjcr= f. For crja< 1, the neutral point

shifts upstream. The linear theory for Ma„ = 1 also allows computation of the pressure distribution on the wing surface. Here, for uncambered wings, wing areas of which the local span remains constant in the chord direction (Fig. 4-50a), or decreases (Fig. 4-50h), do not contribute to the lift (Д cp = 0).

Finally, a few test results [16] are given in Fig. 4-51 for the lift of delta wings at Mach numbers close to unity. The lift slopes dcildot are plotted against the parameter Л2(Мгі — 1), which results from the similarity transformation of compressible flow [see Eq. (4-26)]. The pronounced peak in the theoretical curve of dci/da at Maw = 1 is not fully confirmed through measurements. In the subsonic and supersonic range, theory is well represented by the measurements. Further experimental results on wings in transonic flow are found in Frick [24].