WING OF FINITE SPAN IN SUBSONIC AND TRANSONIC FLOW

4- 4-1 Application of the Subsonic Similarity Rule

It has been shown in Sec. 4-2-3 that the computation of flow about a wing of finite span with incident flow Mach number Mam < 1 can be reduced to the determina­tion of the incompressible flow for a wing of finite span by means of the subsonic similarity rule (Prandtl, Glauert, Gothert). The corresponding problem for the airfoil of infinite span (profile theory) was discussed in Sec. 4-3-2. Computation of incompressible flows was treated in detail in Chap. 2 for the airfoil of infinite span and in Chap. 3 for the wing of finite span. The methods of wing theory for incompressible flow therefore have a significance that reaches far beyond the area of incompressible flow.

The second version of the subsonic similarity rule of Sec. 4-2-3 is the starting point for further discussions. In what follows, the reference wing in incompressible flow that is coordinated to the given wing at given Mach number will be designated by the index “inc.” Thus, the transformation formulas for the wing planform according to Eqs. (4-10) and (4-15) are

The geometric transformation for a trapezoidal swept-back wing in straight flight and in yawed flight for Mach number Ma„ = 0.8 is presented in Fig. 4-44.

For unchanged profile (h/cnc=h/c, (t/c)inc = t/c, and unchanged angles of attack ainc = a, the pressure coefficient of the given wing cp is obtained according to Eq. (4-23) from that of the transformed wing cp-mc as

cP = —===== (version II) (4-69)

У 1 — Ma%>

Compare Figs. 4-8 and 4-9 for the Mach number range 0 < 1. In the case of

airfoils of infinite span, the subsonic similarity rule is no longer valid for Маж = 1 (see Sec. 4-3-2). Approximately, however, it may be applied to Ma„ = 1 in the case of wings of finite span. More details will be given later. Attention should he drawn to the panel method of Kraus and Sacher [44], which includes the influence of compressibility.